OFFICERS OF THE ACADEMY.

1898-1899.

President.

Henry F. Osporn,

American Museum of Natural History.

Vice-Presidents.

N. L. Britton, J. F. Kemp.

Secretary, Corresponding Secretary,

RicHarD E. DonGcE, Wo. STRATFORD,

Teachers College, W. 120th St. College of the City of New York.

Treasurer, Librarian,

CHARLES F. Cox, ArtTuHuR HotLiick,

Grand Central Depot. Columbia University.

Editor.

GILBERT VAN INGEN,

Columbia University.

Section of Astronomy and Physics.

P. H. Dupiry, Chairman, REGINALD Gorpon, Secretary.

80 Pine St. Columbia University.

Section of Biology.

Epmunp B. Witson, Chairman, Gary N. Carxkins, Secretary.

Columbia University. Columbia University,

Section of Geology and Mineralogy.

James F. Kemp, Chairman, Gxo. F. Kunz, Secretary.

Columbia University. 15 Union Square.

Section of Anthropology, Philology and Psychology.

L. A. McLourn, Chairman,

New York University.

A. V. W. Jackson, Secretary for Philology,

Columbia University.

Cus. B. Buss, Secretary for Anthropology and Psychology.

New York University.

NOTE REGARDING PUBLICATIONS

OF THE

NEW YORK ACADEMY OF SCIENCES.

Publication of the Transactions of the Academy is discontinued

with the issue of Volume XVI, 1898. The matter heretofore

printed in the Transactions will be incorporated in the Annals.

The Annals (8vo), beginning with Volume XVI, will appear

with new forms of typography and arrangement of matter; many

changes having been made in the endeavor to facilitate the use of

the volume for reference purposes. A volume of the Annals will

hereafter coincide with the calendar year and will be issued in

three parts. The price per volume is three dollars.

The Memoirs in quarto form will be published at irregular in-

tervals. Part I of Volume I has been issued.

AON IN AS ES

NEW YORK ACADEMY OF SCIENCES,

VOLUME X.

I.— The Nature and Origin of Stipules.

BY A. A. TYLER, A.M.

Read Feb. 8, 1897.

The investigation which has resulted in the preparation of this

dissertation was undertaken with a view to determine the true

nature and phylogenetic origin of those appendages of the bases

of the petioles of leaves which are known as stipules and which

are present in so large anumber of the families of flowering plants.

The data have been collected from every available source; the

evidences to be gathered from known geological facts have been

taken into consideration, observations have been made upon the

morphology and anatomy of the foliar organs in a large number

of cases, and the gradual modification of leaf-forms in the annual

growth of plants from simple scales to adult leaves has been care-

fully studied. In addition to the data so gathered, the literature

dealing with the subject, relatively scanty though itis, has yielded

much valuable material both by the record given of the observa-

tions of others and by the suggestion of lines of investigation.

With all this material in hand, I have endeavored to ground the

theoretical consideration of the problem upon the broadest founda-

tion possible in the present stage of the progress of science, and

from a comparative study of the evidence gathered from all the

various sources of information, have drawn the conclusions set

forth at the close of my paper.

ANNALS N. Y. ACAD. ScI., X, April, 1897.—1.

2 The Nature and Origin of Stipules.

The results of my investigations are herewith given to the pub-

lic with the conviction that conclusions arrived at in the manner

indicated cannot fail of interest to the reader, nor, in some de-

gree at least, of scientific value.

COLUMBIA UNIVERSITY,

NEW YORK, Feb. 8, 1897.

SYNOPSIS.

A Review of important Literature pertaining to Stipules.....................06. 3

The Nature and Origin of Stipules :—

The Meld ot Haqurry detinedsc.a.qeecencs-s0+-ccesereeee cds esese este amen aaa 22

Theoretical Discussion of the Primitive Leaf..................essssesesesscseeee 23

The three Types of Leaf-development as regards the Formation of

Stipules :

a. When all the Parts develop as a Unit...................cseesseeeee 29

b. When a sheathing Petiole, Ligule, or Ochrea is formed......... 32

ce: When Stipulesianeiiormied so. -emseeosee sess seee se aceeeece sees meee eee I¢/

COnGCIUSIONS ..5c.dsccicece<setgacgcusstoans Se oodscinnes Sobosewaedslees veCeE A Een TEE eRe Eee 48

The Nature and Origin of Stipules. 3

A Review oF IMPORTANT LITERATURE PERTAINING TO STIPULES.

Owing to the fact that a large part of the literature pertaining

to stipules is inaccessible to the majority of botanical students,

scattered as it is, for the most part, in the journals of various

scientific bodies, it has seemed desirable to preface the considera-

tion of the results of my research on the question of the Nature and

Origin of Stipules with a brief summary, in chronological order,

of the publications having reference to the general subject of

stipules. I have, however, omitted mention of their consideration

in systematic works and the general allusions and definitions as

they occur in most general works on the Spermatophyta together

with their special consideration in individual species and groups

except in the most important cases.

Stipules have not received a very large degree of attention from

botanists apart from their morphology as used in classification

and the publications to be considered are not very numerous,

but it is thought that a review of those following will be profita-

ble and of general interest :

Malpishi, Marcello.—Opera omnia, 22-39. 1686.

This is one of the earliest works in which stipules are treated.

A considerable number are figured and described under the name

of foliola caduca.

Linnzus, Carolus.—Philosophica Botanica, 50. 1751.

A general definition is given of stipules as scales borne at the

base of the petiole. Buds are spoken of as formed by stipules, by

petioles, or by rudiments of leaves.

Linnzus, Carolus.—Prelectiones in ordines naturales plantarum, 520.

1792. (Cited by Hanstein in Abhandl. Akad. Berlin, 77. 1857.)

In speaking of the whorled leaves of the Stellate, Linnzus

says that only two of these leaves are true leaves, the remainder

are stipules which have grown to the same size as the leaves.

De Candolle, Augustin P.—Theorie de la Botanique, 364. 1819.

The stipule is defined as a foliaceous appendage or accessory

leaf situated at the base of certain leaves. The stipel, first so

named by De Candolle, is defined as a stipule placed on the com-

mon petiole at the base of the leaflets.

4 The Nature and Origin of Stipules.

De Candolle, Augustin P.—Organographie Végétale, 1 ; 334-341.

1827.

De Candolle’s views as here expressed may be outlined as fol-

lows: ‘Stipules do not exist in any monocotyledonous plant,*

nor in any dicotyledons in which the petiole has a sheathing base ;

among dicotyledons with leaves not sheathing, stipules are fre-

quently wanting, especially in plants with opposite leaves. Their

existence is intimately connected with the general symmetry of

plants, and they occur or are wanting in all the species of a family.

“The only essential character of stipules is their lateral position

at the base of the leaves, and it is not impossible that we confound

under a common. name objects really distinct. Their texture is,

in many plants, perfectly foliaceous and in these cases they ex-

hibit so exactly the character of leaves that we can say that they

are small accessory leaves.

“In certain verticillate leaves, such as those of Galium, it is

noticeable that the buds and young branches are not produced in

the axils of all the leaves, but only of two among them which are

opposite to one another. I presume that these two leaves

furnished with buds are the true leaves and that the others should

be considered as foliaceous stipules.

“The natural use of stipules seems to be the protection of the

leaves during their development, but we must admit that in many

cases their smallness or their nature or form make them inappro-

priate to this use, though we cannot well assign another to them,

those which are foliaceous assist in the elaboration of the sap,

those which are changed into spines serve for the defense of the

plant.

“The tendril in the Cucurbitacez is perhaps a modified stipule.

The ochrea of Polygonums is a prolongation of the base oe the

petiole into connate stipules.”

In volume 2, pages 213 and 214, De Candolle says in treating

of buds, ‘‘ They have received particular names according as they

are formed by different parts of the foliar organs, and according

to the degree of their degeneration and adnation.

“1. Buds are called foliar when, the leaves being sessile, the

blade itself, reduced to the form of a scale, forms the buds, as in

Daphne mezereum L.

“2. They are called petiolar when the bases of the petioles dila-

*See also A. Richard. Précis de Bot., 126.

The Nature and Origin of Stipules. oS

ted: into scales form the covering of the young shoot. This oc-

curs in petiolate leaves without stipules, as in the walnut, ash

and horse-chestnut.

“3. Buds are stipular when the scales are formed, not by the

leaves, but by the stipules which are not united with the petioles.

Of these there are two sorts,—those which are formed by a great

number of stipules enclosing a young shoot collectively, as in

oaks, willows and elms, and those in which the stipules, free or

united by theirexterior margins, form a peculiar envelope for each

leaf, as in Ficus and the magnolias.

. “4. When the stipules are adherent with the petiole, these two

organs united into one form the bud scales, and are named ful-

cral. This occurs in most of the Rosacez, and the scales are

frequently three-lobed or three-toothed, indicating the origin of

the scale formed by the petiole and the two stipules united to-

gether.” Plate 21, figure 9, shows the progressive change from

scales to foliage-leaves in buds that are fulcral in nature.

Bischoff, G. W.—Lebrbuch der Botanik. 177-183. 1834.

The subject is here more fully outlined than in De Candolle’s

Organographie. Stipules are defined as peculiar leafy expan-

sions at the base of a free middle leaf. They are recognized as

belonging to the leaf on the ground of their frequent connection

with the petiole, the receiving of their vascular bundles from

those of the leaf and the absence of buds from their axils. Va-

rious kinds of stipules are described and the ochrea, the ligule, the

stipule in the Naiadacez and the ochrea of palms are included

with stipular formations.

Lindley, John.—Introduction to Botany, 99. 1832.

The following statement is of interest: “ The exact analogy of

stipules is not well made out. I am clearly of opinion that, not-

withstanding the difference in their appearance, they are really

accessory leaves ; because they are occasionally transformed into

leaves, as in Rosa bracteata, because they are often indistinguish-

able from leaves of which they obviously perform all the func-

tions, as in Lathyrus, and because there are cases in which buds

develop in their axilla, as in Salix, a property peculiar to leaves

and their modifications.” The character of stipules is denied to

the tendril of the Cucurbitacez and the tendrils of Smilax (p. 96)

are regarded as lateral branches of the petiole. .

ANNALS N. Y. ACAD. ScI., X, April, 1897.—2.

Rea aig, 5

6 The Nature and Origin of Stipules.

Henry, A.—Recherches sur les bourgeons. Nova Acta Acad. Nat. 18 :525-

540. 1836. (Cited by Clos in Bull. Soc. Bot. Fr. 26: 193. 1879.)

Henry says that he recognizes inthe Betulacez and Cupuliferz

that the bud-scales are formed by stipules in an anamorphosed

condition, and that in Platanus they are formed by the ochrea as

he terms the basal foliar appendage in this genus.

Lestiboudois, 'Them.—Etudes sur l’anatomie et la physiologie des

vegetaux. 1840: (Cited by himself in Bull. Soc. Bot. Fr. 4 : 746-747. 1857.)

The author states that he has shown that stipules are parts of

the leaf, formed by the bundles or lateral fibers of these organs,

whether they arise from bundles not yet having left the stem, from

anastomosing arcades which unite the leaves as in the Stellatz, or

from the fibres of the petiole, as in the adnate stipules of Rosacez,

or whether they are in part supplied by bundles directly from the

cauline cylinder, as in Platanus.

In relation to the tendril in the Cucurbitaceae, he states that its

bundles are derived from those which pertain to the axillary bud ;

that it is therefore not a stipule, but the first foliar appendage of

the axillary branch for its fibro-vascular bundles are not disposed

like those of stems, but are analogous with those of petioles.

St. Hilaire, Aug.—Lecons de Botanique. 170, 1840. (Quoted by

Colomb in Ann. Sci. Nat. (VII), 6:28. 1887.)

It is stated that the tendrils of Smilax are to be considered as

lateral leaflets of a compound leaf.

Agardh, J. G.—Ueber die Nebenblatter der Pflanzen. (Reviewed by

Fries and Wahlberg in Flora, 33 : 758-761. 1850.)

Agardh believes that, although stipules have been considered as

degenerate appendages of the leaf or modifications of it, they are

not at all a part of the leaf because they are formed before it, and

must be considered as independent organs. The outer bud-scales

and also the protective coverings of the earliest shoots of a plant

are a kind of stipule-formation, leading to the conclusion that in

the lower part of a shoot or the outer part of a bud the stipule-

formation preponderates, and in the upper or inner parts, the leaf-

formation, so that often at the lowest nodes the leaf does not de-

velop and at the upper stipules are absent. In Twussilago there

are special leafy shoots and the flowering shoots are provided

with stipules only.

The Nature and Origin of Stipules. 7

From these considerations Agardh concludes that there are two

kinds of appendicular organs instead of one, namely stipules and

leaves.

Astaix.—Essai sur la Théorie des stipules, thése de 1’Ecole de pharmacie

de Paris. 1-25. 1841. (Cited by Clos in Bull. Soc. Bot. Fr. 1: 302. 1854.)

The conclusion is reached that the leaf is not a primitive ap-

pendage of the stipule and that the stipule is nothing more than

an appendage of the leaf.

Regel, E.—Beobachtung tiber den Ursprung und Zweck der Stipeln.

Linnea, 17: 193-234. 1843.

Regel has studied the development of stipules in seedlings and

in the growth of individual leaves. He believes, but does not

feel ready to assert, that stipules are present in all Angiosperms in

the earliest stages of growth. He therefore includes in stipular

formations the ligule, ochrea, sheathing petiole and the supernu-

merary leaves of the Stellate. He concludes from his observa-

tions:

]. “That all the leafy organs of phanerogamic plants are di-

vided into two entirely distinct formations, the stipular and leaf-

formations. :

2. “That the stipular formation arises from the base of the

meristem tissue of the leafy axis, covering the summit, but always

with a longitudinal cleft or one passing transversely across the

- apex.

3. “ That perfect stipules are formed by the occurrence of two,

four or more clefts in the original stipular sheath, giving rise to

as many stipular leaflets.

4. “That the stipules receive their vascular bundles directly

from the stem, and are usually parallel veined because of their

forming originally a completely encircling sheath.

‘5. “ That they serve always for the protection of the growing

point and of the true leaves, when these are present, during their

development.

6. “In all plants, organs adapted for protection belong not to

the leaf-formation but to the stipule-formation.

7. “That stipules are to be regarded as a formation preceding

the leaf-formation, since they appear before the leaves.

8. “ That they belong primarily to a nodal ring distinct from

that producing the leaves and situated either above or below it.

8 The Nature and Origin of Stipules.

From these relations, as regards the leaf, interior and exterior

stipules are distinguished.

9. “Interior stipules protect the formation of the following

node and leaves. The leaf at the same node develops somewhat

earlier or at about the same time.

10. “ Exterior stipules develop before the leaf at the same node

and therefore protect their own node with its leaf.

11. “ As stipules are limited in the time during which they are

functional, they lose their significance as soon as this purpose is

fulfilled. They do not produce buds in their axils Sah in cases

where true leaves are not developed.” ;

The following statement (p. 227) should be noted. ‘In some

species of Thalictrum the membrane rising above the inner

margin of the base of the petiole is the analogue of the ligule.”

Kirschleger, F.—Flora, 28:615. 1845.

The tendril of Cucurbitacez is regarded as a normal stipular

formation.

Mercklin, C. E.—Entwicklungsgeschicte der Blattgestalten. 1846.

(Translated into the French in Ann. Sci. Nat. (III), 6: 215-246. 1846. )

The statements of Mercklin are contrary to those of Regel.

He says, “In all cases the stipules of the developing leaf appear

as portions of the lamina; it is only later, during the development.

and elongation of the petiole, that they become sufficiently sepa-

rated to be considered as distinct organs. In all simple leaves.

the stipules never appear at the same time with the first rudiments

of the lamina; they develop only with the inferior parts of the

lamina including the petiole.”

“From my observations of stipules I conclude that in common

with the leaflets they owe their origin to the common petiole

and are formed later than the leaflets.”

Krause, &:.—Einige Bemerke iiber den Blumenbau der Fumariacee und.

Crucifere. B. Crucifere. Bot. Zeit. 4: 137-150. 1846.

Stipules in the Cruciferse are considered (pp. 142-145) and the

homology with stipules of the so-called glands at the base of the

leaves is established by a careful series of observations upon their

development. The glands of the bracts and floral organs are also

included.*

*See also Duchartre, Rev. Bot. 2: 208. 1845-7 and Norman, Quelques

Observ. de Morph. Veg. 1857.

The Nature and Origin of Stipules. 9

Jussieu, Adrien.—Cours d’Histoire Naturelle: Botanique. 108-111.

1852.

Speaking of the leaf-sheath, Jussieu says that ‘“‘ sometimes the

vascular bundles converge little by little, and there is a gradual

transition from the sheath to the petiole ; sometimes the marginal

bundles stop after a course varying in length, or are prolonged

in another plane than that of the petiole, and then there is a clear

distinction of petiole and sheath. Often, however, the paren-

chyma does not unite the lateral bundles to the central ones

which continue in the petiole, and this is the probable origin of

many stipules.”

Trecul, A.—Sur la Formation des Feuilles. Ann. Sci. Nat. (III), 20:

288-299. 1853.

The usual classification of stipules is given with the addition

of extra-foliar stipules to include those of Nelumbium. The an-

thor says, ‘In all adnate stipules that I have seen, they do not

envelop the leaf to which they belong, but that which comes next

after them, and their own leaf is protected by the stipules of the

leaf preceding. Under these circumstances the stipules play the

same role as the sheath, from which they differ very little. We

see thus clearly that there is the closest analogy between the for-

mation of adnate stipules and that of a sheath; the analogy is

such that it is impossible to distinguish between them in princi-

ple.” All the forms of stipules, the ochrea, the tendrils of Smz-

lax and the ligule of grasses are classed together.

Among the conclusions those relating to stipules are as follows :

In basifugal leaf-formation all the parts are formed from below

- upward, the stipules first of all. In leaves with basipetal forma-

tion, the stipules have their origin earlier than the lower parts of

the blade and sometimes even before the upper.

Trécul, A.—Vegetation du Nelumbium codophyllum. Ann. Sci. Nat.

(IV), 1: 291-298. 1854.

In the seedling of this plant the leaves are in two ranks on the

upper and lower sides of the rhizome and each of them is pro-

vided with an axillary stipule. In its later stages the leaves of

the lower rank are aborted with the exception of the stipule of

every second one and in the upper rank every second leaf is rep-

resented by the stipule only. The internodes above the stipules

which stand alone remain undeveloped so that three stipules are

associated with. each leaf, one axillary and two extra-axillary.

10 The Nature and Origin of Stipules.

One of these last is on the upper side of the rhizome external to

the leaf, the other on the lower side.

This paper was presented before the Botanical Socien of

France, May 24,1854. M. Ad. Brongniart took part in the dis-

cussion which followed. He agreed with Trécul in his conclu-

sions and closed with the statement that ‘‘this arrangement re-

calls that of certain buds in which the scales result from the

stipules of leaves of which the petiole and blade are alike

aborted.” M. F. J. Lestiboudois remarked that “to decide

whether stipules are an integral part of the leaf, it is necessary

to study them anatomically. In other plants the same fibro-vas-

cular bundles are distributed to the leaf and stipules. Stipules

should therefore be regarded as appendages of the leaf.”

Clos, D.—Considerations sur la Nature du prétendu Calicule ou involucre

des Malvacées. Bull. Soc. Bot. Fr. 1: 289-303. 1854.

The stipular nature of the parts of the involucre or exterior

calyx in the Malvacez is asserted contrary to the views of Aug.

St. Hilaire (Lecons de Bot. 372. 1840) and the term stepulium is

suggested as applicable to it.

Clos, D.—Du Stipulium chez les Géraniacées, les Légumeneuses et les

Rosacées. Bull. Soc. Bot. Fr. 2:4. 1855.

_ The term stipulium is applied to the exterior calyx of the Mal-

vacez and the involucre of the umbel of some Geraniacez. In

the Cistaceze the bractlets of the calyx are wanting in exstipulate

species.* In many of the Leguminoseze and Rosacez the bracts

are evidently formed by stipules.

Clos, D.—La Vrille des Cucurbitacées, Organe de Dédoublement de la

Feuille. Bull. Soc. Bot. Fr. 3: 545-548. 1856. .

The different theories regarding the tendril in the Cucurbitacez

are briefly stated. They have been considered to be roots ; abor-

tive peduncles by Tassi; stipules by De Candolle, Steks and Aug.

St. Hilaire; leaves by Gasparini, Seringe and Braun; degenerate

branches by Meneghini; superfluous branches by Link; terminal

branches of the axis as in Vitaceze by Fabre; partly leaf, partly

branch by Naudin. Clos concludes that the tendril arises by a

division of the leaf, three fibrovascular bundles entering the leaf

when there is no tendril and two when the tendril is present and.

receives the third bundle.

*See also Aug. St. Hilaire. Lecons de Bot. 326 and 371. 1840.

The Nature and Origin of Stipules. Li:

Clos, D.—Les Vrilles des Smilax ni Folioles ni Stipules. Bull. Soc. Bot.

Fr. 4: 984-987. 1857.

A summary is given of the literature pertaining to the tendrils

of Smilax. They are considered as representing two lateral leaf-

lets of a compound leaf by von Mohl (Ueber den Bau und das

Winden der Ranken und Schlingpflanzen, 41, 1827), Lindley

(Introd. to Botany, Ed. 2,118, 1835), Link (Elem. Phil. Bot. Ed. 2,

1: 478, 1837), St. Hilaire (Lecons de Bot. 170 and 854, 1840), Le

Maout (Atlas de Bot. 23, 1846) and Duchartre (Art. vrille in

Dict. Univ. Hist. Nat.).

Mirbel (Elém. de Physiol. et de Bot., 2: 680, 1815), Trevi-

ranus (Physiol. der Gewachse. 2: 138, 1838), Seringe (Hlém. de

Bot. 175, 1841), De Candolle (Theorie Elément. Ed. 3, 321, 1844),

Trecul (Ann. Sci. Nat. (III), 20: 295, 1854) and Lestiboudois

(Bull. Soc. Bot. Fr. 4: 745, 1857), believe these organs to be stip-

ular tendrils. It is the opinion of Clos that they are neither leaf-

lets nor stipules, but a double lateral prolongation of the cellulo-

vascular elements of the petiole.

Rossman, J.—Beitraige zur Kentniss der Phyllomorphose. 1857. (Cited

by Closin Bull. Soc. Bot. Fr. 26: 192. 1879.)

Rossman considers the problem of the nature of stipules, and

from a study of bud-scales arrived at his conclusions. He figures

the passage from bud-scales to leaves in kibes sanguineum Pursh,

Prunus Padus L., Spirxa sorbifolia L., etc. He notes the pres-

ence in the bud-scales of three median veins, separated at the base

and joining one another at the apex, where the petiole will origi-

nate. The lateral parts of the scale outside of these three nerves

he believes to represent the stipules which show themselves at the

appearance of the blade in two little points at the apex.

Hanstein, J.—Uebersirtleformige Gefassstrang-Verbindung in Stengle-

knoten dicotyler Gewachse. Abhandl. der Akademie der Wissenschaften zu Ber-

lin, 1857 : 77-98. 1858.

The vascular nodal girdle of the Stellatz is treated of at length.

It is shown that from this girdle arise the bundles that supply

those leaves of the whorl which are really stipules, and in some

cases also the veins of the lateral parts of the true leaves. Similar

nodal girdles are shown to exist in other families of plants, nota-

bly in Sambucus, Valeriana, Verbena, Dipsacus, Scabiosa, Dahlia

and Silphium. In SambucusLHbulus L. the girdle sends off vascular

branches to true stipules. In the majority of other cases if

12 The Nature and Origin of Stipules.

branches arise they enter the margins of the petioles or the inter-

foliar portions of connate leaves. In Platanus and Liriodendron

with alternate leaves, each of which receives seven vascular bun-

dles, a similar girdle is shown to pass around the stem posterior

to the leaf, and is there joined by another small leaf-trace bundle.

From this girdle arise a part of the stipular veins, the others being

branches of the sixth and seventh leaf-trace bundles.

Clos, D.—Sépales Stipulaires. Bull. Soc. Bot. Fr. 6: 580-589. 1859.

It is argued from the similarity of the sepals to the divisions

of the involucre (stipulium) and also to the stipules of the fully

developed foliage leaves which is frequently observed, that they

represent stipules. This is held to be true in many Geraniacee,

Malvaceze, Begoniaceze and Cistacez. In concluding Clos adds

the theoretical consideration that ‘‘ whether or not stipules are

admitted to be organs different from the leaf, analogy seems to

demand that in some cases at least they should participate in

some degree in floral formation.”

Cosson, E.— Note sur la Stipule et la Préfeuille dans le Genre Potamo-

geton. Bull. Soc. Bot. Fr. 7:'715-720. 1860.

“The stipule in Potamogeton is very closely like the first leaf

of one of the branches. It is homologous with the ligule of the

Graminez and Cyperacez and is constituted by a single organ,

not by two united by their margins.”

Hichter, A. W.—Zur Entwicklungsgeschichte des Blattes. 22-31, 1861

(Cited by Martin Franke in Bot. Zeit. 54 :45, 1896.)

Stipules are said to arise without exception as a product of the

leaf base of the primordial leaf. This mode of origin of the -

stipules is their chief characteristic. Their form, their more or

less foliaceous condition and their persistence are secondary.

In individual leaf development in the Stellate, the whorl

originates in a uniform ring about the growing point. Then arise

two opposite prominences in the ring. These develop into the

true leaves. Afterthem appear two smaller prominences on each

side of the stem between the first. These are the stipules. <Ac-

cording to the species they develop separately, forming six-leaved

whorls, or grow together giving origin to four-leaved whorls.*

*With this view Gobel agrees (Schenk’s Handbuch der Botanik 3: 230.

1884), except that he does not distinguish the time of appearance of the differ-

ent parts of the whorl.

The Nature and Origin of Stipules. 13

Where a larger number of leaves occurs, an additional prominence

for each arises between the original stipular prominences.*

Jauvet, D.—Probabilité de la Presence des Stipules dans quelques Mono-

cotyedones. Bull. Soc. Bot. Fr. 12: 241. 1865.

A number of cases are considered and the conclusion drawn that

very probably some Monocotyledones are provided with stipules,

but the difference in their form and position has caused them to

be considered as another kind of organ.

Meehan, Thomas.—On the Stipules of Magnolia and Liriodendron.

Proc. Acad. Nat. Sci. Phila. 114-116. 1870.

Mr. Meehan argues for the origin of the stipules of Magnolia

as lobes of the lamina similar to the auricles which occur in JM.

Frasert Walt. by a union of the auricles with the upper surface

of the petiole, and a subsequent adnation of their margins and

separation from the lamina. He says, “ It is scarcely possible to

avoid the suspicion that the stipules of Magnolia are not formed

like the stipules of most plants which are perhaps leaf portions

which have never been well developed, but rather are the tolera-

bly well developed side pinnules of a trifoliate or deeply auricled

leaf.”

Speaking of observations upon the flowers of M. fuscata Andr.,

of East India, the following interesting statement is made: ‘‘ This

observation confirms the views of some botanists as I have learned

from Professor Asa Gray, that it is by metamorphosis of the

petiolar and stipular parts, rather than by modifications of the

- leaf-blade, that petals are formed.”

Duval-Jouve, J.—Sur quelques tissues de Joncées, etc. Bull. Soe.

Bot. Fr. 18: 231-239. 1871.

The presence of the ligule in the J uncacee is treated of. To quote

the author, “If in certain species the ligule is so reduced that it

appears to be lacking between the separated auricles at the apex

of the sheath, in most others these auricles are united by a true

ligule, as pronounced as that of grasses, either entire or cleft at

the middle.”

Dutaily, G.—Sur les variations de structure de la ligule des Graminées.

Bull. de la Soe. Linnéene, 170. 1878.

*F,. Pax (Allgemeine Morph. der Pflanzen, 100. 1890) says, when there

are more than six parts to the whorl, the additional parts must have their

origin in a division of the blades of the stipules.

14 ; The Nature and Origin of Stipules.

It is argued from the presence of a median vein in the ligule of

some of the grasses in which this organ is supplied with vascular

support that it cannot be formed of two stipules grown together.

Hilburg, C.—Dissertation tiber den Bau und die Function der Neben-

blatter. (Reviewed by F. Hildebrand in Flora, (II), 36: 161-167. 1878.)

The general neglect of the subject of stipules and the timeli-

ness of this dissertation is referred to by the reviewer.

The functions of stipules as protecting organs are discussed.

They are considered under the heads of (1) those protecting the

buds in winter, (2) those protecting the growing parts in the

spring, (3) those which serve as protection against insects and

other animals, (4) those which serve as well the function of as-

similation.

The adaptation of most stipules in their form and manner of

growth to the special function they are intended to fulfill and the

apparent lack of function in others is remarked upon.

Clos, D.—Des Stipules et de leurréle a l’infloresence et dans la Fleur.

Mem. Acad. Sci. Toulouse, (VII), 10: 201-317. 1878.

This paper is the first part of an extended consideration of the

subject of stipules. It deals with their occurrence in the families

of plants and their importance in classification on account of the

great variety of their characteristics.

Clos, D.— Dela part des Stipules a l’infloresence et dans la Fleur. Comptes

Rendus, 87: 305-306. 1878.

The stipular nature of the sepals in Geranium, Helianthemum,

Begonia, Oxalis, Alchimilla, Viola and many other genera in dif- ~

ferent families is maintained.

Dixon, Alex.—On the stipules of Spergularia marina. Journal of Botany

(Trimen), 7: 316. 1878.

Attention is called to the anomalous connation of the stipules

of Spergularia marina Griseb. exterior to the petioles of the

opposite leaves.

Clos, D.— Des Stipules considérées au point de vue morphologique. Bull.

Soc. Bot. Fr. 26: 151-155. 1879.

Under this title a summary of the opinions of botanical au-

thorities as to the true nature of stipules is given and the different

theories are briefly discussed.

Various leaves have been considered as stipules, for example

the primary leaves of Asparagus (Dutrochet), the first leaves of

ee ae)

The Nature and Origin of Stipules. 15

the branches of Verbena aphylla Gill & Hook. (Hooker, Bot.

Mise. 1: 116. 1830) and of the Piperacez ( C. DeCandolle, Mém.

sur les Piper. 18-19, 1866), and the first two leaves of the axillary

buds of many Solanacee.

The appendages sometimes accompanying the leaf in some Con-

volvulacez, as Ipomea stipulacea Sweet., have been considered as

stipules (Jacquin. Pl. Hort. Schoenbr. Descer. et Ic. 2: 39. 1797).

Many have regarded stipules as leaflets, as for example in

Vibernum (Baillon, Adans. 1: 372. 1860), and the lower leaflets

in many plants have been taken for stipules, as in Cobewa scandens

Cav. (Blume. Rumphia 3: 142. 1837), and Lotus tetraphyllus

Murr. (Linneus, Trinius, EK. Meyer, Fischer.)

In 1844 Wydler declared that stipules belong to the sheath and

cites examples of transition between the two kinds of organs in

the Rosacez, Polygonaces, Leguminose, etc. Stipules, in con-

nection with the sheath have been ascribed to Ranunculus, Iso-

pyrum and Thalictrum by Liovd (FI. de l’Ouest de Fr. Ed. 2,

1868), to Caltha by Wydler, Kutzing (Grundz. der phil. Bot. 684,

1851-52) and Hooker. They have been recognized in the scales

of the stems of the Aroids.

The so-called “‘ decurrences ” of leaves do not differ anatomically

from stipules and are to be considered as identical with them, as

for example in Crotalaria.

The tendril of the Cucurbitacez has been regarded as a stipule

by Seringe (Mém. Soc. Hist. Nat. Geneév. 3: 1-81. 1825), De Can-

dolle (Organ. Veg. 1: 336. 1827), Kirschleger (Flora, 28: 615.

1845), Stoks (Ann. Nat. Hist. 1846), Payer (Elém. de Bot. 53.

1857-58), Parlatore, etc. Those of Smilax have been so consid-

ered by Cauvet (Bull. Soc. Bot. Fr. 12: 241. 1865), but are looked

on by Clos as ‘‘ simple prolongations of the fibro-vascular bundles

of the petiole without morphological signification.”

The spines of the orange are considered as stipules by Du Petit-

Thouars (Cours de Phytol. 47. 1820). Clos regards them as

branches and those of Amaranthus spinosus L. as leaves, though

they are considered stipular by Lamarck (Encye. Meth. 2: 118.

1786). Ribes shows stipular spines in some species. The spines

of Xanthium spinosum L. mentioned by Sachs as occupying the

place of stipules, Clos regards as representing pistillate flowers.

He looks with disfavor on the doctrine that the glands at the

base of the leaves in Resedacezx, Crucifere, Hpilobium, Lyth-

16 The Nature and Origin of Stipules.

rum and some Euphorbiacez and Balsaminacez as well as the

axillary hairs in some Portulacacee are stipules.

Clos, D.—Indépendance, developpement, anomalies des stipules; Bour-

geons a écailles stipulaires. Bull. Soc. Bot. Fr. 26: 189-193. 1879.

Stipules have been regarded as appendages of the leaf by Du

Petit-Thouars (Cours de Phytol. 46, 1820), Aug. St. Hilaire

(Lecons de Bot. 189, 1840), G. St. Pierre and F. J. Lestiboudois.

Clos agrees with Agardh in considering stipules as independent

organs, giving as his reason that frequently in the Rosacex, Leg-

uminose, Malvacez, Geraniacez, etc., the stipules persist alone,

the leaves having completely disappeared, whether in the inflor-

esence or at the base of stems and branches.

Under the head of the development of stipules the conflicting

opinions of Mercklin and Trécul as to their time of appearance in

relation to that of the leaf-blade is referred to. Agreement with

Trécul is indicated and the evidence is not considered sufficient

as a basis for the theory of the autonomy of stipules on the

ground that they appear before the leaf-blade.

In consideration of stipular bud-scales reference is made to

their recognition by Linnzus (Phil. Bot. Hd. 3,52. 1790), Adan-

son (Familles des Pl. 246, 1763), De Candolle (Ann. Sci. Nat.

(III), 5: 321, 1846)* and Lindley (Veg. Kingdom, 283, 1846).

Gobel, K.—Beitrage zur Morphologie und Physiologie des Blattes. Pt. I.

Die Niederblatter. Bot. Zeit. 38: '753, ete.—845. 1880.

This extended treatise deals with bud-scales and the scales of

subterranean parts of plants and their homologies with leaves.

Speaking of the primordial leaf Gébel says, “it is divided into

two parts, a stationary zone which takes no farther part in the

leaf-formation and a part out of which the lamina is developed.”

He calls these parts respectively the leaf-base and upper-leaf and

states that the petiole arises after the formation of the blade and

is inserted between the two parts.

Bud-seales are regarded as modified foliage-leaves and divided

into those formed from the blade (Syringa), those formed by the

leaf-base (Hsculus, Prunus), and those consisting of stipules

(Liriodendron, Quercus). In Prunus, etc., the formation of the

bud-scales by the union of petiole and stipules is denied on the

ground that the continuous separate development of the petiole

and stipules can be followed.

* See also Org. Veg. 2: 213. 1827.

The Nature and Origin of Stipules. ver

The scales of rhizomes are divided into those formed by a de-

velopment of the leaf-base (Dentaria, Chrysosplenium) and those

formed by a modification of the upper-leaf (Labiate, Onagracez).

Colomb, G.—Note sur l’ochrea des Polygonées. Bull. Soc. Bot. Fr. 33:

506-507, 1886.

“The ochrea of the Polygonums is a complex organ formed of

two parts: one opposite the leaf, the leaf-sheath, the other in its

axil and detached from the petiole. This isa ligule.” ‘ Practi-

cally the same conditions prevail in the Graminez as in Poly-~

gonum with the difference that in the former the sheath proper is

greatly developed and little prolonged beyond the insertion of

the blade, while in the latter, the sheath proper remains short and

is much prolonged above the petiole. By union with the ligule it

forms an ochrea. So considered the ochrea is not peculiar to the

Polygonacee. It is found also in Ficus and Magnolia, establish-

ing the transition between the ochrea and stipules properly so

called.

Vuillemin, P.—Apropos d’une recent communication de M. Colomb.

Bull. Soc. Bot. Fr. 34: 141-142. 1887.

Commenting on the preceding paper, the author says that the

leaf is primitively unifasciculate. The concrescence of a verticil

of elementary leaves, such as occurs in the fossil Asterophyllites,

gave a sheath analogous to that of Hquisetum; the bundle

of one of these elementary leaves becoming predominant and

functioning as a midvein gave rise to an aggregate leaf, the

first stage of a high differentiation. In this way the origin

of the leaf-blade in Polygonum, Platanus, etc. is explained, while

the ochrea, the homologue of the sheath of Hquisetum, remains

as a vestige of the primordial state.

Kronfeld, M.—Ueber die Beziehung der Nebenblatter zu ihrem Haupt-

blatte. Verhand. der Kais.-Konig. Zool.-Bot. Gesellschaft Wien. 37. Abhandl.

69-79. 1887.

The author has made investigations experimenting upon a

large number of plants, by the removal of the Jamina of the

leaves at the earliest possible stage of development, in order to

observe the effect upon the development of the stipules and so

determine their physiological relation to the leaf-blade. Only in

exceptional cases was the ultimate size of the stipules increased,

and those where the stipules were normally foliaceous.

18 The Nature and Origin of Stipules.

Colomb, G.—Recherches sur les stipules. Ann. Sci. Nat. (VII), 6:1-

76. 1887.

This paper is the result of an exhaustive anatomical study of

stipules and their homologues. The results obtained are of great

interest and value. They are admirably summed up at the close

of the paper as follows : “eee

‘““When a leaf is sheathing, the sheath may be prolonged ina

ligule situated above the point of insertion of the blade upon the

_ Sheath.

‘“‘In this organ three regions may be recognized :

“1. The lateral regions into which the marginal bundles of the

sheath are merely prolonged. These regions naturally do not exist

if all the bundles of the sheath enter into the leaf.

“2. The stipular regions, the bundles of which arise from a

doubling of the last bundle of the sheath entering into the leaf.

“3. The axillary region, which unites the two stipular regions, a

lamina, usually of parenchyma, but which may receive bundles

arising from the internal doubling of those bundles of the sheath

which become petiolar.

“The sheath may be reduced even to complete disappearance

without a consequent disappearance of the ligule.

“1. If the ligule is complete with its three regions, I give it

the name of an axillary ligule.

“9. If the stipular and axillary regions only persist, the sheath-

ing regions having disappeared, we have an axillary stipule.

‘3. If finally the axillary region divides into two halves, right

and left (which would not be remarkable, considering its purely

parenchymatous nature), the stipular regions exist alone at the

base of the petiole, and we have then stipules properly so-called.

“Stipules and the ligule are then organs of the same nature,

between which it is possible-to find all forms of intergradation,

the stipule being a portion of the axillary ligule.

“When, finally, the manner of origin of the bundles of the

stipule is studied, we arrive at the following definition of the organ:

An appendage inserted on the stem, at the base of the leaf, all the

bundles of which arise exclusively from the corresponding foliar

bundles.”

Each of the tendrils of a leaf of Smilax is characterized as a

demi-ligule, the ‘‘ stipule ” of Potamogeion as a ligule identical with

that of grasses, the ochrea of Polygonum and Platanus as axillary

The Nature and Origin of Stipules. 19

stipules, the stipules of Ficus elastica Roxb. and Magnolia grandi-

Jlora L. as axillary ligules.

Ward, L. F.—The Paleontologic History of the Genus Platanus. Proc.

U.S. Nat. Mus. 11: 39-42. 1888. :

Professor Ward says (p. 41) in speaking of the fossil leaves of

Platanus basilobata Ward, of the Yellowstone valley, that some

of those found had ‘‘a remarkable expansion at the base of the

blade, projecting backward on the leaf-stalk and having two to

five lobes or points.

“ These expansions are to be interpreted as evidence that the

leaves all belong to Platanus or to some extinct ancestral type of

the genus, since something quite analagous to them is found in

our American plane-tree. The ordinary leaves of this tree are,

it is true, destitute of basilar expansions, but those on young

shoots, and sometimes those on the lower or non-fruit-bearing

branches of trees exhibit this peculiarity.

‘““In place of this backward expansion of the blade many syca-

more leaves have an appendage similar in shape at the base of the

leaf-stalk, as though the once basilar appendage had been sep-

arated from the blade and crowded down the petiole to its point

of insertion.” This is shown in a short-petioled, wedge-shaped

leaf from a young shoot of Platanus corresponding to the fossil

form of Platanus appendiculata Lesq. from the auriferous gravels

of California. The indication is that “the constriction seen in

the fossil forms between the blade of the leaf and the appendage

would seem to represent the beginning of this process of detach-

ment.”

Ward, L. F.—Origin of the Plane-Trees. Am. Nat. 24:'797-810. 1890.

The same cases as those in the preceding paper are discussed,

the appendages in Platanus appendiculata Lesq. being described as

stipular, while those of P. nobilis Newb. and P. basilobata Ward

are not so considered.

Lubbock, Sir John.—On Stipules, their Form and Function. Jour.

Linn. Soc. Lond. 28: 217-243. 1890.

_ “'The primary function of stipules seems to be to protect the

bud. In other species, however, they serve as accessory or deputy

leaves. Their protective function is confirmed by the fact of

their early fall. Some are more persistent than the leaves and

protect the leaves of the following year.

20 The Nature and Origin of Stipules.

‘When stipules are present [in Helianthemum] the petiole is

always very narrow, semiterete, and tapered to the base. Where

they are absent the leaf is often sessile and, whether or not, its

base is always dilated and concave on the inner face, completely

enclosing the bud up to a certain stage of its development.”

The presence of stipules in the lower imperfect leaves of Ailan-

thus glandulosa Desf. is noticed, though the family of the Sim-

arubiaceze has been described as exstipulate. In Ribes sanguin-

eum Pursh. the bud-scales are described as consisting of the

dilated base of the petiole, the lamina being represented by a

small black point. ‘‘One or two succeeding leaves bear a small

lamina sessile on the sheath, which is wholly adnate to the thin

dilated base of the petiole and membranous, especially outside of

the three vascular bundles. The next one or two have a well-

developed lamina, and the sheaths partly separated from the

petiole and corresponding to stipules. Farther up the stipular

sheaths are shorter and wholly adnate to the petiole.”

The form and function of the stipules in a large number of

Species are described.

Lesquereux, L.—U. S. Geol. Surv., Monog. No. 117: Geology of the

Dakota Group. 1892.

Well-developed stipules of a species of Betulites from Kansas

are described (p. 65) as having been found in their original con-

nection with the leaf, and the discovery of leaves of a Cratzgus

with large undoubted stipules, from the Devonian of Wyoming is

mentioned (p. 254). Speaking of a leaf of Aspidiophyllum

(p. 232). Professor Lesquereux says, ‘the basilar appendage or

pelta is like a primordial form of stipules, as in Platanus

basilobata Ward of the Laramie group of Wyoming, P. appen-

diculata Lesq. of the auriferous gravels of California and definitive-

ly in P. occidentalis L. of the living flora.”

Henslow, Rev. George.—On a Theoretical Origin of Endogens from

Exogens. Jour. Linn. Soc. Lond. 29: 485-528. 1893.

The absence of vascular bundles in certain stipules is noted

(p. 494).

Hollick, Arthur.—Wing-like Appendages on the Petioles of Lirio-

phyllum populoides Lesq. and Liriodendron alatum Newb. Bull. Torr. Bot. Club,

21: 467-471. 1894.

These peculiar wing-like appendages are described and fis iad

Their similarity to the appendages in fossil species of Platanus as

The Nature and Origin of Stipules. 21

described by Professors Lesquereux and Ward is mentioned, and

the probability suggested that we have here an explanation of the

origin of the stipules of Liriodendron Tulipifera L. in the same

manner as that indicated for those of Platanus occidentalis L. by

Professor Ward. The presence of an unwinged portion of the

petiole next to the blade in what is evidently the mature form of

the leaves of Liriophyllum, and its absence in the immature ones

is mentioned as tending to confirm the theory.

In commenting on this paper, the Botanical Gazette (19: 515,

1894) says, “The phyllopodium is to be regarded as an axis

which has a tendency to develop wing-like appendages at any por-

tion, notably, of course; in the epipodium. If stipules are

branches of the hypopodium their origin has simply to do with

the branching of that part of the phyllopodium, without any refer-

ence to the method of winging found in other regions.”

Lubbock, Sir John.—On Stipules, their Form and Function. Pt. II.

Jour. Linn. Soc. Lond. 30 : 463-532. 1894.

This paper is a continuation of the author’s former publication.

The presence of stipels in Sambucus Hbulus L. is noticed. The

membranous protective margins of the sheath in Thalictrum

aquilegifolium L. and the ‘membranous stipular processes at

each trifurcation of the lamina ” are mentioned, the latter ‘‘ap-

pearing to differ somewhat in their origin from the primary

sheath.” In treating of Ranunculus aquatilus L., the author

says, ““ The terminal bud is enclosed by the stipules of the two

uppermost expanded leaves. The developing leaves push their

way out at the apex of the stipular sheath. Similarity of condi-

tions have therefore developed in the aquatic Ranunculacee, an

arrangement very similar to that of the Potamogetons.”

The following remarks are of particular interest: “In Mag-

nolia glauca L. the winter bud is covered by a pair of connate

stipules adnate to a petiole that is less than half their length.

Succeeding leaves are perfect, and the stipules are two or three

times as long as the petiole, the free portions being connate by

both edges, like a candle extinguisher, over the bud, so that the

leaf appears to spring from the back. As they are adnate to the

petiole, there is some reason to assume that the stipules once

formed a sheath pure and simple to the leaf of some ancestral

form.”

ANNALS N. Y. ACAD. Sci., X, April, 1897.—3.

22 The Nature and Origin of Stipules.

Franke, Martin.—Bertrage Zur Morphologie und Entwicklungsge-

schichte der Stellaten. Bot. Zeit., 54: 33-60. 1896.

In the part of this paper which treats of the development of

the leaf-whorl the author agrees with Hichler that the stipules or-

iginate later than the principal leaves. But he says that in the

species having four-leaved whorls never more than four promi-

nences arise to develop into the parts of the whorl, and that if

the parts number six or more, there is a distinct prominence

for each. In the last case the supernumerary stipules first make

their appearance in the course of development of the whorl a

little later than the first pair of stipules.

Hollick, Arthur.—Appendages to the Petioles of Liriodendra. Bull.

Torr. Bot. Club, 23: 249. 1896.

The author, referring to his former paper, describes and figures

some abnormal leaves of Liriodendron collected from saplings,

seedlings and new shoots from old stumps. One in particular of

these leaves is of interest on account of its similarity to the

fossil leaves of Liriophyllum populoides Lesq. both in the form of

the lamina and especially in having a short petiole with broadly

winged margins which extend from the base of the petiole and

connect with the base of the leaf-blade.

The question is put whether in this case we have “ stipules ad-

nate to the petiole and leaf-blade, or portions of the leat-blade

which are acting the part of stipular appendages.”

Such, in brief, is the import of what has been written on the

subject of stipules, so far as I have been able to learn. The re-

sults of my own observations are not at variance to any very con-

siderable degree with the opinions of most of the botanists who

have studied the subject carefully, as will appear from the

following exposition of my investigations and the conclusions

at which I have arrived. To these I shall pass at once, deeming

unnecessary farther comment on previous writings, except such as

the statement of my results may imply.

THE NATURE AND ORIGIN OF STIPULES.

Though it is not part of the purpose of this paper to discuss

the problem of the phylogeny of the plant world, it is nevertheless

necessary in order to define our field of inquiry to make a brief

statement concerning the probable relationship of the higher

forms, namely of those in which foliar organs are developed, in-

The Nature and Origin of Stipules. 23

cluding in the widest interpretation the Characee, Bryophyta,

Pteridophyta and Spermatophyta.

As, in the Characee and Bryophyta, the plant body represents

the exer stage of development, there can be no homology

of the leaves of these plants with those of the Pteridophyta and

Spermatophyta in which the plant body is the sporophyte. For

this reason the so-called stipules of the Charas, together with the

basal lobes or saclike and straplike appendages of the leaves of

many Hepaticze need not be taken into consideration.

Accepting the general theory of evolution in nature, we must

admit that the origin of all the higher plants is algal, but just what

the relationship of the Pteridophyta to the Spermatophyta may

be is still an open question. The same is true in greater or less

degree of the affinity of the Monocotyledones, Dicotyledones and

Gymnosperme in the latter group.

This question of relationship is of considerable importance in

connection with the problem before us as determining the homol-

ogy of the foliar appendages in the several groups. The evi-

dence in support of the doctrine of the common origin of all the

Angiosperme is particularly strong and may be considered as

conclusive. But the relationship of the Gymnosperme to the Angio-

sperme is more remote, and that of the Pteridophyta still more so-

and, though there are many points of resemblance, the similar

characters may be cases of parallel development rather than indi-

cations of acommon origin. It is my present opinion, however,

that the Gymnosperme sprang from some generalized hetero,

sporous Pteridophyte,* that the early Angiosperme were differ-

entiated from related forms, and that therefore, the foliar organs

in the three groups may be considered as homologous. But this

homology can apply to the leaves of Pteridophytes in a very

general way only, namely, to such undifferentiated forms of leaves

as the ancestors which gave rise to the early Gymnosperme and

Angiospermz may be supposed to have had. While, therefore,

the foliar organs in the three classes are to be considered homol-

ogous in their origin, they cannot be so considered in their dif-

ferentiation and the evolution of leaf-forms in the Pteridophyta

and Gymnosperme, though analogous in many points to their

evolution among the Angiosperme, should be regarded as inde-

pendent. We may then consider the “stipule” of the Ophio-

* See Campbell, Mosses and Ferns, 300. 1895.

aa ee

24 The Nature and Origin of Stipules.

glossaceze, Marrattiaceae and Osmundacez and the “ligule” of

Selaginella and Isoetes as special developments and as properly

placed in a separate category from the appendages bearing these

names among the Angiosperme. The Gymnosperme present noth-

ing to represent either stipule or ligule and we have left for our

special consideration the ligule, stipule and their homologues as

they occur in the various groups of the Angiosperme only.

Having thus defined our field, we should have, for the consid-

oration of the problem before us, some conception of what sort of

plant the earliest Angiosperm was. In the absence of geological

evidence this conception must be purely hypothetical and, basing

it on a generalization which would admit of the differentiation

from it of all the varied forms of the modern group of Angio-

sperms, we can see that it must have been a plant of very simple

organization indeed. For our present purpose we need not con-

cern ourselves with any other organs of this primitive Angio-

sperm than the leaves which, from the point of view of the pro-

posed generalization, must be conceived of as hardly more than

the bare rudiments of leaves, mere sheathing scales at the nodes

of the plant, serving slightly, if at all, the function of assimila-

tion which was still subserved, as in its ancestors, by the general

surface of the plant, but confined chiefly to that of protection.

The primitive leaf was probably parallel-veined or approximately

SO, giving rise in its earlier differentiation to the parallel-veined

leaves of the Monocotyledones. The geological evidence indi-

cates that these appeared before the Dicotyledones* which must

have sprung from them later at one or more unknown points, and

netted-veined leaves are of a more recent evolution. Consequently

the tendency of aquatic Dicotyledones to revert toward mono-

cotyledonous structure is rather a case of atavistic degeneration

than an indication of the origin of Monocotyledones from Dico-

tyledones in ancient times through the effects of aquatic habit.}

Now, as advance in evolution proceeded, the need of greater as-

similative capacity arose and, as the foliar organ was the one best

* Professor L. F. Ward. Sketch of Paleobotany. Fifth Ann. Rep. U. S.

Geol. Surv. 448, 1885. Professor A. C. Seward, on the contrary, does not be-

lieve that we have satisfactory evidence of pre-Cretaceous Monocotyledones.

Notes on the Geologic History of Monocotyledones. Annals of Botany, 10 :

220. 1896.

+See Rev. George Henslow. Jour. Linn. Soc. Lond. 29: 485-528. 1893.

The Nature and Origin of Stipules. 25

adapted for specialization in this direction, it was the one upon

which the oftice devolved. Every botanist knows what an endless

variety of forms and special adaptations of particular foliar

parts have arisen in the course of evolution which was inaugu-

rated when this setting aside of the leaf to bear in future the

weight of the assimilative function took place, or rather when this

additional function was placed upon it, for the old protective

function has always been retained, though it has become less no-

ticeable as the new function has overshadowed the old.

There has been in the line of vegetable descent a progressive

development of the foliar organ, and a history of this devel-

opment, together with that of other organs, if it were obtainable,

would give us a complete phylogeny of the flowering plants, and

leave no morphological problem unsolved,* but as the geological

record is very incomplete, and we have in the lower Cretaceous

an already well developed and much differentiated angiospermous

flora of the earlier history of which almost nothing is known, we

must seek other sources of information in determining the homol-

ogies of parts. At this juncture we may safely follow the exam-

ple of the zodlogists and turn to embryology for the evidence

which geology, as yet, refuses to give except in fragments

Among animals, as the phylogeny and ontogeny are found to par-

allel one another, so we may feel confident they will be found to

do among plants when the geological record shall be more com-

pletely unearthed.

It has become a well established part of the theory of evolu-

tion that each individual organism epitomizes more or less fully

in its development the historical steps in the evolution of the

type to which it belongs.+ By the application of this law of re-

* “On this same view of descent with modification most of the facts in mor-

phology become intelligible, whether we look to the same pattern displayed by

the different species of the same class in their homologous organs, to whatever

purpose applied, or to the serial and lateral homologies in each individual ani-

mal and plant.’? Charles Darwin, Origin of Species, 1859. Am. Ed. 6, 2.

264. 1889. See also p. 239, et seq.

+ This theory, known as Von Baer’s law, was promulgated by that scientist

in his Ueber Entwicklungsgeschichte der Thiere, 224. 1828-37.

See also F. M. Balfour. Comparative Embryology. Ed. 2,1: 2. 1885.

Opposed to this law is Adam Sedgewick. On the Law of Development

commonly known as Von Baer’s Law. Quar. Jour. Mic. Soc. (II), 36: 35.

1894.

26 The Nature and Origin of Stipules.

capitulation to the development of plants we may arrive at valu-

able and trustworthy conclusions. The question would at once

be asked, where shall the embryology of the flowering plants be

studied, and the answer would naturally be, in the development

of the seed in the ovary. And here indeed, we trace in outline

an epitome of the course of development from the simple unicel-

lular organism, represented by the fertilized egg-cell of the ovule

to the highest thalloid form, the “embryo,” with its bud (plu-

mule) which is to develop into the full-formed plant perfect in all

its parts. For a summary of the further development of the

Angiosperms we must look to the growing bud which is the

essential reproductive organ of the sporophyte stage and, doubt-

less, a more primitive one than the seed, for it is common among

the more ancient Pteridophytes and these have no seed. The

embryo of flowering plants does, however, correspond pretty

closely to that advanced stage of development of the egg-cell of

some of the higher Pteridophyta now generally spoken of as the

embryo and should be regarded as a young plant ina state of

arrested development. In this state it remains during a period

of rest, in a highly specialized environment in the seed, await-

ing favorable conditions for farther growth. Because of the

highly specialized environment of the embryo, it has itself be-

come correspondingly specialized and has been variously modi-

fied to suit the special conditions of its surroundings. The plu-

mule cannot then be regarded as any longer representing a prim-

itive form of bud and its development is so altered by secondary

modifications that the series of phylogenetic changes is disguised

and imperfectly represented. A parallel case is found among

animals in the development of Echinoderms, in which the changes

that have taken place through secondary modification are so great

that the relationship of the group cannot be satisfactorily deter-

mined by developmental evidence.

It is not then in the seedling that we should expect to find rep-

resentations of primitive leaf-forms, though later ancestral forms

paralleling those of fossil leaves, of which we shall speak, are found

in some seedlings, as for example in Liriodendron. But it is in

the growth of the less specialized buds developing under more

primitive conditions that we should expect to find them. Such

buds are the ordinary leaf-buds of perennial plants, and especially

those occurring on basal and subterranean portions which I con-

The Nature and Origin of Stipules. 27

ceive to develop under conditions somewhat more primitive than

is the case with aérial buds. But in both these the recapitulation

of the development of leaf-forms may be traced with a consider-

able degree of confidence, from the primitive sheathing protective

seale to the most highly differentiated and complex of modern

leaf-forms.

It is at this point that the fragmentary geological evidence

sheds its strongest light on the problem under consideration. In

the Cretaceous and Tertiary floras which preceded the modern,

the present degree of differentiation had not as yet been attained

and but few modern species made their appearance before the

close of the Tertiary.* The species, however, which immediately

preceded those which now exist were very closely related to them,

being their immediate ancestors, and differed from them only in

showing a somewhat lower degree of differentiation, and their

leaf-forms are accordingly more primitive than those of the ex-

isting species which have descended from them.

Now it is a well-established fact that the lower leaves of young

branches and shoots, and especially of those which spring from

the stumps of felled trees, are frequently unlike the adult forms

which occur higher up and bear a close resemblance to the fossil

leaves of extinct species, so close indeed, as oftentimes to be in-

distinguishable from them. This is strong evidence in favor of

the doctrine that the lower foliar organs represent not reduced

leaves, as botanists have commonly supposed,} but the primitive

foliar organs, and that in an ascending series from the lowest scale

to the mature adult leaves of the upper part of the stem, giving

a more or less perfect summary of the phylogenetic development

of the foliar organ from the most primitive type upward to the

most highly differentiated.{ In other words, a single stem may

represent the whole phylogeny of the foliar organs of its type.

It is true that there are simple leaf-forms which have become so

* Our modern species of Corylus are recorded from the Eocene by Professor

J.S. Newbury. Later Extinct Floras of North America. Ann. N. Y. Lye.

Nat. Hist. 9 : 59-60. 1868.

7 See DeCandolle. Org. Veg. 2:212. 1827.

{‘‘Most modern botanists now regard the varying forms of leaf seen on young

shoots and near the base of trees as valuable hints at the probable stages

through which the final forms have passed in the history of their development.’’

Professor L. F. Ward. Proc. U.S. Nat. Mus. 11:41. 1888.

28 The Nature and Origin of Stipules.

by reduction but, as an organ cannot be reduced until it has been

developed, these are to be looked for above and not below the

perfect leaves, and are found in bracts, involucral scales and the

parts of floral envelopes, reduction taking place in inverse order to

the course of development, and only the most primitive structure,

the simple sheath, persists in the petals of most flowers. Re-

duced leaves are also common in parasites, and in the flora of

desert regions as is well illustrated in some of the Leguminosz

of Australia the leaves of which are little more than spines, or

are developed into bladeless phyllodia, while in the seedlings the

ancestral pinnate or bipinnate forms occur.*

We thus have shown in each season’s growth of a plant, though

not clearly in annuals because disguised in the seedling, a more

or less complete series of foliar organs which may for illustration

be compared with the vertebrate series among animals, the lowest

leaf-scales being comparable in degree of development to the sim-

ple structures of the fishes and the most highly developed leaves

to the complicated ones of mammals. Each leaf in the series is

equally perfect for the function it is intended to perform, but the

lowest of a lower type of organization, as are the fishes, and rep-

resenting an earlier stage in the phylogenetic series.

Now in animals we look to the developing egg of the more gen-

eralized fishes for the least abbreviated embryological recapitula-

tion of the early development of the vertebrate branch, for in the

mammals the early stages are passed through so rapidly and with

so many disguises as to be of comparatively small importance in

giving the history of the branch, unless viewed in the light of the

embryological development of the lower types. So the lower

foliar organs of a branch or shoot are embryologically of far

greater importance than the upper, for in the beginning of the de-

velopment of one of the upper leaves we have but the early stages

of a highly organized appendage. These early stages are conse-

quently abbreviated and more or less disguised. The formation

of the stipules in the growth of the upper leaves is therefore not

a salient point in the consideration of our problem though it has

had much stress laid upon it, yet it is of interest to note that in

general the stipules appear earlier than the leaf-blade, thus giving

evidence that they are of more ancient origin. It may be added,

*See Sir John Lubbock. On Seedlings. 1: 474. 1892. Seealso p. 440 as

to the similar case of Lathyrus Aphaca.

The Nature and Origin of Stipules. 29

and it is a matter of common observation, that the petiole is the

last portion of the leaf to develop ontogenetically and is therefore

to be regarded as the most recent part to be added phylogeneti-

cally. This helps to explain the common occurrence of sessile

and petiolate leaves even in different species of the same genus,

as variation more readily occurs in recent than in ancient struc-

tures, while on the contrary it has been a matter of remark among

even the earlier botanists that stipules when they occur usually

characterize all the species of a family, an additional evidence of

the antiquity of their origin.

Let us now take up, in the light of the foregoing conclusions

the consideration of the destiny of the primitive foliar organ as

it has been modified and developed in the course of evolution.

For convenience in making our inquiry, I would divide the

primitive leaf into the central-basal, axial, apical and lateral por-

tions. Each of these figures prominently in the evolutionary his-

tory of foliar organs, for from the original condition there has

been progressive development along several lines of varying de-

grees of relationship and the morphological result of the develop-

ment of the several parts has been quite different in the divergent

groups, so much so as to render the question of homology a

doubtful one to many minds. We shall endeavor to establish its

reality.

The lamina of the leaf, as we shall see, has been developed

chiefly from the apical portion, usually from scarcely more than

amere point, though it may also include the axial and lateral por-

tions. The true petiole, when present, is developed from the

axial portion,* the sheathing petiole from the central basal to-

gether with the lateral portions, stipules and structures of the

same signification from the lateral portions. It is with the lateral

portions, therefore, that we are chiefly concerned.

With reference to the formation of stipules there are three

principle types of leaf-development: that in which the several

portions of the primitive leaf have developed together into a sim-

ple unappendaged blade, that in which a sheathing petiole is

formed with or without a ligule or ochrea, and that in which

stipules properly so-called are present.

In the first and simplest case the development of all the parts

*See S. H. Vines. Text-book of Botany, 1: 49. 1894.

30 The Nature and Origin of Stipules.

together gives rise to such leaf-forms as are found in Vaccinium

and Sassafras, the principal portion of the lamina being formed

by the development of the apical portion, but including at the

base the lateral, central-basal and axial portions which are con-

tracted below into a short petiole.

If we observe the development of the leaf in Sassafras the

relative growth of the several parts can be readily traced. The

first four leaves (fig. 1) are very simple. In the fifth (fig. 2) con-

siderable development has taken place. The apical portion, now

forming about half of the organ, is provided with the three typi-

cal veins as they appear in the adult leaf, but starting out sepa-

rately from the very base. The lateral portions have reached

their highest development and each is furnished with a pair of

veins. In the sixth leaf (fig. 3) there is a very close approach to

the adult form. The upper part has expanded and the lower parts

have elongated, removing the point of separation of the three

principal veins of the leaf to a considerable distance from the

stem. At the same time there has been a basal contraction look-

ing toward the formation of the petiole with a considerable de-

generation of the lateral portions, one of the veins having disap-

peared from each of them, while the other has become associated

with the midvein. The seventh leaf (fig. 4) represents the un-

lobed adult form and differs but little from the sixth.

A similar condition is observable in Ailanthus glandulosa Desf.

(figs. 5-10), but resulting in this case in the final separation of

the lateral portions as small gland-bearing fugacious stipules, com-

parable to those at the base of the leaves of many of the Ranun-

culacee. The comparison of Sassafras and Ailanthus shows how

small a difference in development may determine a leaf as stipu-

late or exstipulate.

The case of Syringa vulgaris L. is like that of Sassafras,

though more difficult to trace, owing to the larger number of veins

in the leaf, but the homologies of parts may be followed more or

less distinctly from the second leaf up to the sixth, the first adult

leaf (figs. 11-14). The lateral portions are seen to have degen-

erated almost entirely and, their bundles having disappeared, they

remain only in the margin of the petiole.

The Composite furnish examples of a similar course of develop-

ment but often with a closer approach to the true stipular condi-

tion, as the lateral portions are supplied with vascular tissue by

The Nature and Origin of Stipules. 31

small branches coming off at the base of the leaf from the main

lateral bundles.

In Erigeron annuum (L.) Pers., for example, there are three

fibro-vascular bundles in the leaf-trace which pass up through

the central portion of the petiole, converging as it narrows.

But almost immediately on their departure from the stem each

of the lateral bundles gives off a branch in the same manner as

when true stipules are present. This branch forks at once and

supplies the wings of the petiole. In the cauline leaves (fig. 15)

its branches can be distinctly traced into the lower lobes of the

leaf. The basal leaves of Aster undulatus L. show a condition

very closely similar to that found in Hrigeron annuum (L.) Pers.,

but in the cauline leaves there is a considerable modification by

which the large lobes of the base of the petiole (fig. 16) are

formed. The stipular bundle curves outward through the lobe

giving off branches which form a net-work supporting its paren-

chyma. It then passes up through the wing of the petiole and

into the basal part of the leaf. In Solidago juncea Ait., there

are eleven bundles in the leaf-trace and a stipular bundle is given

off on each side, supplying the margins of the petiole. Artemisia

vulgaris L. affords a very interesting variation. The lateral

portions of the primitive leaf have branched in a very curious

manner (fig. 17), forming several small leaflet-like appendages to

the base of the petiole. That they belong to the lateral portions

and are stipular in their character is shown by the fact that they

are supported by branches of the stipular bundle which is given

off a little higher up than in Hrigeron, passes on through the

wings of the petiole after giving off the branches and enters the

base of the blade as in other cases. This is the nearest approach

to the true stipular condition that I have observed among the °

Composite.

The embryonic development of the foliar organ among the

Composite is in general too much abbreviated to give much evi-

dence in the consideration of the present question, and it should

be so expected from the position which the family holds at the

head of the vegetable kingdom.

Petioles of the kind seen in this type of leaf-development are

very often short and usually more or less margined or winged by

_the contracted basal parts of the lateral portions of the primitive

leaf. They are evidently genetically different from the petioles of

32 The Nature and Origin of Stipules.

stipulate leaves which are developed by the elongation of the axial

portion alone. Sessile leaves also are of this type, hence the ab-

sence of stipules, the stipular tissue being incorporated into the

basal part of the blade. But even where stipules are present, the

lateral basal portions of the leaves are often in the closest

anatomical relation with the stipules. This may be seen in Viola

obliqua Hill (fig. 18) in which, near the bundle which passes into

the stipule,a similar one arises, takes its course up the petiole

supporting its narrow wing and is distributed to a small part of

the basal portion of the lamina. We shall find several cases

similar to this when we come to the consideration of the Rosacez.

There is in this a suggestion of the occasional separation of only

a part of the lateral portions to form the stipules and the incor-

poration of the remainder into the petiole and blade.

The second case is that of the sheathing petiole as it occurs in

the Graminz, Araceze and Umbellifere. In this case the central-

basal portion of the primitive leaf is very largely developed and

with it the lateral portions which form the margins of the sheath-

ing petiole. The lamina and true petiole are later developments

of the apical and axial tissues. We are strongly supported in

this view by the fact that the sheathing petiole is interchangeable

with petioles of the ordinary type accompanied by stipules. This

occurs in the Umbellifere. In Hydrocotyle and a few other

genera the sheathing petiole is wanting and stipules are present.

The closely related Aralia racemosa lL. also has stipules. Still

more striking is the case of Comarum palustre L. in which the

basal leaves have the sheathing petiole remarkably developed with

no indication of stipules (fig. 19), while the upper leaves possess

well developed stipules adnate for not more than half their length

(fig. 20).

But the identity of the marginal tissue of sheathing petioles is

perhaps best shown in the Ranunculacez. In the upper basal

leaves of Ranunculus bulbosus L., the separation of the lateral por-

tions is seen actually to have begun, presenting exactly the ap-

pearance of adnate stipules. The development can be clearly

traced from below upward. The first leaf has a short sheathing

petiole of the ordinary type (fig. 21). This is slowly modified

till in the fourteenth leaf (fig. 22) the vascular bundles have drawn

closer together, the sheath has grown shorter and the broad lateral

The Nature and Origin of Stipules. 33

portions, hyaline in texture and requiring no special support other

than that of the surrounding leaves, are rounded off distinctly at

the top at the point of beginning of the true petiole. In the

fifteenth leaf (fig. 23) there is a further reduction in size and the

tips of the lateral portions are free. Another interesting case

among the Ranunculacee is that of Thalictrum polygamum Muhl.

in which the sheathing petiole is of a very generalized type (fig.

24). The lateral portions are chiefly hyaline, though sometimes

faintly netted-veined and their margins turn in at the apex and

meet in the central dorsal channel of the petiole at its base, form-

ing a ridge between the sheathing and true petioles. This ridge

supports a very narrow hyaline membrane which appears to me

as the rudiment of a ligule. It would become typical by a little

further development of marginal tissue. I believe this to be the

origin of the ligule wherever it occurs, though it does not appear

so clearly evident in highly specialized groups, nor should we

expect such to be the case. There is also present at the first and

second forkings of the petiole a transverse hyaline scale very

much like a ligule.

It is noteworthy that the ligule always occurs in connection

with the sheathing petiole, as in the Graminee and Cyperacee,

or where there is evidence that there has been a sheathing petiole

which has disappeared by degeneration, leaving the ligule axillary

as in some of the Naiadacez which we shall presently consider.

When the ligule has developed sufficiently to require special

support, it is supplied by the introduction of vascular bundles.

These bundles have their origin most frequently as tangential

branches of the main leaf-bundles at their point of passage from

the sheathing petiole into the true petiole, or, where the latter is

undeveloped as in the grasses, into the blade. This mode of ori-

gin of the ligular bundles is seen in some of the tropical grasses

and in the ligular portion of the stipule of the Naiadacev and the

ochrea of the Polygonacer. Richardia shows an exceptional ve-

nation of the ligule.

The best marked examples of the sheathing petiole among the

Monocotyledones are found in the Aracee, the Cyperacez and the

Graminez. If we examine a developing plant of the common

hot-house calla (Richardia Africana Kunth.), the first leaf (fig.

25) is seen to be a short, broad sheath, the second (fig. 26) has in-

creased to a considerable length and the apical and axial tissues

34 The Nature and Origin of Stipules.

have developed into a minute blade and petiole. The third leaf is

of the adult form, but smaller, though all the parts have increased

very much in size. This is contrary to what is observed in

fianunculus where the sheathing petiole degenerates while the

other parts advance. The margins of the sheathing petiole of

Richardia curve inward at their apices and meet in the middle ©

line of the leaf as in the case of Thalictrum polygamum L., but

they are much broader and form a distinct ligule which is sup-

ported by the incurving and union of the marginal veins of the

sheath instead of by tangential branches. In Arisema triphyl-

lum (L.) Torr., the transition is not so well marked, owing to the

small number of leaves the first of which is but a sheath as in

fichardia, while the second bears a mature lamina.

Scirpus polyphyllus Vahl. (fig. 27) will serve well to illustrate

the ligule in the Cyperaceex. It is but little developed as a slight

hyaline outgrowth upon the ridge at the union of the sheath and

lamina, but the sheath is closed, as is typical in the family. and a

little farther development of marginal tissue would produce an

ochrea. Typical of the ligule in our common grasses is that of

Phalaris arundinacea L. (fig. 28). It consists of a considerable

outgrowth of hyaline tissue which is continuous laterally with the

marginal hyaline tissue of the sheath. This continuity strongly

supports the position taken as to the origin of the ligule. The

purpose of the ligule is evidently to prevent the flow of water

from the upper parts of the leaf down between the sheathing pet-

iole and the stem which together with the axillary bud it invests

and protects, and neither the ligule nor the primitive ridge which

bears it are found in those cases where the sheathing petiole does

not closely invest the stem, at least in the early stages of growth,

and its purpose could not be in any considerable measure ful-

filled.

The usually axillary position of the “stipule” in the Naiada-

cez has occasioned considerable discussion as to its real re-

lation to the ligule of grasses and to stipules proper. That it

is in reality a development of the lateral portions of the primi-

tive leaf, and that it corresponds to the ligule together with

the margins of the sheathing petiole of grasses and is rendered

more or less nearly axillary by the degeneration of the central-

basal portion, becomes clear from the fact that in some species of

Naiadacez the sheathing petiole retains a considerable degree of

The Nature and Origin of Stipules. 35

what should be regarded as its ancestral development, and a con-

dition approaching that which occurs in grasses is found. /Po-

tamogeton crispus L. is one of our species which will serve well for

an illustration. The first leaves do not develop a blade, but the

lateral and central-basal portions are well developed. In the adult

leaves there is present a true sheathing petiole (fig. 29). The

fibro-vascular bundles of the central-basal portion pass into the

blade, giving off tangentially, at the point of transition from

sheath to blade, the bundles of the ligular part of the stipule.

The bundles of the lateral portions do not in this case curve about

to join those entering the blade but are prolonged upward, re-

maining parallel and supplying the lateral portions of the stipule

with supporting tissue directly. In Althenia jfiliformis Petit.

(fig. 30), the conditions are more primitive in the larger relative

development of the lateral and central-basal portions. In Ruppia

the ligule is not developed, and the tips of the lateral portions

are free as in ordinary adnate stipules.

The condition found in Potamogeton is almost exactly repeated

in Polygonella articulata (L.) Meisn. (fig. 31). The ochrea is

cylindrical, surrounding the stem. The central-basal portion is

long and narrow, bearing at its apex the terete lamina which is

deciduous before flowering. ‘The lateral portions form the prin-

cipal part of the sheath, are parallel veined with a few anastomos-

ing bundles and are prolonged above the central-basal portion,

growing in along the ridge between it and the lamina. This middle

portion shows its origin by a deep median sinus and receives its

bundles typically as tangential branches from those entering the

lamina. We do not have then in Polygonella a typical ochrea as it

occurs in Rumesx and Polygonum, where, because of the small de-

velopment of the central-basal portion, the sheathing petiole is

very short or almost wholly wanting. The lamina, being of much

greater importance than in Polygonella, receives all the bundles of

the leaf-trace. They are more or less abruptly deflected into the

true petiole, generally developed in these genera, according to the

degree of degeneration of the central-basal portion. The lateral

portions receive their supporting bundles as branches of the lateral

ones of the leaf-trace. In Polygonum sagittatum L. (fig. 32), the

marginal tissues do not extend across the petiole and we have a

stipule opposite the leaf. In Rumesx crispus L. (fig. 33) and

Polygonum Virginianum L. (fig. 34), the ochrea is complete and

the axillary parts receive the typical tangential bundles.

36 ~The Nature and Origin of Stipules.

The ochrea of palms is doubtless of the same character, though

I have not had opportunity to examine its anatomical structure.

In those species which I have examined morphologically, the case

is that of the ochrea associated with a remarkable development

of the sheathing petiole. There is no true petiole and the ligule

may be seen even a little above the base of the blade on the upper

surface of the midrib. From this point the lateral portions may

be traced down the margins of the sheath, though dried up and

very much torn and broken by the more rapid development of

the central tissues, till they unite with those parts which in their

development have formed the “‘ ochrea.” The degeneration of the

sheathing petiole with the probable concomitant formation of a

true petiole would give the same conditions as in Polygonum

with its typical ochrea.

The ochreate stipule of Platanus differs little morphologically

from the typical ochrea, except in the absence of development of

the central-basal portion and the possession of a horizontal limb,

but there is no fibro-vascular support for the ligular part and this

usually splits, leaving apparently a single stipule opposite the

leaf.

The case of the tendrils of Smzlax is one which has occasioned

much discussion, but the embryological together with the anatom-

ical characters make it sufficiently clear that in Smilax the ten-

drils are true stipules found in connection with the sheathing

petiole. Ifa young shoot of Smilax rotundifolia L. be examined,

the first leaf (fig. 35) is seen to be of the typical primitive form.

In the second (fig. 36), the apical portion has developed into a

blade of considerable size and there is a well-marked sheathing

petiole. In the third (fig. 37), the true petiole has begun to de-

velop, the central-basal portion is degenerating and at the same

time the lateral portions have begun to separate, forming rudi-

mentary tendrils which in the adult leaves come to considerable ©

length by secondary development in adaptation to. their new and

unusual function of support. In cross section the bundles of the

tendrils are seen to arise as branches of those of the petiole, so

that anatomically, as well as embryologically, they answer to true

stipules.

Pastinaca sativa L. (fig. 38) furnishes a good example of the

sheathing petiole among the Umbelliferze. The lateral portions are

broad and furnished with several vascular bundles parallel with

The Nature and Origin of Stipules. 37

those of the central basal portion. The lateral portions remain

of considerable breadth to the top where they are distinctly

rounded off, and their bundles, with the exception of two or three

of the exterior ones. curve around and unite with those entering

the petiole. This free condition of the exterior lateral bundles

with the anastomosing network between them shows a consider-

able degree of approach to the true stipular condition.

In the third case true stipules are developed. They are formed

by a very early separation of the lateral portions from the main

body of the primitive leaf, a separation which can be very clearly

traced progressively in the embryological history of leaf develop-

ment. The function of the lateral portions in their primitive

connection with the main body of the foliar organ is, in common

with the other portions, protective, and while the apical portion,

having had placed upon it the special function of assimilation,

goes on in its development together with the accessory axial por-

tion in adaptation to this purpose, the lateral portions usually

serve their ancient function only, sharing it with the central-basal

portion when this has not disappeared by degeneration. The

central-basal portion also supports the main body of the leaf, a

function from which the lateral portions have been freed by sepa-

ration.

It isin consequence of this separation that all the main vascu-

lar bundles of the leaf-trace in the third type of leaf-development

are deflected toward the central one that they may pass up through

the petiole into the lamina and give the required support to these

important parts. The support of the lateral portions is left to

comparatively small lateral branches from the two exterior bun-

dles of the trace, evidently developed expressly for the purpose.

This we may conclude, since vascular tissue is the most modern

of plant tissues and introduced because of the necessity of sup-

port in the evolutionary development of the primitive ground

tissues. It would, therefore, follow and not precede the evolution

of leaf-forms, being introduced where needed and disappearing

again when degeneration or other support of particular parts ren-

ders its presence unnecessary. This will appear in some of our

examples. In the first and second types of leaf-development the

lateral portions may retain in greater or less degree their inde-

pendent venation.

ANNALS N. Y. ACAD. Scl., X, May, 1897.—4.

38 The Nature and Origin of Stipules.

As the other portions of the primitive leaf have been so won-

derfully modified in the course of their development and altered

from their original condition, so the freed lateral portions to

which we may now apply the term stzpules have not retained their

primitive proportions in adult leaves nor the identity of all their

parts. But as the central basal portion has often almost wholly

degenerated, the same thing has happened to the basal parts of

the lateral portions. The parallel degeneration of the two por-

tions has brought the stipules into closer and closer apparent re-

lation to the stem, so much so as to lead to the enquiry whether

they are not accessory leaves and to suggest their origin from the

reduction or lack of development of a portion of the leaves as in

Selaginella and their subsequent association in close relation to

the larger ones, but in all my investigation I have not found

the slightest evidence in support of this theory. The degener-

ation of the stipules may continue until they become vesti-

gial or finally disappear altogether. This is evidently the case in

those families of plants a few species only of which still possess

stipules, as for example the Caprifoliacee.

But opposed to the basal degeneration of stipules, there has

very commonly been a longitudinal development corresponding

to that by which the lamina has been evolved. This has resulted

in the adaptation of the stipules to the peculiar requirements of

each genus and species. Often in this secondary development

they remain membranous, serving the protective function only,

and when free are early deciduous. But in numerous cases they

have acquired the assimilative function also, developing abundant

chlorophyll and sometimes, as in the pea (Pisum sativium L.), be-

coming of equal assimilative importance with the lamina. In

Lathyrus Aphaca L., they even replace it almost entirely.

Among all these varying forms we should expect to find closer

similarities in those plant groups of nearer relationship as we do

in floral structures, and conversely these similarities of foliar de-

velopment should also point to relationship, due allowance being

made for parallel development in adaptation to similar environ-

ment and for secondary functional modifications which find mor-

phological expression. Also in types more recently evolved and

more highly differentiated wide divergence from the typical mode

of development may be looked for. The Caprifoliacez, before

mentioned,are of such a type, with stipules usually wholly aborted;

The Nature and Origin of Stipules. 39

_ another is the family of the Rubiacez with anomalous stipular

development in the group of the Stellate. The oaks also, though

of lower organization, are an advancing type and still actively

undergoing differentiation as evinced by the close relationship and

difficulty of determination of the species of any given group. In

this genus all but the upper part of the primitive leaf has disap-

peared by degeneration even in the earliest stages represented in

embryonic leaf-development,and the well developed stipules are

distinct and separate from the very base of a developing shoot.

Not until the fifteenth node, in Quercus rubra L. (fig. 39), is there

any appearance of lamina. The apical portion of the protophyll

must however be regarded as potentially present between the

stipules at their base. It begins its development unusually late

in the series and exhibits several stages, of which the twentieth

leaf (fig. 40) is illustrative, before reaching adult size. The axial

portion of the protophyll being aborted, the petiole, here again a

Short one, is formed by the contraction of the basal part of the

lamina itself. The case of Fagus is very similar, but the lamina

appears as early as the eighth node (fig. 41), indicating a less de-

gree of specialization. In related genera a different course has

been followed. The lamina develops still earlier and the stipules

of the lowest nodes are united, separating only on the appearance

of the first accompanying lamina.

In the family of the Juglandacez the genus Hicorza furnishes

a very interesting example. The lower foliar organs are of the

primitive type with an unusual development in size in some

species. The transition to the adult leaf-form is commonly

rather abrupt, but I have observed, in both Hicoria alba (L.)

Britton and H. microcarpa (Nutt.) Britton, the frequent occur-

rence of intermediate forms, the lateral portions remaining as

typical adnate stipules (fig. 42).

I have not seen the typical representation of embryonic leaf-de-

velopment better exemplified than in the case of Baptisia tine-

toria (L.) R. Br. where at a glance one is struck with its clear-

ness. It is also especially full and accurate as occurring in the

development of subterreanean buds. The first five leaves are ex-

tremely primitive, completely surrounding the node, though only

slightly developed onone side. The fifth (fig. 43) shows at its apex

a minute apical tooth, the beginning of the lamina which is farther

developed in the sixth leaf. In the seventh (fig. 44) the three leaflets

Ye ee

40 The Nature and Origin of Stipules.

are plainly distinguishable, the petiole has begun its development

and the separation of the stipules has made considerable advance.

The ninth leaf (fig. 45) is well developed, with the large stipules

still showing considerable adnation. But in the tenth (fig. 46)

they are wholly free and much reduced, and higher up disappear

altogether. We could hardly have a more complete series in

illustration of the formation of stipules than this, giving as it does

all the stages from an extremely primitive leaf-form to that very

highly organized condition where the stipules have entirely dis-

appeared. By a comparison of the venation in the seventh and

ninth leaves, it will appear that the separate condition of the

stipules has been attained in the manner already described, partly

by the formation of an apical cleft, partly by the degeneration of

the central-basal portion bringing the base of the cleft lower down. .

Meanwhile there has also been a considerable apical development

of the stipule itself. But this increase in size is lost again in the

tenth leaf and the reduction continues to final abortion. Melz-

lotus alba Lam. presents very similar though somewhat less

primitive conditions.

While considering leguminous plants, a few words concerning

stipels, which are so characteristic of the family, would be in

place. They have been denominated as “ the stipules of leaflets,”

but I am convinced that they have no connection with stipules

whatever, but that they represent rudimentary leaflets which have

their origin in a tendency to increased compounding. The habit

has become so fixed in the Leguminose that evidence of its ori-

gin is seldom met with. I have however seen,in Lespedeza capi-

tata Michx., one of the earliest leaves with the terminal leaflet

only developed and the two lateral ones represented by stipels.

I have found more light on the question in other families where

the same tendency to increased compounding often occurs. In

Sanguisorba Canadensis L. (fig. 47) for example, very vigorous

plants sometimes show rudimentary leaflets, more developed in-

deed than typical stipels, but in the same position. Their char-

acter as leaflets of secondary rank is evinced by their occasional

removal to a little distance from the primary petiole. A more

striking case is that of Sumbucus Canadensis L. In this species

the leaves of young shoots springing up where the bushes have

been cleared away are frequently partially bicompound and there

are all gradations between the ordinary pinnate form and the

The Nature and Origin of Stipules. 41

bipinnate condition (figs. 48-50). In this case it is remarkable

that the first appearance of the secondary leaflet is in the shape _

of a small body with both the form and position of a stipel, with

the same small supporting vein and differing only in greater thick-

ness. These facts seem to give evidence sufficiently conclusive

that stipels are in reality rudimentary leaflets. That their de-

velopment is not confined to the Leguminose is farther shown by

their characteristic occurrence in Staphylea trifolia L.

Another frequent foliar variation among the Leguminose is the

development of the phyllodium, which might be thought to have

some connection with stipules, but the presence of both together

in some genera disproves the idea.* The stipules in the Legu-

minose often take the form of spines which serve for the general

protection of the plant. We have an example in the well known

Robinia Pseudacacia L. (fig. 51). In some of the tropical Aca-

cias,as for example A. spadicigera C. &S. (fig. 52), they take the

form of enormous hollow horns which are appropriated as homes

by some species of ants.

Sambucus Canadensis L. presents another remarkable char-

acter. The leaves of the vernal shoots from subterranean buds

are furnished with stipules of the same form and in the same po-

sition as those of Sambucus Hbulus L., but smaller. There are

four of them at each node, they are ovate or nearly orbicular in

form, small, rather fleshy and persist but a short time. Each is

supplied with a small vascular bundle, originating as a branch of

the nodal girdle which connects the leaf-traces. These facts

give evidence of the close relationship of these two species of

Sambucus, and of the characteristic presence of stipules in the

ancestral form. In Sambucus Hbulus L., they are still typically

developed, but in our species have become so far vestigial as to

appear only in connection with the early leaves of shoots from

subterranean buds, an additional evidence of the importance of

the leaf-forms successively developed from such buds, in their

bearing on the evolutionary development of modern adult forms.

If now we turn to the family of the Rosacez we shall find many

illustrative examples of the same facts as those born out in the

case of Baptisia tinctoria (L.) R. Br. But it frequently happens

that basal degeneration does not take place or is only partial, re-

* Bentham and Mueller. Flora of Australia, 2: 304. 1864.

f Belt. Naturalist in Nicaraugua, 218. 1874.

42 The Nature and Origin of Stipules.

sulting inthe adnate stipules characteristic of somany genera and

_ species of the family. Agrimonia striata Michx.,in the develop-

ment of its subterranean buds in the spring, presents an excellent

series of embryonic leaf-forms. The lower ones are all simple

sheathing scales completely surrounding the stem at their inser-

tion. Not until the eleventh leaf (fig. 53), whichis three-toothed

at the apex, does the differentiation of parts begin. The central

tooth is the beginning of the blade with its petiole; the lateral

portions with their tips now free are the stipules. To say that

they are “adnate” indicates only that they retain their primitive

connection with the central-basal portion. In the twelfth leaf

(fig. 54), there has been some basal degeneration, as shown by the

lower point at which the three main bundles of the leaf converge

and the lower position of the zigzag plexus of the stipular veins.

The free tips, on the other hand, have increased in size and a small

blade supported by a petiole is present in consequence of the de-

velopment of the central tooth. The fifteenth leaf (fig. 55) shows

a stronger development of all the parts, and a branch of the main

stipular bundle is seen to pass up the petiole. The adult form is

attained in the seventeenth leaf (fig. 56). In it some further

basal degeneration has taken place, but the adnation of the sti-

pules is still very prominent.

Prunus Cerasus L. gives a very good morphological series, but

the venation is obscure. A view of the several forms can be had

by an examination of the tenth, thirteenth, fifteenth, sixteenth

and seventeenth leaves (figs. 57-61). They show the transition

from the simple primitive scale to the mature condition in which

the stipules are rendered entirely free. The series is similar in

Rubus occidentalis L., Pyrus Malus L. and Pyrus communis L.

In Rubus villosus Ait. (figs. 62-66), the basal degeneration is not

carried quite so far and the stipules in the adult leaf-forms re-

main adnate for some distance from the base of the leaf. The

tips of the stipules have taken a larger comparative development

than in Agrimonia. Anatomically, however, Rubus villosus Ait.

resembles the latter in having a vein which enters the petiole,

neighboring to the main stipular bundle much as in Viola obliqua

Hill (fig. 18). The venation in Pyrus Malus L. (fig. 67) is still

more like that in Agrimonia.

The stipules of Fragaria and Rosa show the highest degree of

adnation and little, if any, basal degeneration seems to have taken

The Nature and Origin of Stipules. 43

place, though the lateral leaf bundles curve in toward the median

one at but a short distance from the stem. This arrangement of

the bundles is probably secondary in these forms for the purpose

of giving a firmer support to the leaf by an axial concentration

of the vascular tissue in the sheath and a corresponding thicken-

ing of the surrounding tissues, a firmer support than could be

given by only three bundles if they did not converge till they ap-

proached the point of their entering the petiole. The venation of

the stipules is also peculiar. In Fragaria Virginiana Duchesne

(fig. 68), there is a single strong bundle running out into the free

tip of the stipule. From this are sent out one or two weak veins

above, and below there is a faint vascular network confined mostly

to the region of the tip and extending in a long curve toward the

outer portion of the base, where it gradually fades out without

forming any connection with other vascular tissue below. This

condition seems to indicate a former basal connection of these

stipular bundles, either with the lateral bundle of the leaf or pos-

sibly with those of the stem, forming an additional leaf-trace bun-

dle distributed to the stipules only. The former case is far more

likely. A probable explanation of this degeneration of the basal

stipular bundles can be found by a consideration of the conditions

of the environment. All the leaves being basal, the stipules are

clustered together and are supported by one another and by the

surrounding soil. They are more or less fleshy, destitute of chlo-

rophyll, and in their moist surroundings loss of water by evapo-

ration is comparatively slight. All these circumstances lessen

the necessity of the supply of freshsap. The rapidly conducting

vascular tissue has come into disuse, and its degeneration and

disappearance is the natural consequence. Thesame arrangement

in forms with leafy stems is not so readily explainable except by

the supposition that the arrangement is ancestral. This seems

rather evident in the case of Agrimonia striata Michx. (figs. 53—

56), where the same condition of the bundles occurs, for the

earliest leaves representing the ancestral forms develop under the

same conditions as the adult leaves of Fragaria. But in Rosait

would be by no means clear did we not have such intermediate

types as Agrimonia. Rosa humilis Marsh. (fig. 69) may be taken

as typical of the genus. The venation of the tip of the stipules

is nearly like that in Fragaria, but with a little larger develop-

ment above the main bundle. The vascular network below is

44 The Nature and Origin of Stipules.

much more extensive and is reénforced by several small branches

from the lateral bundle which enters the petiole, below the main

stipular branch. This additional supply of vascular tissue is evi-

dently rendered necessary by the exposure of the stipules to the

light and air and the development of chlorophyll. Itseems to be

of secondary introduction.

The nearest approach to the stipular conditions occurring in

Fragaria and Rosa which I have observed among the Legumi-

nos is found in the adnate stipules of Trifolium pratense

L. (fig. 70). There are two sets of stipular bundles. One of

these supplies the tip of the stipule and consists of three veins of

which the lowest corresponds to the single large bundle of the

tip of the stipules of Fragaria and Rosa. The other has its ori-

gin as branches from the lateral bundle of the leaf-trace at the

base of the leaf, the usual point of origin of the veins of free stip-

ules. This set of veins is distributed to the lateral and basal

parts of the stipules and apparently corresponds to the lower net-

work of the stipules in Fragaria. These stipules are mainly

protective in function. Their meshes are filled with hyaline tis-

sue, but there is some green parenchyma along the veins.

Two very interesting cases in the family of the Rosacez are

those of Cliffortia graminea L. f. of South Africa (fig. 71 ) and

Potentilla fruticosa L. (fig. 72). In the former the leaves very

closely simulate those of grasses with the linear lamina sessile

upon a sheathing petiole. They differ in having the tips of the

lateral portions (stipules ) free instead of turning in across the

insertion of the lamina to form a ligule. In the latter the con-

ditions are very closely similar to those of the ochrea of Polygo-

num. There isa short sheathing petiole, above the apex of which

the tips of the stipules rise. Each of them is supported by a

strong vein which has its origin at the base of the true petiole.

But instead of being free from one another as in Rosa, the stip-

ules are connected back of the petiole by a hyaline ligular tissue.

The lateral portions of the sheathing petiole are also united to

one another on the opposite side of the stem, at least in young

leaves, to a considerable degree. Thus an ochrea is formed, not

quite a typical one it is true, yet more nearly so than that of

Polygonum sagittatum L. ( fig. 32 ).

The fact that such forms as these can occur in the same family |

of plants along with typical stipules, both adnate and free, goes to

The Nature and Origin of Stipules. 45

show how small is the real difference between the various stipular

forms. Not all stipules possess supporting tissues but, just as is

the case in the ligule of most grasses, may be without any fibro-

vascular bundles whatever. This is the casein Vitzs, in Partheno-

cissus and Hydrocotyle. Vitis Labrusca lL. (fig. 73) shows a

somewhat thickened central streak at the base of the membranous

stipule, but in Hydrocotyle Americana L. (fig. 74), the thickness

is uniform andthe stipule very thin. ‘These facts give some au-

thority to the supposition that the pectinate interpetiolar appen-

dages which occur in the Composite Willoughbya scandens (L.)

Kuntze (fig. 75) are true stipules. They are hyaline in texture,

without supporting tissue, and may possibly be merely of epider-

mal origin. To determine this point requires opportunity to ex-

amine their development.

It is of importance to state that ne tendril of the Cucurbita-

cee, regarded by many as a stipule, has been determined by ana-

tomical examination to represent the first leaf of the axillary

bud.* The spinesof Xanthium spinosum L.,simulating stipules

in position, are degenerate pistillate flowers. As proof of this,

they often bear a greater or less number of hooked prickles like

those of the flowers, and there may be a spine on one side and a

flower on the other, showing them to be of the same significance.+

The stipules of Comptonia peregrina (L.) Coulter (fig. 76) de-

nied by some to be properly so-called, do not differ anatomically

from other stipules notwithstanding their peculiar morphology,

and are to be included under the term. Oneof the chief reasons

for their exclusion seems to have been the absence of stipules in

Myrica. Thisis doubtless a case parallel with that of Viburnum,

of which most of the species have lost their stipules by degener-

ation,

While it is not a generally accepted view, there is no good reason

why stipules should not sometimes be distinguishable in floral

parts. They are clearly present in the sepals of Rosa and Rhodo-

typus, and the smaller intermediate lobes of the calyx of Potentilla

probably represent pairs of united stipules, one from each neigh-

boring calyx-lobe in the manner of interpetiolar stipules.{ The

teeth of the filament in Deutzia are very suggestive of stipules in

*See Lestiboudois, Bull. Soc. Bot. Fr. 4: 746-747. 1857. Cited on p. 6.

t See also Clos. Mem. Acad. Sci. Toulouse, (IV), 6: 66-75. 1875.

{See Engler and Prantl. Pflanzen Familien. 3: Abt. 3, 6. 1894.

46 The Nature and Origin of Stipules.

stamens, and the corona of Silene may very probably represent a

ligule. The glands of the leaves of Ranunculacez which have

been homologized with stipules, as already stated, can often be

traced up into the flowers and are familiar in connection with the

petals of Ranunculus.

One of the most interesting families of plants in the develop-

ment of its stipules is that of the Rubiacez, the development

being very unusual in the group of the Stellate. Though the

foliar anomaly in this group was early remarked upon and was

anatomically explained as early as 1840,* there are considerations

which make its present discussion desirable.

In the greater part of the family the leaves are opposite, or oc-

casionally in whorls of three as in Cephalanthus occidentalis L.,

and are usually stipulate. - The stipules are of variable character

and often interpetiolar, the adjoining stipules on each side of the

stem being connate. In the group of the Stellatz however, com-

prising ten or twelve genera, the stipules usually are apparently

wanting and the leaves in whorls.: There is a tendency toward a

verticillate arrangement of the leaves in others of the Rubiacez,

as shown by the frequent occurrence of whorls of three in usually

opposite-leaved species. Now an anatomical examination of the

whorled leaves of Mollugo verticillata L., Silene stellata (L.)

Ait. f., Leptandra Virginica (L.) Nutt. and Cephalanthus occt-

dentalis L. reveals the fact that in other families, as well as in

the Rubiacez exclusive of the Stellate, each leaf of any whorl

receives its fibro-vascular bundles directly from the cauline cylin-

der. But in Galium the case is different. Two leaves only of

the whorl receive their bundles in the manner stated, and only

these two produce buds in their axils. All the others receive their

vascular supply from what may be termed a nodal girdle, each

half of which is formed by the union of two bundles arising,

one from each of the two leaf-traces in the same manner as those

supplying stipules of the ordinary form. From this girdle arise

the bundles which supply the additional leaves, whether there be

only one on each side, as in Galium circezans Michx. and G.

lanceolatum Torr., two, asin G. triflorum Michx. and G. tinc-

torium L., or even three or four, as occurs in G. Aparine L. The

distribution of the vascular bundles may be seen in a cross sec-

tion of the node of Galium tinctorium L. (fig. 77).

* See page 6.

The Nature and Origin of Stipules. AT

This anatomical arrangement shows that the so-called addition-

al leaves of the whorls in Galium are in reality stipules and that

the Stellate agree with the rest of the Rubiacez in having oppo-

site leaves. The tendency of the family however to produce ver-

ticillate leaves has been strongly felt in this group but has taken

an unusual course, the increased assimilative area having been

evolved through the stipules instead of by an increase in the

number of true leaves. The explanation is thus made compara-

tively simple except in those cases where the number of stipules

at a node is more than four.

As a general rule, in plants with stipulate leaves, each leaf is

provided with two stipules. But when the leaves are opposite,

the two on the same side of the node often coalesce, forming a

single interpetiolar stipule, as in the case of Cephalanthus

(fig. 78). That this coalescence is secondary is shown by the

fact that the distal portions only of the veins of the two stipules

have united. Now in the Stellatz also, this must have been the

original condition, but the interpetiolar stipules have been greatly

developed to serve assimilative purposes, the veins having mean-

while united completely to form a midrib. The increase in size

has advanced until in Galium the stipules are of the same size

and form as the leaves and morphologically indistinguishable from

them, except in G. bifoliwm where the stipules are smaller. In

this condition they remain in the broader-leaved species, as G.

ptilosum Ait., G. latifolium Michx. and G. lanceolatum Torr.

But in the narrower-leaved species, a still greater foliar expan-

sion being desirable, separation has been re-accomplished, proceed-

ing probably from the tip downward, as is illustrated in Rubia

peregrina L. with whorls of four. In this species stipules are

occasionally found with two midribs (fig. 79), most widely sepa-

rated at the apex or even coalescing toward the base. In Galium

Aparine L. and other species in which the number of stipules is

abnormal, we may suppose this condition to have arisen from a

repetition of the process of division which has produced the six-

leaved whorls. This is not improbable, since even in the four-

leaved forms the stipules have already entirely lost their original

morphological character and have taken on a more generalized

nature, making them fit material for development along new lines

of evolution. Embryological evidence is not wholly wanting, al-

though the family stands so near the head of the plant series. In

48 The Nature and Origin of Stipules.

Galium Aparine L., in common with the six-leaved species, the

earlier whorls are of four leaves only, representing the ancestral

condition. In Rubia tinctorium L., the opposite leaves of the

subterranean portion of the stem are exstipulate. At the first

aérial node there is a whorl of four, interpetiolar stipules being

present, and in the higher whorls there are six leaves.* This is

a series of long range, though lacking in intermediate steps.

Another case in which there is present a nodal girdle from

which the stipular bundles arise is that of Humulus Lupulus (fig.

80), but there are three bundles in each leaf-trace. They are

placed at about equal distances around the circumference of the

stem, and the girdle-bundles proper occupy only about one-third

of the periphery on each side. From them a part of the stipular

bundles arise, the remainder originating directly from the lateral

bundles of the leaf-traces.

It would be to small purpose that examples should be further

multiplied. From those already cited we may confidently deduce

the following conclusions :

1. The sheathing petiole has its origin independently of the true

petiole and is formed by a concomitant development of the lateral

and central-basal portions of the primitive leaf.

2. The ligule is a special development of the apical parts of the ©

lateral portions of the primitive leaf along the ridge between the

sheathing petiole and the distal parts of the leaf. It may be sup-

plied with veins either by the marginal bundles of the sheath or

by tangential branches from those entering the blade. The

sheathing petiole may disappear by degeneration, rendering the

ligule axillary as in many species of Potamogeton.

3. The ochrea is related to the ligule and is generally associated

with the sheathing petiole. It consists of the apical tissues de-

veloped in those cases where the sheathing petiole completely sur-

rounds the stem or did so in the ancestral condition. The part

of the ochrea posterior to the lamina or petiole may be called its

ligular portion and is usually supplied by bundles arising tan-

gentially from the main ones.

4. The lateral portions of the primitive leaf, when separated in

greater or less degree, constitute stipules in the usual acceptation

of the term. They are variously modified by subsequent evolu-

*Sir John Lubbock. Jour. Lin. Soc. Lond. 30:504. 1894.

The Nature and Origin of Stipules. 49

tionary changes, by increased development, by basal or total

degeneration, by secondary adnations and various textural modi-

fications. They receive their vascular bundles typically as

branches of the lateral ones of the leaf-trace.

5. The lateral portions of the primitive leaf therefore represent

in potential the ligule, the ochrea, the margins of sheathing peti-

oles and stipules, but they are often incorporated with the other

portions as the wings of petioles and as lateral basal portions

of leaf-blades.

ANNALS N. Y. ACAD. ScI., X, June, 1897.—4.

IIl.—The Ascidian Half-Embryo.

BY HENRY E. CRAMPTON, JR.

Read March 8, 1897.

The development of isolated blastomeres of the ascidian egg

has afforded a subject of considerable discussion on the part of

many theoretical embryologists. Chabry* approached the subject

from the experimental side, and, from the results of his many de-

tailed observations and experiments, was led to the conclusion

that one of the isolated blastomeres of the two-celled stage pro-

duced a strict half-embryo. As it was well known that the first

cleavage-plane divided the egg into right and left halves, this con-

clusion seemed altogether probable and of considerable interest.

A number of writers, however, among them Hertwig,} Driesch,}

Weismann,§ Barfurth|| and Roux,§ were led, on the grounds of

Chabry’s results, to opinions more or less at variance with his.

Barfurth considered Chabry to be in greater part correct. Roux

and Weismann believed that during the later development the

missing part was supplied by the other cells through “‘ postgene-

ration.” Hertwig states that, in his opinion, Chabry was in er-

ror; and Driesch also argued that a typical total development oc-

curred. Finally, Driesch** in 1893 repeated Chabry’s experiments,

upon the eggs of Phallusia mammillata, and by the results

wholly confirmed the theoretical conclusions of his previous paper.

*Chabry L. Contribution 4 ’embryologie normale et teratologique des

ascidies simples. Journ. de l’anat. et de la phys. X XIII. 1887.

+ Hertwig, R. Urmund und Spina bifida. Arch. f. mikr. Anat. XXXIX.

1892.

t Driesch, H. Der Werth der beiden ersten Furchungszellen in der Echino-

dermentwickelung. Zeit. f. wiss. Zool. LILI.

@ Weismann, A. Das Keimplasma. 1882.

|| Barfurth, D. Halbbildung oder Ganzbildung von halber Grésse. Anat.

Anz. VIII. 1893.

{ Roux, W. Uber des entwickelungsmechanische Vermégen jeder der bei-

den ersten Furchungszellen des Hies. Verhandl. d. Anat. Ges. Wien. 1892.

** Driesch, H. Von der Entwickelung einzelner Ascidienblastomeren.

Archiv fiir Entwick. der Organismen. I. 3. 1895.

The Ascidian Half-Embryo. 51

Although at that time reluctant to admit anywhere the occur-

rence of “ partial ” development, Driesch has since proved, in con-

nection with Morgan, the existence of a partial early development

in the ctenophore egg.* And ina recent paper by the writer +

it has been shown that the isolated blastomere of the snail pos-

sesses the power of forming only a corresponding portion of an

embryo. In a later paper, Driesch,{ developing an idea suggested

by Prof. E. B. Wilson and myself (loc. cit.), recognized the ex-

istence of a series among animal eggs, from the nearly isotropic

eggs of the medusa, Amphioxus, fish, sea-urchin, etc., at one ex-

treme, to forms such as the frog are ctenophore, aa finally to

the snail, at the other extreme, where the blastomere possesses

such an organization that but a part of an embryo can be formed

and postgeneration cannot occur.

The ascidian egg, however, remained unexplained by the contra-

dictory results of Chabry and Driesch. From this consideration

the author was led to an examination of the facts in another

ascidian. The results will, it is hoped, clear up the confusion to

some extent, and will show how far the development is a ‘‘ partial ”’

one and in what respects it is “ total.”

The experiments were performed during the past summer at the

Marine Biological Laboratory, Wood’s Holl, upon the eggs of

Molgula manhattensis, which grows very abundantly upon the

piles and wharves at New Bedford, Mass. Artificial cross-fertil-

ization was resorted to, and the eggs at the desired stage were

spurted in a watch-glass by means of a fine spiral pipette.§ Those

egos presenting isolations were placed separately in watch-glasses,

and camera drawings of successive stages were made at inter sl

using a Zeiss oc. 4, and obj. C.

As to nomenclature, the system proposed by Kofoid || and ap-

* Driesch, H., and Morgan T. H. Von der Entwickelung einzelner Cteno-

phorenblastomeren. Archiv fiir Entwick. der Organismen. II. 2. 1895.

{7 Crampton, H. E., Jr. Experimental Studies on Gasteropod Development,

with an appendix on Cleavage and Mosaic Work, by E. B. Wilson. Archiv

fur Entwick. der Organismen. III. 1. 1896.

{ Driesch, H. Betrachtung tiber die Organisation des Eies und ihre Genese.

Archiv ftir Entwick. der Organismen. IV. 1. 1896.

¢ As previously described in connection with the gasteropod experiments.

|| Kofoid, C. Onsome laws of Cleavage in Simax. Proc. Amer. Acad.

Arts and Sgeaws. Vol. XXIX. 1894.

bas)

52 The Ascidian Half-Embryo.

plied by Castle * to the Ciona egg has been used for obvious

reasons. According to this system, now well known, each cell is

designated by a letter referring to the particular quadrant of the

four-cell stage from which it arose; in addition it receives an ex-

ponent denoting the generation to which it belongs, and a second

exponent denoting its place in that generation, counting from

below upward.

DETAILED DESCRIPTION OF CLEAVAGE.

A. Normal Cleavage.—The cleavage of the Molgula egg is pre-

cisely the same as that of Czona and other ascidians, as far as it

has been followed. Therefore, it is unnecessary to discuss the

normal phenomena further than to emphasize a few of the facts

which are important in connection with the cleavage of the frag-

ments.

The first and second cleavage-planes are meridional, while the

third is equatorial. An eight-cell stage results (fig. 1) which,

seen from the side, consists of two tiers of four cells each. The

upper tier is shifted anteriorly upon the lower, so that the poste.

rior upper cells are in contact with the anterior ventral cells-

This relation is constant, and characteristic of probably all as-

cidian eggs (Castle. loc. cit., p. 228). Passing to the 16-cell

stage, all the eight blastomeres divide. The spindle axes are in-

clined in such a manner that the anferior products of the anterior

cells (fig. 2: B®, b 5-#) lie slightly below the median products ;

while the posterior products of the posterior cells le slightly

above the other cells (fig. 2: C °1,¢%?). When activity is again

resumed, the dorsal cells remain quiescent, while the ventral cells

segment, and a 24-cell stage results (fig. 35). After a period of

rest the dorsal cells pass into the same generation (sixth) with

the ventral cells, and a morula of 32-cells results. Then the ven-

tral cells divide at about the same time, while the dorsal cells re-

main quiescent, giving a 48-cell stage.

Further details are unnecessary for our purpose. We empha-

size the fact that, beginning with the 16-cell stage, there is a well-

marked alternation of activity between the cells of the upper and

those of the lower hemisphere of the embryo.

* Castle, W. E. The Early Embryology of Ciona intestinalis. Bulletin of

Mus. of Comp. Zool. Harvard. Jan. 1896.

The Ascidian Half-Embryo. 53

B. Cleavage of the 4 blastomere.—As is well known, the isola-

tion of an ascidian blastomere is effected by the death of its

neighboring cell or cells, and not by an actual separation. The

dead cell partially disintegrates and exerts upon the living cell no

modifying influence, such as mechanical obstruction to rounding

during division, etc.

4, At the normal time, viz: at the time of division of control

eggs, the injured blastomere divides about equally (figs. 4 and 13).

Often when the eggs are operated upon when passing into the 4-

cell stage, evidence of division in the dead cell will remain. In

such cases the division plane of the living cell is seen to be meri-

dional and at right angles to the first. Therefore, it corresponds

with the second cleavage-plane of the normal embryo. In all

cases where it is possible to ascertain the facts this relation ob-

tains. Driesch finds in Phallusia that no such constancy of rela-

tion exists.

4. After anormal period of rest the two cells divide at the

same time. There are thus produced four cells which are ar-

ranged in a manner exactly similar to the half of a normal 8-

celled embryo. Seen from the side (figs. 5, 9) the cells lie so that

two are separated, while two are in contact; these latter are the

posterior dorsal and the anterior ventral cells, as shown by the

succession of the cleavage planes of the fragment. Precisely as

in the normal 8-celled embryo, there is an anterior shifting of

the dorsal cells upon the lower cells. According as this shifting

is to the right or left, in lateral view, one is confronted by a right

or left half-embryo. From a comparison of the figures, it is seen

that the embryo in fig. 5 is the same as the half turned toward the

observer of fig. 1; while that shown in fig. 9 is derived from a

right 4 blastomere. The appearance of the ¢ embryo in end view

is shown in fig. 14, and a characteristic crossing of the spindle

axes is exhibited, which is similar to their crossing in the com-

plete egg (vide Castle for figures). The four-celled fragment,

then, is in nowise a counterpart of the normal four-celled embryo,

but, on the contrary, corresponds in every particular to the half of

an eight-celled embryo.

From Chabry’s fig. 106, it appears that a typical ¢ stage occurs

also in Ascidiella.

38. At the next cleavage, all the cells divide (figs. 6, 10).

Exactly as in the origin of corresponding normal cells, (fig. 2)

yeaa

Bree ik:

“

54 The Ascidian Half-Embryo.

the anterior products of the anterior cells (fig. 6: B®, b> ; figs. 10

and 16: A®-1,a%-?) lie slightly below the other cells; and, the

posterior products of the posterior cells (fig. 6: C52, ¢54; figs

10 and 16: D®-?,d°%-*) lie slightly above the median products.

On a comparison of fig. 6 and fig. 2, it will be seen, however, that

the topographical relations of the cells of the fragment are quite

different from the normal. For example in fig. 6, the cell c®-* is

in contact with B®-+ and b?-?, while in the normal egg it lies at the

other end of the embryo. A similar rearrangement is still better

shown in fig. 10, that of a right =8; embryo, where D°®-? is in con-

tact with A®>-!, while d®-4 is in contact with A®! and a°-3. This

rearrangement is obviously rendered possible by the absence of

the other half of the embryo, so that the cells cohere in a spherical

form just as a corresponding number of soap-bubbles. It cannot

be considered as a “‘ gliding,” for the spindle-axes are from the

first accommodated to the changed conditions. That is (figs. 15, 16),

the anterior end of the anterior spindles, and the posterior ends

of the posterior mitotic figures are swung somewhat toward the

original first cleavage-plane of the embryo.

Chabry’s fig. 113 leaves no doubt that the 8, embryo of Asev-

diella is precisely the same as that described above for Molgula.

From Driesch’s fig. 5, there is no doubt that in Phallusia the

eight cells are arranged as the normal 8 cells.

8-12, When activity is again resumed, only the four lower

cells are affected, while the dorsal cells remain quiescent. A 12-

celled fragment results (figs. 7 and 11), which is exactly equivalent

to a half of thenormal 24-cell stage (fig. 3). The quiescence of the

dorsal cells during the division of the ventral cells is the first in-

dication of the alternation of activity in the rhythm of cleavage,

which was found to be characteristic of this type of segmentation.

As in the preceding stage, when the resting condition is assumed,

there is a passive rearrangement of the cells. For example, the

cells A®® and A®+ were segmented along an axis inclined at an

angle of 45° to the axis joining their centres at the resting stage.

Again the cells D®? and D®-* have retreated around the posterior

end of the fragment.

46, While the eight cells of the lower hemisphere are resting,

the four dorsal cells likewise pass into the sixth generation, and a

16 stage results (figs. 8,12). Its resemblance to the half of a

normal 32-cell stage is still less marked than that of a $2 embryo

The Ascidian Half-Embryo. 55

to a half of the normal 24-celled stage. This is so, for the reason

that further passive rearrangements of the cells occur, obscuring

the partial character of their origin, and causing the cell complex

in its solid, or “complete,” condition to resemble a normal or

“complete” embryo. Nevertheless, the succession of rhythmic

cleavages, relation of successive cleavage-planes, etc., point to the

operation of factors which are counterparts of those operating in

a half of the normal embryo.

Later development. The embryo is now “ complete,” and gives

rise to a complete blastula and larva. Although the process of

gastrulation has not been carefully observed, enough of the later

development has been ascertained to prove that a larva arises

which resembles the normal larva, except as regards its smaller

size and certain minor defects. My results, therefore, are en-

tirely confirmatory of those of Driesch upon Phallusia.

C.— Cleavage of the + blastomeres.—One of the isolated blasto-

meres of the four-cell stage, is divided at the next cleavage by a

plane which is seen to be at right angles to both of the preceding

planes. Therefore it corresponds to the third cleavage plane of

the normal embryo. The 2 stage is shown in fig. 17. A subse-

quent cleavage cuts each of the cells equally, and a 5% stage re-

sults (figs. 18, 19), until this time, one is left in doubt as to the

true nature of the fragment, that is, whether it will segment as

a quarter or as an entire egg. However, from this time on, the

character of cleavage is exactly that of a quadrant of a normal

embryo.

When division next occurs, only the two cells toward the ob-

server segment (fig. 20), and a stage of six cells results, which is

evidently comparable to a .; embryo only, and not to any stage

of the normal development. After a normal period, the dorsal cells

(lower in the figure) pass into the sixth generation, and an 48,

embryo (fig. 21) is the result. As in the previously described

fragments, passive rearrangements occur when the resting condi-

tion is assumed, and the cells flatten down upon one another

(fig. 22). The cells of the ventral half segment at the next period

of activity (fig. 23), while the dorsal cells remain undivided. The

resulting 12 stage, although solid, is nevertheless derived from

the + blastomere through a segmentation of a partial character.

This partial character is expressed chiefly in the characteristic

rhythm of cleavage.

56 The Ascidian Half-Embryo.

Concerning the later stages, the results of Driesch are again con-

firmed. The young larve represented in Figs. 25,26 of this paper

illustrate one point further, although of minor consequence. It

will be seen that the long axis of the + larva in fig. 25, and the.

long axes of the + larve derived from the same egg, in fig. 26;

are approximately parallel to the principal dorso-ventral-axis of

the original egg.

SUMMARY AND CONCLUSION.

An isolated blastomere of the Molgula egg segments as if still

forming a corresponding part of an entire embryo. The cleavage

phenomena are strictly partial,as regards the origin of cells,

the inclination of cleavage-planes, and especially in respect to

the rhythm of segmentation. The general appearance of the frag-

ment differs materially from that of a half of a complete embryo, for

the reason that rearrangements of the blastomeres occur, which

tend progressively to mask the partial nature of development.

The end result is a larva of less than normal size, and with defects

in certain of its systems. These defects are undoubtedly due to

the fact that but a portion of the normal amount of material is

available for the formation of the larva; that, for instance, the

chorda of a larva derived from a one-half blastomere, receives but

one-half of the normal number of cells, and consequently a chorda

of one row, and not two rows of cells, results.

In conclusion, one is constrained to adopt the view of Roux-

namely, that in Molgula as in the well-known case of the echino,

derms (Driesch, Wilson, and others) the development begins as

a partial one, but that the missing part is gradually supplied by

the cells already present. Driesch is also entirely correct, as far

as the end result, a nearly complete larva, is concerned.

EXPLANATION OF PrhatEe IV.

Magnification of figs. 1-3 about 280 diameters; of all other figures, 250

diameters. . The arrows show the direction of cleavage.

Fig. 1, 8-cell stage of Ciona from Castle (fig. 23), from the left side.

Fig. 2, 16-cell stage of Ciona from Castle (fig. 24), from the left side.

Fig. 3, 24-cell stage of Ciona from Castle (fig. 43), from the right side,

Figs. 4-8, cleavage of the left 1 blastomere of Molgula, from the side.

Fig. 4, 2 embryo.

Fig. 5, ¢ embryo.

The Ascidian Half-E'mbryo. 57

Fig. 7, meaee on 2 embryo.

Fig. 8, +3 embryo.

Figs. 9-12, cleavage of the right 14 blastomere, from the side.

Fig. 9, ¢ embryo.

Fig. 10, Bs embryo.

Fig. 11, 4 2 embryo.

Fig. 12, $$ embryo.

Figs. 13-16, cleavage of the Bent 46 blastomere, from the front.

Fig. 13, 2 embryo.

Fig. 14, ¢ embryo.

Fig. 15, passage to ;°; embryo.

Fig. 16, complete ;'; i ebeys

EXPLANATION OF PLATE V.

Figs. 17-24, cleavage of the 14 blastomere, ventral view.

Fig. 17, 2 embryo.

Fig. 18, passage to +.

Fig. 19, complete ;.

Fig. 20, embryo.

Fig. 21, 8; embryo, immediately after division.

Fig. 22, 2; embryo, in resting condition.

Fig. 23, passage to 12 stage.

Fig. 24, complete +2 embryo.

Fig. 25, 4 larva. The arrow indicates the long axis.

Fig. 26, two 4 larve, from same egg. The arrows indicate the principal

axes.

Ill.— The Rutherfurd Photographic Measures of Sixty-five Slars

near 61 Cygnt.

BY HERMAN S&8. DAVIS.

Read May, 1897.

1. It was but natural that Mr. RutHERFuRD, in developing the

art of astronomical photography, should try his skill upon that

star which has attracted the attention of so many investigators

ever since BxrssEL proved by it the possibility of determining

stellar parallax.

Of these photographs of 61 Cygni and its surrounding stars

taken by Mr. RuTHERFURD, nineteen, exposed between 1871, Nov.

9,and 1874, June 13, were measured by Miss Ida Martin more

than twenty years ago, but have remained unreduced until re-

cently placed in my hands for that purpose by Professor J. K.

Rees, Director of the Observatory. The present paper contains

the results of measures of position of stars surrounding 61 Cygni,

and will be followed by a second paper containing the results of

an investigation of the Parallax of 61: Cygni. The methods of

reduction used so far as measures of distance are concerned are

those presented by Dr. Harotp JaAcosy in earlier Contributions

from this Observatory.

2. In Table I are given the general data of exposure of the

plates, including the computed values of the zenith-distance, par-

allactic angle and refraction factor.

3. Table II contains the means of the seiactons computed for

the Hastern and Western impressions from the data of Table I by

the formule

o 8 — x [tan?€ eos? (p—q) +1]

7 —p=—+4« cosec 1’/ tan? ¢ sin 2 (p—q).

The argument for entering this table is p.

4. Table I1I.—The corrections to the position-angle due to pre-

cession, nutation and aberration will be found in column two.

These were computed by the formule

Sixty-five Stars near 61 Cygni.

a! = 20.//06 sin a sec 0

Vs cos a sec 0

Ap= (T—t) a! — Aa! — BB! — Cy! — Dd’.

- The epoch 7 = 1873.0 has been selected to which to reduce all

the observations. The substitution of the codrdinates of 61! Cygni

for this epoch gives:

Ap = —36!+- [1.254] 4 + [9-956n] B+ [9-746] C+

Apy,=—18 + [1.254] A+ [9.956n] B

Aps—= 0 +[1.254] A+ [9.956] B+ [9.7460] C-

Apy=+18 + [1.254] 4+ [9.9562] B-

Where 4p,, denotes the correction to be applied to the posi-

tion-angle for the plates made in 1871, and so on in the other years

as denoted by the subscripts.

5. Precession and nutation have no effect upon the distances;

y' = cosa tan 0

0/ sin a tan 0

+ [9.742] D.

+ [9.746n] C+ [9.742] D.

+ [9-742] D.

+ [9-746] C+ [9.742] D.

but aberration does have, and its amount is given by:

y'/= (tan esind + sinacos 0) sin 1//

0'/—=— eos a Gos 6 sin 1//

As =(Cy!/+ Do!’ s

For 61! Cygni this becomes

As=§[4.14In]C+ [4.433n] D?s

and is additive to the distances to reduce them to 1873.0. This

factor of s is given in column three of Table III.

6. The logarithms of the Besselian day-numbers, taken from

the American Ephemeris, are:

Plates. log A.

ite 9.692

2, 3, 9.699

A, 9-774

5, 6, 9.816

Te 9.821

8, 9, 9-788

10, 9.800

Wei, 1), Tas 9.805

5, 9.336

iG, 17, 9-411

18, 19, 20. 9.417

4, In the second portion of Table IIT. is given the mean of the

log B.

0.035n

0.022

0.583n

0.580n

0.582n

0.807n

0.802n

0.80In

0.857n

0.854n

log C.

1.104

TOV,

0.840

0.244

0.038

I.043

0.985

0.958

0.776n

0.418n

0.364n

for all years,

log D.

1.178

T.198

1.279

T.309

{.310

J.218

1.244

DES

Te2S 7

T.306n

esa

60 Rutherfurd Photographic. Measures of

Hast and West zero-corrections computed for each by the

formula *

v=tketand—y+-a

in which v is the zero-correction to be added to all observed posi-

tion angles of each plate.

In the next column are the special corrections + required by the

position-angles of the Western impressions in consequence of

using the same zero-point in measuring both Eastern and West-

ern impressions.{ The sum of these two columns is then given in

column six, which, therefore, contains the final correction as

actually applied in the reductions.

8. In Table IV. is given the tangent correction. This is always

negative and its unit is .ooor divisions of the micrometer. It

has been computed by the formula:

Correction = — 48° d? sin? 1/' =[1.7887n ] s?

where s denotes the distance in divisions of the glass scale and d

is the value of one division of the scale in seconds of are.

Taste V.—Measures of Distance.

9. The first column contains the numbers of the stars in order

of right ascension and also in parentheses, for convenience of ref-

erence to the original measures and plates, are the numbers as as-

signed by RurHERFURD. The number of the plate is given in col-

umn two,after which follows the observed distances for the Hastern

and Western impressions. The numbers set down are the frac-

tional part of the measured distance expressed in divisions of the

glass scale, the whole number of divisions being ordinarily the

same as that given in the final corrected distance. Where there is

a change of .8 or .g in the observed distance, it is an indication of

a change of a unit in the whole number of divisions in passing

from the observed distance to the corrected mean. In columns

five, six and seven are placed the corrections as applied for refrac-

tion,§ aberration|| and scale respectively ; these, with addition of

* Annals N. Y. Acad. of Sci., Vol. VI., p. 272.

Tt Ibid., p. 278.

tIbid., p. 240.

@ Table II and Paragraph 2.

|| Table III and Paragraph 4.

{| Pleiades, pp. 242-251.

Sixty-five Stars near 61 Cygni. 61

the tangent correction only—which may be obtained directly from

Table IV, being practically constant for each star—present all

the corrections which have been applied to the observed mean dis-

tance of the Hast and West impressions to get the corrected mean

of column eight.

10. It is noticeable that among these corrected means the dis-

tances belonging to some of the plates are always larger than the

average and to other plates always smaller. To get rid of this

variation of scale value, whatever may be its cause, I have

selected the following four stars as standards:

No. Distance. sin p. Cos p.

5 77.2926 —0.998 +0.054

23 89.2118 —0.068 0.998

32 77.0019 +0.127 —0.992

48 50.7333 -+0.962 —0.274

Sums 294.2396 -+ 0.02 Ok

Now, if s,, So, S32, Sag represent the distances of stars 5, 23, 32

and 48 from 671 Cygni on any given plate and >s, the sum of the

standard distances, there must be added to every distance on that

plate for any other star its proportional part of the difference be-

tween the mean of the sums of the distances of the standard stars

and their separate sums for that particular plate, or:

28; — (85 ++ 853 + Ss + Sag) ¢

Liss

Seale variation =

The following table gives the value of this coefficient of s for

each plate. The individual values of scale variation are given in

column nine of Table V.

CO aaa

Se ia!

62 Rutherfurd Photographic Measures of

Piate, | Sg Variation

I + .1948

2 -+ .2275

3 -+ .1666

4 — .0027

5 + .0439

6 + .0894

7 + .0928

8 — .1272

Qo Glic ap One

TOR — .0408

II — .0714

12 — .0598

13 — .0129

15 — .1047

16 — .0670

1 — .o714

18 — .0537

19 — .0326

20 — .1241

11. The measures of distance are next to be corrected for the

proper motion of the central star. For this purpose let :

¢ = date of the plate.

7—t—1373.0

p =annual motion on great circle

X = position-angle of that great circle

S, = eos (¥ —p)

ey eri

S, =— 5, sin? (y—p)

J == 7p

The correction for proper motion, additive to observed distances,

will then be:

As = 8, P; + 8, Pp -

I have adopted AuweErs’s values of

= + 0.3444, fe =-+ 3.230,

as given in the /undamental Catalog. Corresponding to these

are: .

“ a lo} / “

p = 5.1904 = 0.18528, if == Fn BO) SE

The values of p used in the above formule were the means after

correction for “zero” and refraction, as explained in paragraph

7; and the values of s were after correction for scale variation.

Sixty-five Stars near 61 Cygni. 63

12. The values of S, and S, will be found in columns two and

three of Table VII. The following table gives t, P,, and P,:

For Proper Motion.

Plate. T

BP, =

it — 1.142 — 0.2116 + 0.045

2 — 1.134 — 0.2101 + 0.044

3 — 1.134 — 0.2101 -- 0.044

4 — 0.085 — 0.0157 -+ 9.000

5 — 0.041 — 0.0076 -++ 0.000

6 — 0.041 — 0.0076 + 0.000

Gy] — 0.036 — 0.0067 -+ 0.000

8 + 0.876 + 0,1623 + 0.026

9 ++ 0.876 + 0.1623 ++ 0.026

ago) -++ 0.890 + 0.1649 + 0.027

II + 0.895 + 0.1658 + 0.027

12 + 0.895 + 0.1658 + 0.027

13 + 0.895 + 0.1658 ++ 0.027

15 + 1.418 -+ 0.2627 -+ 0.069

16 + 1.448 + 0.2683 + 0.072

iF + 1.448 + 0.2683 + 0.072

18 + 1.451 + 0.2688 + 0.072

19 +- 1.451 + 0.2688 + 0.072

20 + 1.451 ++ 0.2688 + 0.072

13. As the quantity which depends on the square of the time is

always small for a star having even so large a proper motion as

61 Cygni, its values may be tabulated for limiting values of S,..

Such a table as used in the present paper is:

Plates A

SEIS 7 i % 9 12 > Tes

7 13 20

(0) fo) fo) Xo) fo) fo) fo)

Be Spin 1G | “BETS | WAS MO).|| TIC Ko) |} eS Hee 6.9

his 5 33-5 | 34.0 Si-O) oA On 217) 20.7

ae 3 55-8 | 56.7 95:0] 91.2 | 36.2 34.7

ae 4 Then || Foe) BIE || AIS) ||| OLY 48.5

See 100.5 | 102.0 164.2 65.2 62.4

we ? 122.8 | 124.6 200.8 | 79.7 76.2

has 7 145-1 | 147-3 94.2 90.1

=n 8 108. 104.0

— .0009 123.2 117.8

137-7 | 131.7

64 Rutherfurd Photographic Measures of

The figures at the tops of the columns are the numbers of the

plates to which the columns are applicable as determined by their

values of P,. Selecting, therefore, the proper column and using

S, as the argument in the body of the table (where it is expressed

in units of the fourth decimal place), one will find in the first col-

umn the desired value of S, P,, expressed in divisions of the scale.

Column ten of Table V gives the total proper motion correction.

' 14, A correction for parallax of the principal star was rext ap-

plied. Using Auwers’s values of the codrdinates of 611 Cygni

reduced to 1873.0

h m 8

a—21 O1 12.329

d6=38 07 33.40

and the almanac values of r and ©, the radius vector and longi-

tude of thé sun respectively, the values of S,,S8,, P; and P,

were computed by the formule

g sin G =sin 0 cos a hsin H=sin 6 sin a

g cos G=sin a h cos H==—cos 0

fsin F=h sin (H+ e)

f cos F=— COs @ cose

S;=fsin(p+F) -

S,=g sin (p+ G@)

/A4==7 Sa (©)

P,=—r cos ©

The value of p used here was the mean of the position-angles

after correction for proper motion and orientation variation, as

described in paragraphs 17and 19. The values of P, and P, are:

Sixty-five Stars near 61 Cygni. 65

- For Parallax.

Plates. ;

Ps P,

I + 0.727 + 0.672

2 + 0.761 + 0.632

3 + 0.761 + 0.632

4 + 0.915 + 0.366

5 + 0.979 -+ 0.096

6 + 0.979 -- 0.095

7 + 0.982 + 0.061

8 + 0.798 + 0,583

9 + 0.798 + 0.583

ae) + 0.845 + 0.511

Il + 0.862 + 0.481

12 + 0.862 + 0.480

13 + 0.862 -+ 0,480

15 — 0.962 — 0.322

16 — 1.006 — 0.142

17 — 1.006 — 0.142

18 — 1.008 — 0.125

19 — 1.008 == OL125

20 — 1.008 — 0.125

In Table VIII, columns two and three, will be found S, and S,.

The coefficient of the parallax, as printed in column eleven of

Table V is

S3P; + SP,

and the correction, additive to the distances, is

(8; P3 + S,P,) BROAN

where JJ is the parallax expressed in seconds of arc. Table XI

gives values of this quantity corresponding to limiting values of

the coefficient. The method of using this table is the same as

described in paragraph 13. In its construction I used*

Il = + 0.73597

15. The distances thus corrected for all known disturbances af-

fecting the central star, 611 Cygnt, are given in column twelve of

Table V. In this column are also the means of the distances.

Taste VI.—Measures of Position-angle.

16. This table has been put on pages opposite the correspond.

. *The Parallax of 611 Cygni as deduced ec pe pene

Measures, by Herman S. Davis. Contribution No.

ANNALS N. Y. ACAD. Scl., X, August, ane

> NS a

66 Rutherfurd Photographic Measures of

ing measures of distance in Table V. The first column is a repeti-

tion of the number of the plate. In columns two and three are

given the observed angles for the eastern and western impressions.

The number of degrees for the west column are the same as

printed in the east column, except where there is an obvious

change of + 1° indicated by a difference of nearly 60’ in the min-

utes of the two columns.

In column four are placed the zero-corrections of paragraph 7

plus the special corrections due to the precession, etc., mentioned

in the same paragraph. This quantity is taken from the last col-

umn of Table III. The correction for refraction from Table II

is in column five. The mean of the east and west impressions

thus corrected is placed in column six.

17. In column seven of Table VI is the correction due to

proper motion of the central star. This has been computed from

the following formulee : *

Let ¢, 7, S,, P,, P., e and vy have the same meaning as in para-

graph 17; also let

S,; =sin (v¥—p)

——

(oy

Sy —=/S)5 Se

P; =7Tp cosec 1//

K=— }P, sin x tand-+ 3 P, sin 1’’ sin y cos x (1+ 2 tan? 0)?

Then will the correction for proper motion, additive to observed

angles, be

Ap =S,P; (1+8,P,-S8,)+ kK.

Throughout these formule p and oc are to be expressed in divi-

sions of the scale, whereas K and 4p are in seconds of are. The

convenience of expressing 4p in this form is more noticeable

when it is remembered that S,P, has already been computed for

use in correcting the distances; see paragraph 11. Here o is to

represent the value of s after being corrected for scale variation

and proper motion.

18. As K is obviously a constant for all stars on the same

plate, being only that part of the variation in (7— p) due to the

* Handbuch der Vermessungskunde von Dr. W. Jordan, Bd. III. 8. 359.

Vierte Aufiage.

Sixty-five Stars near 61 Cygni. 67

effect of meridian-convergence upon the value of 7 at different dates

we have for 611 Cygni:

k=— 17.2094 P,

the term in P, being neglected, as its maximum value in the

present research is only -o.’’ooo15.

The following table gives & for the various plates, and also the

values of P;; while in columns four, five and six of Table VII

will be found S;, S, and S,.

For Proper Motion.

Plate. j

iq Jz.

I + 3-6 — 43644

2 + 3.6 — 43338

3 ae eo — 43338

4 + 0.3 — 3248.

5 + 0.1 — 1567.

6 + 0.1 — 1567.

7 + 0.1 — 1376.

8 — 2.8 + 33478.

9 = 2S + 33478

ae) — 2.8 + 34013

II — 2.8 ++ 34204

12 — 2.8 ++ 34204

13 = 28 + 34204

15 — 45 ai LO

16 40 + 55338

17 Ale ae Sees

18 — 4.6 + 55452.

19 — 4.6 + 55452.

20 —= Ae + 55452.

19. Orientation Variation.—When the angles have been cor-

rected as described above, observation of the corrected mean plus

proper motion in Table VI reveals a variation of measures on

some of the plates from the mean of all that is erratic, and in

some cases very considerable in magnitude. This is undoubtedly

due to the method which RutTHERFuRD used for the orientation of

his plates.

It was his custom in making the exposures to take two impres-

sions of the stars on each plate. After the second, or western

impression, the telescope clock was stopped, and the stars were

allowed to trail across the plate for a distance of sixty to eighty

68 Rutherfurd Photographic Measures of

scale-divisions. The clock was then again made to run long

enough to permit the formation of another image of the central

star. The line joining this last image with the central image was

used as the origin of the position-angles. Angles so measured

were made in the present paper to conform to the custom of count-

ing from the north point towards the east by addition of 270° to

the observed readings, as seen in Table VI.

Of course the position-angle of this last impression of the prin-

cipal star is not exactly 270°, however, unless there has been ab-

solutely no shifting of the telescope in declination during the

formation of the trail, or when clamping in the clock for the final

image. It is a priorz probable that such shifting did occur; but

with such alterations in the balance-weights of the tube, in the

pointing of the telescope, and in the other conditions of exposure

of many plates during the course of several years, we may fairly

assume, on the other hand, that such shifting in declination is not

systematically in the same direction; that, consequently, the

mean of the position-angles of a given star as determined from all

the plates is its most probable value. Hence,if all the stars were

found on all the plates, it would be unnecessary to apply a cor-

rection for error of orientation. But such is not the case. Fur-

thermore it is desirable to use the individual measures separately

for a determination of the parallax.

This correction may be deduced from standard stars by taking

from the mean of all the angles of all the plates the angle meas-

ured on each plate separately, and regarding the residual as the

orientation variation of that plate. For any particular star such

residuals would not, however, be the true correction ; for it would

contain the effect of both the proper motion and the parallax of

the central star. Several stars should, therefore, be selected as

standards; and they should be so distributed in distance and

angle as to eliminate both parallax and proper motion from the.

mean of their residuals for each plate severally. Since the prob-

able error of measures of angle vary inversely as the distance,

these means should be taken by weight proportional to the square

of the distance.

Expressed symbolically these conditions are:

‘ T0286, , S026,

To =O an So) = ¢

Sixty-five Stars near 61 Cygni. 69

The significance of S, and S, will be found in paragraph 22, and

of S, in paragraph 17.

20. It is easily seen that both A and B cannot be satisfied at

the same time, unless the direction of proper motion of the prin-

cipal star coincide with the major or the minor axis of the paral-

lactic ellipse. This fortunately is very nearly the case with 611

Cygni ; wherefore it would have been immaterial here whether the

angles of the standard stars had been corrected for proper motion

or not, though as a matter of fact they were so corrected; as would

ordinarily be necessary.

21. If stars can be found on all the plates which will satisfy

only very closely, but not exactly, condition A, the residuum of

the parallactic effect may be more nearly eliminated by adding to

the orientation variation deduced from such stars the quantity

| (P;/ — Ps) %0?S, ; ( P,f — P,) 2078, } Tl’

Zo? do2

where the primed P,’ and P,’ are the means of the values of P

and P, for all the plates, and where I/’ is an approximate value of

the parallax, or a value deduced from the measures of distance.

In this paper the following six stars were selected as the

standards:

Star 028, oS, S, o?

5 —4238098.2 +227748.4 + 0.008588 5962.

6 — 90170.0 + 550938.7 — .000240 QOI7.

13 —611921.1 —381846.5 -- .009566 9667.

23 —459811.3 —441482.6 + .009229 7969.

32 +418587.4 + 364040.6 — .o1111s 5920.

48 + 322758.0 — 85914.0 — .016022 2580.

These give:

Tos, Zor2S, er

Foz 20-5 = + 5.7 zs, = — -000003

which shows that they are admirably adapted to the present pur-

pose. From these stars, therefore, and with I’ —-0.’’4o have

been deduced the following corrections, additive to observed

position-angles.

70 Rutherfurd Photographic Measures of

Orientation

Plate. Variation.

a yt

O ON Auf NH

fe}

22. In column eight of Table VI are given the parallax coeffi-

cients. They have been computed by the formule: i

where: ae

5, — So 8, om (n+)

So = S, cos (77 + G@)

= an

and where f,g, Ff, G, P;,and P, have the same meaning as in

paragraph 14. The value of the position-angle used here, z, is the

angle p corrected for proper motion and orientation variation.

The quantities S,,S,,and S, are in columns four and five of

Table VIII and five of Table VII respectively. P, and P, are

tabulated in paragraph 14.

23. After adding to the observed angle the correction

(Ss Ps +S Py) TI

taken from Table XI with the parallax coefficient of column eight,

Table VI, as the argument we have the final corrected angle given

in the last column of Table VI.

Sixty-five Stars near 61 Cygni. . TL

24, Table I[X.—Column three contains the mean of the final

position-angles of Table VI, and column two the mean of the dis-

tances, converted to seconds of are by the scale value 28.’’0124.

These are followed in columns four and five by the differences of

right ascension and of declination derived by aid of the formule :

Logarithms for Plates of

611 Cygni only.

n=osint

Mm =— 0 COST ae

P= sec 0 = [0.104215]

Q = [4.685575 | tan 6 sec d = [4.6846 |

R = [8.89403,, | tan? 0 sec 0 = [8,7373, ||

S = [8.89403 ] secd (1 + 3 tan? 0d) = [9.4528 |

T = [4.384545,] tan 0 = [4.2793, ]

U = [8.59300, ] (1 + 3 tan?) = [9.0475, ]

V = [3.579601 | seco tan d (1 + 3 tan? 0)

W = [3.57960 ] seco tan (2 + 3 tan? 0)

a’ —a = Pn+ Qnm + Rn3 + Snm? + (Vn3im + Wnmi)

d/ —d = m + Tn? + Un?m

where o and =z are the final corrected mean distance and _ position-

angle respectively of the star whose a’ and 0’ are desired. It was

found also that the terms in V and W were not needed, since they

are so nearly equal and have contrary signs.

In column six is the number of plates on which the image of

the star was impressed; though it is proper to state that the

given position is the result of at least twenty measures of distance

and twelve of position-angle for each plate recorded in this column.

In columns seven and eight are the Durchmusterung number

and magnitude for as many of the stars as could be identified. A

few of those found in the Durchmusterung but not found on

these plates, though of much brighter magnitude than many

which are on the plates, no doubt are missing because of their

color; as obviously light from reddish stars affects the plate but

little, though optically it may appear quite bright.

25. Table X is on pages opposing Table IX and gives the

right ascensions and declinations of each star. These were ob-

tained by adding the a’ — a, 0’ — 0 of Table X to AUWERS’s posi-

tion of 611 Cygni reduced to 1873.0 with the constants given in

the Fundamental Catalog:

h m

C= Fy Ort 10,9

[o} 1 a 2 t 1873.0

O== Be) C7 Savio

by this formule: :

T—1873)2

or — “ere us J(T— agra) ae

(1— 1873)?

O7 = Oig73 + L( T— 1873) + eee

ve Stars near 61 Cygni.

ty-fi

ODNM OO

Oo AD OV

She OhRY Ann nnM nnnnnme

YO CO

os 09 st oD mostra an

\0 0

inn

Ono

¢I sung

¢1 oune

¢reune

zrounr

zI oun

I oune

[aA

(oy4

“AON

"AON,

“AON

EYE

“0a

“AON

“AON.

“AON

"AON,

INDO r~CO AO

ee Nl on le on |

HSN OD

Ss eS ht

co]

HA OD THOM CO

‘sndo0T ote ;

M 79'°9S SS b= ‘SuoT

8s Ww q

“TIO,

[vere pls

SSP ty op = "4e7

"YIOK MON ‘panjroyyny "PW '] JO A10ywaresqQ—ViVG IVuaNaH—'] AIAVY,

Rutherfurd Photographic Measures of

Taste I].—CorReEcTIONS FOR REFRACTION.

Position Angle,

PLATE 1.

+-440

-436

_ 422

.402

-377

-350

325

304

.291

.286

.291

304

2325

-350

377

-402

-422

436

+-440

PLATE 3.

PLATE 2.

+.427

-423

AIL

394

3372

-349

B27

.310

298 |

-204 |

.298

-310

“GAT

-349

-372

-394

411

423

427

PLATE 4,

+.494

.488

471

-444

411

-377

-344

318

-300

-294

.300

-318

-344

377

-4II

-444

471

.488

+.494

+-473

-468

-453

.429

.400

-369

-340

301

.296

.301

-317

-340

.369

-400

-429

-453

-468

+.473

Sixty-five Stars near 61 Cygnit. 15

TABLE I].—CorRECTIONS FOR REFRACTION. ( Continued.)

Position Angle, | >—$ Position Angle, | 7—S$ =

p. 8 =e ™—p Dp. 3 « 10 7™—/p

PLATE 5, PLATE 6.

70° 250° +.458 0.0 65° 245° +.678 - 0.0

.80 260 453 — 5.8 75 255 .666 —13.6

90. 270 ~ -439 —IIl.o 85 265 -633 —25.7

100 6. 280 .417 —14.8 95 275 .581 —34.6

IIO 290 .390 —16.8 105 285 -518 . — 39-3

I20 300 361 —16.8 II5 295 -451 —39.3

-333 125 305 -388 | —34.6

135 - 315 -336 —25.7

145 325 _ +303 —13.6

155 335 -291 | 0.0

165 345 -303 +13.6

175 355 -336 aoe

185 5 388 +34.6

195 T5 -451 139-3

205m 25 518 +39.3

215 35 581 +34.6

225 45 Shi res) 7

235 55 .666 |. -+13.6

245 65 +.678 0.0

PLATE 8.

69° 249° +.482 0.0

79 259 -476 — 69

89 269 -459 —I2.9

99 279 -433 —17.4

109 =. 289 402 | —19.8

II9 299 307 —19.8

129) 399 -336 —17.4

139 ©6319 .310 —12.9

149 329 -293 — 6.9

159 339 .287 0.0

169 349 2203 ae xg)

LIS) SiS) 310 “12.9

189 9 -336 Sct!

199 19 367 +19.8

209 29 .402 +19.8

219 39 -433 17.4

229 49 -459 12.9

ZEN) | ISVs inal + 6.9

249 69 -+.482 + 0.0

76 Rutherfurd Photographic Measures of

TABLE IJ.—CorreEctTions ror REFRACTION. (Continued.)

aes Angle, 5108 ee NED Angle, an x 108 7p

PLATE 9. PLATE 10.

66° 246° +.612 0.0 TiC 25a +.376 0.0

76 256 .602 —II.5 83. 263 374 — 2.9

86 266 574 —21.5 93 ~~ 273 307 — 5.5

96 276 .53I | —29.0 103 283 -356 — 7.3

106 =~. 286 -477 —33.0 Lr) 293 342 — 8.4

116 =. 296 -421 —33.0 123 303 .328 — 8.4

126 306 368 —29.0 Is > BIER -314 = 72

136 §=63,16 ©3325 —21.5 WA Bo -304 — 5.5

146 326 .297 —II.5 Ge), RaNe .296 — 2.9

156 336 .287 0.0 163-343 .294 0.0

166 346 297 +11.5 173 353 .296 + 2.9

176 356 «325 tp les) 183 3 -304 = 55

186 6 .368 -++29.0 193 13 314 + 7.3

196 16 421 +33.0 203 23 328 + 8.4

206 26 Avia +33.0 213 BR -342 + 8.4

26) 4) 36 -531 + 29.0 223, 43 -356 sine

226 46 574 +21.5 233).1° 1058 -367 42°55

236 56 .602 +11.5 243 63 -374 + 2.9

246 66 +.612 0.0 253 73 -+-.376 0.0

PLATE 11. PLATE 12.

a“ a

74° 254° ar 352 0.0 Fi2e en 2520 + .406 0.0

84 264 .350 — 2.1 82° » 262 .403 — 4.0

94 274 -345 Tm!) 92 «272 -393 RS

104 284 sO QT — 5.2 Io2 282 .378 —I10.0

TI4 294 3277) — 6.0 II2 292 -359 —II.4

124 304 317 — 6.0 I22 302 339 —II.4

134 314 308 — 5.2 132 312 .321 —I0.0

I44 324 .300 — 3.9 TAD 322 .306 — 7.5

154 334 .295 — 2.1 152 332 .296 — 4.0

164 344 293 0.0 162 342 .293 0.0

174 354 -205 + 2.1 172-352 » 2209 + 4.0

184 4 .300 + 3.9 182 2 .306 + 7.5

194 14 308 + 5.2 192 12 «VS32N +10.0

204 24 RUF + 6.0 202 22 -339 +11.4

214 34 S27 + 6.0 212 32 -359 +11.4

224 44 SBT + 5.2 222 42 .378 —+10.0

234 «54 -345 + 3-9 232 8 §2 -393 aed

244 64 -350 + 2.1 242 62 ~ 403 + 4.0

254 74 +.352 0.0 252 72 -++.406 0.0

Sixty-five Stars near 61 Cygni.

TaBLE II. CorRECTIONS FOR REFRACTION. ( Continued.)

Position Angle, | *™—$ cas Position Angle, | 7—S\,,

a & serene 108 ™—~p : ; x 103 ™— Dp

PLATE 13.

70° 250° +.481 0.0

80 260 475 — 6.7

90 270 -459 —I12.5

100 =. 280 -434 —16.9

TIO 290 -403 —19.2

I20 300 -370 —I19.2

130 310 -339 —16.9

I40 320 314 —12.5

WFOm ssn) |. 208 — 6.7

160 340 | 292 0.0

170 350 .298 + 6.7

180 fo) -314 +12.5

190 10 -339 +16.9

200 20 .370 +19.2

210 30 -403 +19.2

220 40 -434 +16.9

230 50 -459 +12.5

240 60 475 + 6.7

250 70 +.481 0.0

PLATE 15,

To8°

118

128

138

148

158

168

178

188

198

208

218

228

238

248

258

268

278

288

+.389

= By)

Sete etestteh

een ln |

OPNOHHONWO

OOR OWWOBRW O

PLATE 16.

II4

124

134

144

154

164

174

184

194

204

214

224

234

244

254

264

274

284

294

+.593

583

*559

«512

+459

+403

+350

-307

-279

.269

.279

0.0

—II.4

—21.5

—28.9

—32.9

—32-9

—28.9

—21.5

—II.4

0.0

mits Rutherfurd Photographic Measures of

TABLE IJ.—CorrecTions FOR REFRactions. (Concluded.)

Rao? a > 108 felis eon Angle, o—* x108 7p

PLATE 17. PLATE 18.

292° 112° +.492 0.0 ARO Tete -++.576 0.0

302 122 -485 — 7.8 ZR, -507 —I0.5

QUA. 10 -466 —I4.7 BA aR 541 _—19.7

222) a Ae -437 —I19.8 323 143 I SESOE —26.6

BOQ) N52 -400 —22.6 333 153 -453 —30,2

342 162 -362 —22.6 343 163 402 —30.2

252 aml 72 -326 —19.8 253 7s Ee —26.6

DD As) .296 —I4.7 Bylo .314 —19.7

I2 192 Lary — 7.8 13-193 .288 —I10.5 ~

22 202 .270 0.0 23 203 W279 0.0

22 e212 277 + 7.8 Be DIR .288 — +10.5

42 222 .296 +14.7 43 223 .314 -+19.7

5 2te 232 326 —-19.8 5B e236 353 -++ 26.6

62 242 -362 +22.6 63 243 .402 +30.2

T2252 -400 22.6 TR | Gases -453 -+ 30.2

82 262 -437 +19.8 83 263 .501 +26.6

92 272 -466 +14.7 93 273 541 +19.7

Io2 282 485 + 7.8 103 283 .507 +10.5

II2 292 +.492 0.0 113 203 +.576 0.0

PLATE 19. PLATE 20.

291° 111° +.482 0.0 289° 109° -+.409 0.0

30I 121 -476 — 7.1 299 ~=«dII9 -405 — 4.5

BIl) ast -459 a4 309-129 +394 ene

RON aes -432 —18.0 319 =-« 139 aval —II.5

gu ube -399 —20.5 329 ©1149 -356 —13.1

341 161 -363 —20.5 339 159 +333 arse

351 I7I 6331 —18.0 349 169 .312 —II.5

ih atehie 304 —I3.4 359 179 -295 — 8.6

TL tok .286 7a 9 ©189 284 — 4.5

ar 201 | .280 0.0 19 199 .280 0.0

Bit AL .286 == 7.1 29 209 284 + 4.5

AI 221 -304 +13.4 39 219 -295 + 8.6

5h) 231 331 +18.0 49 229 -312 -+I1I.5

61 24 -363 + 20.5 99 = 239 -333 “F13-1

71, 251 -399 -+20.5 69 249 EB50 13.1

8r 261 -432 +18.0 79 259 BOW +11.5

gl 271 “459 +13.4 89 269 -394 ais O20

TOUS Zor -476 ap fe 99 279 -405 ap th 5)

IIE AG)Ie -+.482 0.0 Iog ©6289 -++.409 0.0

Sixty-five Stars near 61 Cygni.

TaBLE III.—CoRREcTIONS FOR PRECESSION, ETC., TO 1873 AND

ZERO

CORRECTIONS.

Precession, etc. a Br

Plate | — Zero Correction eipreeie

Ne: Position Angle| _ Distance ga East esl) SIMonne eal tay eae a

Correction. Factor x 103

I —25. —.0584 +12 29 —27 412 2"

2 —24. —.0593 13 52 —24 13 28

3 —24. —=.0593 13 58 ——24 13 34

4 + 23. —.o6II uA it —22 I2 39

5 + 8 —.0576 II 57 —I19 Ir 38

6 + 8 —.0576 I2 12 —34 II 38

7 + 8 —.0568 iz, @ —I7 T2 52

8 -+-20 —.o601 12, BR | —20 12 @

9 +20 —.O601 I4 50 —20 I4 30

Io +21 —.0609 TEX D7/ —z20 12 9/

II +22 —.o611 14 34 — 21 WAL Tg

12 +22 —.o61I I5 56 —21 I5 35

13 +22. —.o61I 12 By —I9 iy)

15 +21. -+.0608 12 45 —32 1A ie

16 +19 +.0584 II 27 —29 Io 58

17 +19 + .0584 Ir 38 —28 II 10

18 +19 -++.0582 II 29 —26 Toa

19 +109. -+.0582 II 45 —23 II 22

20 +19. +.0582 +13 3 --25 +12 38

TABLE IT V.—TANGENT CORRECTION.

This correction is always negative, and is here expressed in terms of the fourth

decimal place of the micrometer readings.

ees On ete Se lege, A 5. Ge le fel 8s) 29%

20. |— o|— o|— of— o|— o|— 1\— T]— — II

30. 2 2 D 2 2 3 3 3 a

40. Aalen tc 4 5 5 6 6 Zi 7

30. 8 8 8 9 9 Io Io II II 12

60. 13 12 14 15 16 17 17 18 19 20

70. 21 22 23 24 25 26 27 Bri. XO) | vent

80. Sense So) le GOl nazi a gOnls e4Ors Abit 42), Ag

90. Ata AC) ae AON eso iS 2h eve SG h Sie (5 70\. SOs ar OL

100. Coa O4 tein On, eZ ear OO) larg Lil ASN) = 75 15s 77 l sO

110. 81 83 85 87 go 93 95 98 | I00]| 103

120. UGE) TGS) A) acre |) ON) | aes |e eI Ae airs) || aree

130. —135 —138 —141 |—145 |—148 |—151 |—155 |—158 |—162 |—165

80 Rutherfurd Photographic Measures of

TABLE V.—RESULTS OF MEASURES OF DISTANCE.

ty | Observed Dist. Corrections for Cor-_ | geale Parallax | . Final ;

| 2 | ee | toon |

T | .5188 | .5206| 479 | —79 4 | .5452 | +262] +.0502 | +0.612 | 134.6295

1 2 | .4992 | .5242| 458 | —8o 4 | .5349 | +306] +-.0499 | + .582 .6229

3 | -5392 | -5166| 479 | —8o 2 | .5531 | +224| +.0499 | + .582 -6329

(16) 5 | .5864| .6211| 464 | —78 I2 | .6285 | + 59| +.0018 | + .157 .6382

6 | .5898 | .6182 | 513 | —78 5 | .6330 | +120] +.0018 | + .157 .6488

7 | .6063 | .6018 | 493 | —77 Io | .6316 | +125 | +.0016 | + .129 6474

IO | .6539 | .6502] 439 | —82 Io | .6737 | — 55 | —.0394 | + .490 .6351

I5 | .6880 | .7412| 516 | +82 5 |-7599 | —141 | —.0629 | — .343 .6785

16 | .5970 | .6074| 774 | +79 6 | .673I | — 90 | —.0643 | — .197 -5973

I7 | .6227 | .6303| 650 | +79 6 | .6851 | — 96 | —.0643 | — .197 .6087

Mean 134.6339

3 |.7912|.7799] 532 | —65 | 112 | .8357 | +181 | +.2096 | +0.925 } 109.0753

2 II | .2029 | .2003| 384 | —67 | 117 |.2371 | — 78| —.1654 | + .970 .0764

I2 | .1825 | .1745 | 438 | —67 | 112 | .2189|— 65 | —.1654 | + .970 .0595

(25) | 13 1). 1650). 1473, |) 507 |), 67) EE2 2045) | 14) 65a oe .0502

I5 | .2923 | .2717| 355 | +66] 106 | .3267 | —114 | —.262I | —1I.o11 -0402

Ig | .3074 | .3010] 382 | +63 112 | .3519|— 36] —.2682 | —o.g91 .0674

Mean 109.0615

2 | .0674 | .0344 | 474 | —68 | 105 | .0930 | +260] +.2I00 | +0.892 | 114.3405

3 | IL | -4735 | -4343 |) 397 | —70 | 123 | .4897 | —.82|—.1658 | -- .950 +3279

13, | .4314 | .4084| 533 | —70 |] 114 | .4685 |— 15|—.1658|-+ .950] - .3134

(26) | 15 | .5538| .5548| 361 | +70 | 105 | .5987 | —120| —.2626 | —1.004 oun

18 | .5716| .5540| 395 | +67 | 107 | .6106 | — 62] —.2687 | —o.997 .3229

Mean 114.3232

4 2 |.5200|.5410| 451 | —66| 114 | .5722 | +252] +.2094 | +0.868 | 110.8179

12 | .8999 | -9155 | 435 | —68 | 114 | .9475 | — 66| —.1653 | + .932 .7876

(27) Mean 110.8028

5 I | .0086 | .o100| 327 | —45 | I15 | .0462 | +150) +.1583 | +0.934] 77.2315

2 | .0038 | .0036| 320 | —46| 115 | .0398 | +175/ +.1571 | + .925 .2263

(19) | 3 | .0032 | .0030 |. 360 |.—46 | 115 | .0432 | --128| +.1571 | += .925 .2250

4 | .2026|.1564| 350 | —47 | 115 |.2185|— 2] +.o0117| + .827 .2406

) 5 (| 1722 )'.1676 | 339 | Aa") 105) | 2080) 34") oa571 | age .2257

6 | .1544|.1458| 463 | —44 | 117 | .2009|-+ 69] +.0057 | + .670 .2221

7 | .1684 | .1552| 397 | —44, 115 |.2058);-+ 72] -+.o050| + .646 .2263,

8 | .3030 | .29088 | 352 | —46'| 115 | .3401 | — 98] —.1216] + .o12 .2204.

9 | .2870 | .2860} 438 | —46 | 15 | .3343 |— 34| —.1216| + .o12 .2210

IO | .3072 | .2922| 289 | —47 | I15 | .3325 | — 32| —.1235 | + .889 eh

II | .31I10} .3048 | 271 | —47 | 115 | .3389|— 55|—.1242 | + .877 .2205

I2 | .3072] .3017| 307 | —47 | 115 | .3391|— 46] —.1242 | + .877 .2216

I3, | .3002 | .2900] 355 | —47 | 115 | .3345 |— I10| —.1242 | + .877 .2206

I5 | .3853 | .3863 | 300 | +47 | 117 | .4293|— 81| —.1968 | — .824 .2138

16 | .3727 | .3607| 432 | +45 | 116 | .4231 | — 52|—.2010 | — .720 .2077

17 | .3793 | -3739| 368 | +45 | 116 | .4266 | — 55 | —.2010 | — .720 .2109

18 | .3771 | .3737 | 424 | +45 | 116 | .4310 |— 42] —.2014 | — .709 .2163

19 | .3878 | .3854) 358 | +45 | 116 | .4356|— 25 | —.2014 | — .709 .2226

20 | .3781 | .3947| 313 | +45 | 116 | .4309|— 96] —.2014 | — .709 .2108

Mean 77.2211

Siaty-five Stars near 61 Cygni. 81

TABLE VI.—ReEsutts oF MEASURES OF ANGLE.

Observed Position Zero Paral-

lar} 2 Cor- 5

E tion pius| Refrae tected | SHOPS | cy. | peuted Atle

° East. | West. |_Preces- ae ficient F

sion, etc. Pp 7

eso ka 2o ent 2) es 2 no Ao) 230) ——s) rr! Ai | 307) A4n 1o

2 35 59 | 3 24) 13 28 | —13 | 49 26) —5 9 | —43 45 2

3 36 36/37 10| 13 34 | —18 150 9| —5 9 | —43 44 51

5 BOIS SG) Ae Ee BS) 1S AS ee) ——O ET |) 51 44 24

6 33 2|33 30] 11 38 | —32 | 44 22| —o 11 | —51 44 10

7 29 2/29 22| 12 52 | —23 ]41I 41| —o Io | —52 44 33

10 Hee F338) Iie 0) AO, ty tA | AG 43 42

15 25 con 25) Sat Le ould ANS) 27 Wet O20. | She 52 43 53

16 2053) 27) 27) 10. 58) |) £8) 3750:), 4-6 34 | =F 54 44 14

17 28 18/28 40] II I0 | —I2 |39 27] +6 34 | +54 44 15

Mean 307 44 19.4

3 | 325 IE 34|12 22) 13 34 | +10] 25 42) —o 23 | --2I | 235 25 33

II Io 54|11 18| 14 13 | + 3 ]25 22| +0 18 | +12 25 13

12 8 2) 858/15 35 | + 6/24 11] -+o 18 | +12 24 44

12 II 20/1 12] 13° 8 | +10 | 24 34| -+o Io | =-12 25 21

15 12°55 | 13 37] 12 13,| -FIE 25 49) --O 29 | — 3 25 49

19 13 8|13 48] Ir 22] +18 |25 8] +0 30] + 9 25 4O

Mean 235 25 23.3

2 |319 54 34/54 28) 13 28| +9] 8 8| +0 13 | +26] 230 9 30

II BA AS one te taeles 4 | 9) 23)|,— OF LO) 7 8 48

13 55) 2255) 25013) 8! | 1-83) 1 8 45, —O 10 || E17 9 5

I5 57 15|58 I2| 12 13 | +10 ]10 6|] —o 16 | — 9g 28

18 Bits 59032 NTE. 3 leate2on elo) 81 ——O 165) 93 9 3

Mean 230 9 10.8

2 | 316 42 20] 43 42| 13 28 | +10 |56 39] +0 35 | +30 | 226 58 25

12 42 20|43 42} 15 35 | + 9158 45| —O 27 | +22 58 37

Mean 226 58 31.0

I 3 0 28] I 28| 12 2 | —rIrI |12 49) —6 12 | —26 | 273 6 41

2 2 58 36/59 32) 13 28 | — 9 |12 25| —6 9 | —30 Gp

3 59 6/59 40/ 13. 34 | —I5 |12 42| —6 9 | —30 6 28

4 55 20/55 48/ 12 39 | —13 }] 8 o}] —o 28 | —5Ir 6 39

5 SSE SO So he) Bont Ee 7 338.|| Omg |) 66 6 53

6 See 500524) ee BOR SSNS le ——O 1G) |) 00 6 43

7) 50 38/51 27| 12 52 |—20] 3 34] —o 12 | —68 6 I9

8 49 32/49 50} 13 3 | —I5 | 2 29| +4 44 | —35 6 48

9 48 3/48 53| 14 30 | —26] 2 32| +4 44 | —35 6 33

10 ASa G5 AS 831300) 2 teen 2 Of a4 490) Ae 6 I9

II ANON or 27 TET a le A233) SA ssan As 6 37

I2 45 58/46 20| 15 35 |— 8] I 36] 4-4 50 | —43 6 22

13 48 28) 49 23/13 8 | —I3 | I 51) +4 50 | —43 6 50

15 AGN TAZ TO\i12 -13)|--- 6) 1.59.57 | 47-40 | 41-56 6 38

16 47 32147 38| Io 58 | +23 |58 56] +7 49 | +66 6 4o

17 48 15|49 23| II 10 | +13] 0 12| +7 49 | +66 6 20

18 46 56/47 58) 11 3 +20 ]58 50| +7 50 | +67 6 14

19 46 37/47 II| Ir 22 | +32 158 28| +7 50 | +67 6 41

20 A518 4546) 1238 | 7158 17) 4-7 50 Ih 67 6 45

Mean 273 6 36.6

ANNALS N. Y. ACAD. SciI., X, August, 1897.—6.

82 Ruther furd Photographic Measures of

TABLE V.—REsuULTS OF MEASURES oF Distance. (Continued.)

Observed Dist. Corrections for Cor-_ | geale Parallax Final

as)

Star S rected | Varig- | Proper Co- Corrected

: oO Mean. | 4j Motion. i i :

6 I | .6858 | .6818] 4or | —55 | 131 |.7262|+185| -+.2115 | +0.871] 94.9674

2 | .6928 | .6910| 393 | —56 | 130 | .7333 215 .2100 | + .892 -9763

(24) | 3 | .6920| 6812} 455 | —56 | 130 | .7342 | +158) +-.21G0 | +- ©8902 -9715

An e8980 |-8830)" 437. | 58.) 134-0305) Sila Ol 57a neo ge -9644

5 | .gor4 | .8962 | 423 | —55 | 138 | .9441 | + 42] +.0076 | + .962 9683

6 | .8773 | .8578 | 626 | —55 | 132 | .9326|-+ 85 | -+.0076| + .962 -Q611

7 | 8896 | .8944! 503 | —54 | 138 | .9454|-+ 88] +-.0067 | + .956 -9732

8 | .0688 | .0660] 445 | —57 | 134 | .1143 | —121 | —.1623 | + .916 -9517

9 | .0571 | .0546| 564 | —57 | 135 | .1145 |— 42| —.1623 | + .916 -9598

IO | .cQ23 | .0755| 352 | —58 | 134 | .1214 |— 39, —.1649| + .942 -9647

II | .0848 | .c872! 330 | —58 | 134 | .1213 | — 68| —.1658 | + .950 .9609

I2 | .0814 | .o812| 376 | —58 | 136 | .1214 |— 57] —.1658 | + .g50 .9621

13, | .0632 | .0488 | 444 | —58 | 134 | .1027 | — 12] —.1658 | +0.950 -9479

I5 | .1924 | .I991 | 300 | +58 | 132 | .2394 | —I00 | —.2626 | —I.005 -9539

16 | .1892 | .1790| 322 | +56 | 132 | .2298 |— 64 | —.2682 | —I.000 9424

17 | .2069 | .2078 | 323 | +56 | 132 | .2531 !|— 68] —.2682 | —I.oco -9653

18 | .1939 | .1912| 328 | +55 | 132 | .2388 | — 51 | —.2687 | —o0.998 -9522

Ig | .2206 | .1926] 319 | +55 | 136 | .2523 | — 31 | —.2687 | — .998 .9677

20 | .2064 | .2074 | 304 | +55 | 132 | .2506 | —118 | —.2687 | — .998 -9573

Mean 94.9615

4% 2 | .0818 | .1088 | 341 | —48 | 125 | .1337 | +185 | +.2097 | +0.923| 81.3738

13 | -4722 | .4627| 244 | —50 | 126 | .4960|— 11] —.1655 | + .969 -3418

(23) Mean 81.3578

8 2 | .0438 | .0356| 213 | —36 | I00 | .0660 | +139| +.0676 | +0.650] 61.1558

3, | .0383 | .0341 | 228 | —36 | loo | .o640 | +102 | +.0676 | + .650 { - 1501

(17) | II | .1636|.1495| 196 | —37 | Io0 | .181r | — 44] —.0538 | + .541 .1298

I2 | .1595 | .1823 | 209 | —37 | loo | .1967 | — 37 | —.0538 | + .541 . 1461

13 | .1678 | .1622| 214 | —37 | Too |.1913|— 8|—.0538|-+ .541 .1436

15 | .1983 | .2245 | 237 | +37 96 | .2471 | — 64| —.0854 | — .426 .1498

Mean f 61.1459

9 2 | .4752| .4860| 416 | —68 | 115 | .5178 | +260) +.1873 | +0.631 | 114.7392

3 | .5146| .4676| 458 | —68 | 122 | .5331 | +191 | +.1873 | + .631 -7476

(29) | 11 | .8372| .8280| 371 | —7o | 120 | .8654 | — 82] —.1478 | ++ .740 -7189

13 | .8130 | .8001 | 449 | —7o0 | 120 ! .8473 | — 15 | —.1478 | -+ .740 -7075

I5 | .9240 | .9426| 327 | +70] 21 | .9758 | —120| —.2343 | — .849 .7186

18 | .9489 | .9477 | 328 | +67 | 120 | .9905 | — 62| —.2398 | — .912 -7328

Mean 114.7274

10 IO | .0253 | .0063 | 300 | —60 | 132 | .0469 |— 4o| +.0296 | +0.097} 99.0737

I2 | .0295 |.9887 | 298 | —60 | 132 | .o400|— 49/ +.0298 | + .069 .0648

(78) | 15 | .9722 | .9822| 337 | +60 | 128 | .0236 | —104| +.0470 | + .077 .0612

18 | .9556 | .9712| 460 | +58 | 132 | .0223 | — 53) +.0480 | + .233 .0680

Ig | .9687 | .9714| 404 | +58 | 132 | .0233 | — 32] +.0480 | + .233 .O71I

20 | .9906 | .9534] 352 | --58 | 132 | .o201 | —123 | +.0480 | ++ .233 .0588

Mean 99.0663

Siaty-five Stars near 61 Cygni.

Observed Position

OVC

East. West.

Zero

Correc-

tion plus

preces-

sion. ete.

Refrac.| rected

Mea

TABLE VI.—ReEsuLts or MEAsuRES OF ANGLE.

Cor-

( Continued.)

Final Cor-

rected Angle.

O ON ADUNBW bY H

294 17 35|18 20

61 42 56| 44 Io

a a

Tu 2

Tee28

13 34

T2 39

Il 38

DPAADOOOOADOOADADAOAOG OO ©

(oe)

+4+4+4+4++

WOO Om n

204 35

~204 35

332

Rutherfurd Photographic Measures of

TABLE V.—ReEsvutts or MEASURES ofr DisTANcE. ( Continued.)

Wd Observed Dist. Corrections for Cor- | Scale - Parallax Final

ie rected | Varia- ronan Co- Corrected

II | .1390] .1408| 223 | —45 | 124 | .1675 53 | +-0261 | +0.090} 74.1895

I2 | .1531 | .1270| 225 | —45 | 124 | .1679]— 44] -++.0261 | + .ogo .1908

I5 | -1319| .1356|) 255 | +45 | 123 |.1736|— 78| +.0412 | + .056 .2077

Mean 74.1960

It | .6700 | .6604 166 | —33 99 | .6874 | — 38| —.0056 | +0.276} 53 6815

13, | .6836 | .6730| 172 | —33 99 |.70II|— 7|—.0056|-+ .276 .6983

15 | .6732 | .6743| 195 | +33 96 | .7053 | — 56| —.c0g0 | — .138 .6889

Mean 53.6896

I | .3524|.3614| 285 | —57 | 136 | .3874 | +192) —.0720| +0.092] 98.3358

2 | .3630 | .3550| 293 | —58 | 136 | .3901 | +224) —.0715 | + .050 -3416

3 | -3642 | .3513| 295 | —58 | 138 | .3894 | +164) —.0715 | + .050 -3349

4 | .2984 | .2968| 207 | —60 | 136 | .3289|— 3] —.0053 | — .I91 -3208

5 | .3068 | .2918 | 293 | —57 | 136 | .3305 | + 43 | —.0026 | — .3904 -3271

6 | .2970| .2951 | 299 | —57 | 136 |.3278|-++ 88 | —.0026 | — .3094 .3289

7 | 3084 | .3063 | 298 | —56 | 136 | .3356|-+ 91 | —-.0023 | — .419 -3370

IO | .2354 | .2393 | 294 | —60 | 136 | .2684|— 40] +.0559 | — .066 -3195

IL | .2419| .2395 | 204 | —60 | 136 | .2716 | — 70| -++.0562 | — .094 3196

I2 | .2335 | .2293 | 293 | —60 | 136 | .2624 |— 59| +.0562 | — .094 23115

13 | .2352 | .2496| 293 | —60 | 136 | .2734|— 13| -+.0562 | — .094 3271

15 | .1947 | .1884| 317 | +60] 136 | .2369 | —103 | +.0889 | + .242 .3186

16 | .181r|.168r| 413 | +57 | 136 | .2293 | — 66) +.0908 | + .378 .3184

17 | .1604 | .1670| 366 | +57 | 136 | .2137 |— 70) +.0908 378 -3024

18 | .1569|.1686| 407 | +57 | 136 | .2169|}— 53] +.0910| + .390 .3076

19 | .1873 | .1810| 361 | +57 | 136 | .2336 |— 32] +.cgIO| + .390 3264

20 | .1854| .1686| 329 | +57 | 136 | .2233 | —122| ++.co9I10 | + .390 .3071

Mean 98.3226

2 | .5585 | .5620| 127 | —2I | 106 | .5811| + 79| +.0881 | +0.723| 34.6864

3 | .5667| .5729| 135 | —21 | 105 |.5914|-+ 58] +.c881 | + .723 -6946

To | .7285 | .712I1 | 119 | —2I | 104 |.7402|— 14|—.0698|-+ .646 .6773

Ir | .7369| .7223| I15 | —21 | 105 |.7492|— 25|—.0702 | + .625 6845

I2 | .7356|.7166| 123 | —21I | 105 |.7465 | — 21|—.o0702 | + .625 .6822

13, | .7I9I | .6993 | 135 | —2I | 104 |.7307|— 4|—.0702 | + .625 .6681

15 | .7756|.7645 | 136 | +21 | r02 |.7956|— 36] —.1115 | — .521 .6738

16 | .7510| .7642! 208 | +20 | 106 | .7907*|/ — 23 | —.1140 | — .384 .6695

18 | .7750|.7772 | 203 | +20 | 108 | .8089 |— I9|—.1142 | — .370 .6880

19 |.7717|.7725| 169 | +20 | 105 | .8012 | — I1|—.1142 | — .370 .6811

20 | .7780 | .7722| 143 | +20] 108 | .8019 |— 43] —.1142 | — .370 .6786

Mean 34.6804.

2 | .9422|.9548) 201 | —31 | 106 | .9753 | +118| +.2018 | +0.760] 52.1987

3 | .9428 | .9546| 227 | —31 | 110 |.9784|-+ 87] +.2018 | + .760 .1987

10 | .3307 | .3272 | 183 | —32 | 106 | .3537|— 21 | —.1584 | + .835 .2039

Ir | .3287 | .3188 | 175 | —32 | 106 | .3478|— 37 | —.1593 | + -850 .1957

12 | .3230'|-3271 || 14 || —32 | Tee | -3510)|—= 31 | —. 15938 | ae .850 -1995

13 | .3143 | .3105| 223 | —32] I10 |.3416;— 7|—.1593 | + .850 .1925

£5 | 4327-4583 | 194 | +532 | 94 | 24760)|——55)| —.2523) | eae .2068

18 -| .4623 | .4506| 163 | +31 | Ior | .4851 | — 28] —.2583 | — .972 .2115

Mean 52.2009

SO ae

r°

Sixty-five Stars near 61 Cygni. 85

TABLE VI.—Resutts oF MEASURES OF ANGLE. (Continued.)

Observed Position Zero A Paral- ‘

= Angle. Correc- |p frac ioe Proper | lax Final Cor-

ion plus o|| Bs

= t Pp Mean. | Motion. | Coef- | rected Angle.

East. West. | Preces- jicient.

sion, etc. p T

Ml Mi / Ue / “ e} Ui 4d

fe} 44 ‘

EX) NCOl27 37 |27 48) 14 13 | — 3 | 40 52) +> 7 33'|— 97] 330 48 19

12 25202536) L503 5-048 50-1 7 33 |— 97 48 8

15 23 52) 23 32) 12 13 | —II [35 44) +11 57 | +Io1 47 58

Mean 330 48 8.3

II | 49 29 30/30 22| 14 13 | —4 {44 5)|-+10 34|—130| 319 53 21

13 30 2/30 36) 13. 8 | —13 | 43 14/-+10 34|—130 53125

15 2305/24 5) 22) 13) LO) 136) 4) 1G) 44-137 53 18

Mean 319 53 21.3

I | 7 19 56/19 39| 12 2 O31 50) 10) 545 73)\| 34ue 24i43

2 1G). DS | 077 BA) 13) BS Oo |30 21|— 6 51|/— 73 DAA!

3 TONES NAS ES SA ate LSU 55) |=) 6) Si) 73 24 44

4 I3 42/14 30| 12 39 | + 1 | 26 46)— 0 31|/— 72 25 14

5 IZ, 6|14 22} Ir 38 | + 1 |25 23|/— 0 15|— 66 24 36

6 T2 30\13 43) 11 38 | + 8] 24 53|/— 0 15|— 66 24 31

7h SrA) 25) tei 52 0-93 2 58/0) 13) — 65 24 43

10 7. 2) 7 TL 3 7 | —— B20) 12) -= 5) 23 |= 7a 24 47

II 5 35| 6 38| 14 13 | —1]20 I19/+ 5 25|— 74 24 46

12 SPASMS SO) MES Me Seek po 23095 25) 74 24 32

13 5 57| 6 16| 13 sip Pe ES) TSnlel = 5,25) 74 24 37

15 SOA Aye awh Ek Na GON OSA lta. 74 24 21

16 AWAG) OBZ | MOMPSOn S305) Siiiat= Oo) A5i| a1 09 24 38

17 GS orth ON) 23) [17 39)) 1-8) 45) 69 24 44

18 458} 5 50) Ir 3 | —30]16 51|+ 8 46/+ 69 25 12

19 3 38] 4 32) II 22 | —20]15 7|\+ 8 46/+ 69 24 17

20 2B 5t SiS) 239 ja 13 UA) 59)) 51-8 40) F369 24 24

Mean 341 24 38.4

2| 2654 6/55 10/ 13 28 | —14 | 7 52|—18 53|—140] 296 49 9

2B 54 0/56 16| 13 34 | —20 | 8 22|—18 53/|—140 48 45

10 NOMS 7 VS 7 Alia ON G3 SEs 14 45) tao 46 58

Il 19 26/19 38| 14 13 | — 6 133 39) +14 50|—162 47 Oo

12 17 28|\17 46| 15 35 | —Irt 133 1/|/+14 50|—162 47 4

13 20 3/20 21) 13 8 | —19 ]33 1/+14 50|/—162 A IF

15 I2 35|1L 37| 12 33 | — 3 |24 16| +23 28] +185 48 32

16 IO 30|12 42} 10 58 | — 3 | 22 31/| +23 58} +196 47 10

18 II 42\11 58| 1 3 | — 3 ]22 50/+24 1|-+1097 47 12

19 IO I10|12 35| If 22 | — 4 |22 4go|/+24 1|-+197 47 51

20 Io 2| 9 56] 12 38 | — 3} 22 34/+24 1|-+107 48 oOo

Mean °296 47 43.5

2a oop Oe Ol 40 Sh 6285p Ea) 4 aT 3) 55h 87) 215) 19157

3 TSAR 274203) 34 soul kon Mt | =" 3) 55a 87 20 43

ae) IO 13/1I 25) 13 7|/+ 8]/24 4|—3 3\/+ 74 Bi

II ORSON oes Malt O24 oxi 3, Ai) 71 20 56

I2 658) 816] 15 35 | +11 |23 23/— 3 4/-+ 71 20 56

13 9 44|1o 6/13 8} +19 | 23 22/— 3 5/-+ 71 ak

15 74 53/16 10) 12 13 | — 27 36|/— 4 52|— 54 22 6

18 TAG SES Le Seale On ZORA Siic—wA! 59) | 132 20 44

TABLE V.—RESULTS OF MEASURES OF DISTANCE.

Rutherfurd Photograrhis Mesaures of

( Continued.)

Observed Dist. Corrections for Cor-

pia = z pas E nected eae: pee Fae Corrected

16 2 | .0451 | .0651 |} 33t | —18 | 107 | .0769 |) + 68) +.1978 Hs 976| 30.2940

3 | .0509 | .0502| 15r | —18 | 107 | .0743 = 50! +.1978 | + .976 -2896

(20) | Io | .4275 | .4128| 116 | —19 | 108 | .4405 12} —.1554| + .984 .2965

II | .4162 | .4188] 103 | —19 | 108 | .4369 | — 22 | —.1563 | + .982 .2910

13 | .4499 | .4011 | 148 | —19 | 108 |.4490|/— 4 | —.1563 | + .982 -3049

15 | -5196 | .5287) 108 | +19 ) 136 | .5503 |— 32] —.2475 | — .984 .2870

16 | .5260 | .5298 | 3137 | +18 | 104 | .5536|— 2 | —.2528 | — .926 .2868

18 | .5404 | .5371 | 137 | --18 | 106 | .5647 | — 16; —.2533 | — .920 .2980

Mean 30.2935

17 2 | .4646| .4644| 246 | —49 | 135 | .4942|+188) —.0712 | +0.052] 82.4425

TO | .3210 | .3434 | 246 | —50 | 136 | .3618 |— 34 | +:°0555 | — .064 -4131

(13) | IL | 3304 | -3316| 246 | —50 | 136 | .3607 | — 59| +.0558 | — .0g2 -4094

13 | .3578 | -3466| 246 | —50 | 136 | .3818 | — 11| +.0558 | — .092 -4353

I5 | .2947 | .2895 | 266 | +50 | 136 | .3338|— 86| +.0884 | + .240 -4167

20 | .2928 | .2669| 276 | +48 | 135 | .3223 | —102| +.0904 | + .388 -4075

Mean 82.4207

18 2 | .9388 | .9421 |. 230 | —4r | 128 |.9701 | +159) —.0607 | +0.103] 69.9266

Io | .8614 | .8647 |. 210 | —43 | 127 | .8903 | — 29] +.0472 | — .o13 -9344

(12) | 11 | .8696 | .8500] 209 | —43 | 127 | .8870|— 50| +.0475 | — .o40 -9290

12 | .8637 | .8578 | 209 | —43 | 128 | .8881 | — 42] +.0475 | — .o4o -9309

13 | .8604 | .8524 | 209 | —43 | 127 | .8836|— 9] +.0475 | — .o40 -9297

15 | .8128 | .8102| 230 | +42 | 128 | .8494 | — 73); +.0752|-+ .188 -9197

18 | .8071 | .8033 | 304 | +4 | 128 | .8504 |— 37! -+.0769 | + .339 -9280

19 | .8118 | .8030] 251 | +41 | 127 | .8472 | — 23] +.0769 | + .339 .9262

20 | .8181 | .8011 | 237 | +41 | 127 | .8480|— 87| +.0769 | + .339 .9206

; Mean F 69.9272

19 | rr | .9849| .9861 | 397 | —79 23 | .0064 | — 92] —.1211 | +0.529} 128.8829

: 12 | .9814 | .9767| 410 | —79 23, | .0013 |— 77 | —.121T || Fa520 .8793

(62) | 15 | .0476 | .o500| 366 | +78 2 Cy Sais | C7 | = 49152 .8686

IQ | .0705 | .0634| 381 | +75 De EMO) | ie} || UG \o | —= .715)3; .8914 |

Mean 128, 8806

20 2 | 8045 | .8214| 223 | —44 | 120 | .8403 | +168 | —.0985 | —0.087] 73. 7575

3 | .8395 | .8172| 226 | —44 | 120 | .8561 | +123 | —.0985 | — .087 -7688

(11) 9 | .6494 | .6636] 228 | —44 | 120 | .6844 | — 33 | +.0758 | — .136 +7552

Io | .6614 | .6699| 221 | —45 | 120 | .6927 |— 30| +.0770 | — .203 .7641

Ii | .6725 | .6640| 220 | —45 | 115 | .6948 | — 53] +.0774 | — .230 -7639

T2 | .6730| .6656| 221 ; —45 | 120 | .6964|— 44| +.0774 | — .230 -7664.

13 | .6560| .6576| 223 | —45 | 120 | .684r |— 10] +.0774 | — .230 7575

15 |-G516)| 5942 | 228) | 4-45) 120) (634777 | tee 225 eee 7543

16 | .5856 | .5666| 282 | +43 | 118 | .6179/— 49] 4.1251 | + .502 -7445

18 | .5646! .5910| 278 | +43 | 118 | .6192|— 4o}] +.1253 | + .514 -7471

19 | -5870 | -5912| 252) —-43 | 116))| 56279 | 24 | ar53) Seat 7574

20 | .6028 | .5880| 233 | +43] 118 | .6323 |— 91/ +.1253| + .514 -7551

Mean 73.7570

Sixty-five Stars neur 61 Cygnt. 87

Taste VJ.—ReEsutts of Mrasores or ANGLE. ( Continued.)

rd Chega’ Boson eee Cor- Paral-

= . Trec- F {

2 : tion plus | Refrae. necied Moton® (heser | tecreckanete

Fast. West. | _Preces- i ficient.

sion, etc. | p | 7

DONATI 7 ATA a5 O:|2b3) 28 o|19 16/— 8 o|+ 13] 251 12 21

3 7 48) 6 20| 13 34 | — 2|20 36|— 8 o/-+ 13 12 47

Io | 340 53 52/54 38/ 13 7 |-+ 1] 7 23/-+ 6 12|— 15 13, ©

II 51 57/52 45| 14 13) + 1] 6 35)/+ 6 15|— 22 iD Wei

13 5 GL EG SONU SB Gul eG) ui ee 15 25

15 AOWAA NESTS 3) eae o a Ele ie Siesta O52) 12959 12 55

16 5I 14/49 54| to 58 | +33] 2 5!+10 4|-+ 92 1D 12

18 SE ALS | SS PAY Ae BW SRO) ee 7 ape) oS YL 12 56

Mean 251 12 59.6

| Gab ats eval |p Te) 3) ata} AS) o | 28 49|— 8 11|— 87] 341 21 7

Ao) 2 41| 2 43) 13 7/|— 1/15 48/+ 6 26|— 88 Die Diy

II I 3] 0 38/ 14 13 | —11]15 2/-+ 6 28;/— 88 20 27

13 Im5| 2 23/13 8] + 1/]14 58/-+ 6 28|— 88 21 18

15 | 70 58 12|59 25| 12 13 | —II | Io 50|-+10 14|+ 88 20 13

20 57 58/57 30/ 12 38 | —13 |I0 9/-+10 29/-+ 82 20 22

Mean 341 20 48.0

2| 68 17 43/17 50) 13 28 | — I |3I 13|— 9 49| —103| 338 21 47

IO I 25| 3 22/13 7 | —2|715 28|+ 7 43 |—103 22a

II I. 3) 0 58] 14 13 | — I |]15 13|/-++ 7 46|—r104 21 51

12 | 67 58 2/58 56/ 15 35 |—3]14 1/+ 7 46|—104 2I 21

13 | 68 0 20/ 215/13 8 | — 2/14 23)-++ 7 46|—104 21 56

I5 | 67 57 33/57 45| 12 13 | —11 | 9 41|-+12 18] +105 22 18

18 58 53/59 22| Ir 3 | —30 | 10 34|+12 36/-+ 98 22 55

19 57 8/58 34| Ir 22 | —20] 8 53|-+12 36/-+ 98 DG

20 56 12/57 7| 12. 38 | —13 | 9 4)|-12 36] 98 22 29

Mean 338 22 5.9

TI }278 5 48) 7 0] 14 13 | + 4]20 41|— 3 4/)-+ 48] 188 17 23

12 AO) Ane! Sa S5e Westen) 54y-—= Be 4a 1-445 17 18

T5 TO 45|1I 25} 12 13 | — 4 | 23 14|— 4 52|— 44 17 47

19 TL) 47 | 10 52) rr 22) |) — 23 2|/— 4 58/— 36 17 50

Mean 188 17 34.5

2 | 79.23 48,24 47| 13 28 | + 4 |37 50|— 8 35|— 98} 349 29 40

3 23 40) 25 500 Sh SAN Bei 7iGo) 61 | 18) 35 |= 98 29 27

9 8730) 9N 50 240030) ts 23 591s. 0839) — 07 29 33

Io To 40/10 56) 13 7] + 2 |23 57|/+ 6 45|— 96 29 46

II IO 7|10 20| 14 13 | + 1 | 24 28|-+ 6 48|— 95 30 II

12 © AS Ee Se us Sas See oO AS ik 29 21

13 IO I2|II Oo} 13 + 7 |23 51;/+ 6 48|— 95 30 29

15 6 4] 7 24) 12 13 | —1o0 |18 47|+10 46|+ 94 29 48

16 8 53] 9 40} Io 58 | —3rI |19 43}+11 o|+ 86 30 45

18 8 12] 8 35] Ir 3 | —28 |19 48|+11r 1/-+ 86 30 30

19 6 40] 7 37| It 22 | —I9 |18 11|+1311 1/-+ 86 29 42

20 5 42| 7 2) 12 38} —11 |18 49|/+11 1/+ 86 30 35

Mean 349 29 58.9

hae a |

88 Rutherfurd Photographic Measures of

Taste V.—ReEsvutts or MEAsuRES OF Distance. ( Continued.)

ty | Observed Dist. Corrections for Cor-_ | geale Parallax Final

He. We aleaeer eae Mean. | 2™="| Motion: | emcee ena

. -| ti : i istance.

i ° East. | West. | Refrac.| Aberr.| Scale. s Hon. epieae nts ‘ Fi a

21 2 | .0277 | .0658 82 | —13 | 100 | .0636/-+ 50] +.1945 | 4-0.692] 22.2720 |

10 | .4069|.4061| 77 | —14 | 100 | .4227|— o9|—.1520)| += .775 2789 |

(21) | II | .4056 | .3932)) 73 | —I4 | Ioo |.4152|— 16| —.1537 | + .792 -2701 |,

I2 | .3958 | .3944 80 | —14 | 100 | .4116|— 13} —.1537|-+ .792 .2668

13 | .3989 | .3947 QI | —I4 | 100 |.4144|/— 3] —.1537]|-+ -.792 .2706

I5 | .5047 | .5059 64 | +14 | IoL | .5231 | — 24] —.2436 | — .892 .2656

20 | .5184 | .5169 65 | +13 | 102 |.5355|— 28] —.2492 | — .943 .2714

Mean 22.2708

22 2 |.7426|.7498| 340 | —66 | 123 |.7777 | +-252| —.1171 | —o.187]} 110.6834 |

3 | .7438 | .7714| 350 | —66 | 123 | .7901 | +185 | —.1171I | — .187 .6891

(9) | 13 | .5671 | -5651| 345 | —68 | 128 | .5983 |— 14| +.0922 | — .327 .6849

I5 | .4800 | .4844 | 331 | +67 | 128 | .5266 |—116)| +.1461 | + .472 .6672

16 | .4590 | .4456| 386 | +64 | 128 | .5018 |— 74] +.1492 | + .590 .6512 |!

19 | .4759 | -4712| 358 | +64 | 128 | .5204 |— 36] +.1495 | + .599 6740 |

20 | .4736 | .4740! 340 | +65 | 132 | .5193 | —137| +-.1495 | + -599 .6628

: Mean 110.6732

23 I | .3538 | .3482 | 271 | —52 | 134 | .3820|-+174| —.1201 | —0.156] 89.2773 |)

| 2 | .3584 | .3390| 276 | —53 | 134 | .3801 | +203 | —.1192 | — .199 .2786 |

(10) 3, | .3613 | .3465 | 284 | —53 | 134 | .3860| +149) —.1192 | — .199 -2791

4 | .2602 | .2464] 280 | —55 | 135 |.2849/— 2] —.0089 | — .430 .2703

5 | .2526).2460| 277 | —51 | 135 ,.2810| + 39] —.0043 | — .604 2728 |.

6 | .2462 | .2428| 309 | —5rI | 134 |.2793|-+ 80] —.0043 | — .604 .2752 |i

7 | .2490| .2478| 290 | —5I | 135 |.2814| + 83] —.0038 | — .623 -2779 |

8 | .1524 | .1357| 432 ) —54 | 135 | .1910 | —113| +.0919 | — .248 .2684 |

9 | -1444 | .1497| 293 | —54 | 135 | -1801 |— 39] +.0919 | — .248 .2649

Io | .1484 | .1524] 270 | —54 | 135 | .1812|— 36! +.0933 | — .314 .2669

II ) .1523|.1553| 268 | —55 | 135 |.1843 |— 64] +.0938 | — .339 .2673

I2 | .1550| .1485 | 272 | —55 | 135 | -1826 | — 53] +.0938 | — .339 .2667

13 | .1528|.1490| 278 | —55 | 135 | .1824 |— 12! +.0938 | — .339 .2706

I5 | .0830|.0692| 267 | +54 | 135 | .1173 |— 93] +.1485 | + .484 .2627

16 | .0650| .0636| 310 | +52 | 135 | .1096 |— 60} +.1517 | + .600 .2630

I7 | .0568 | .0660} 284 | +52 | 135 | .1042|— 64/ +.1517 | + .6co .2572 |

18 | .0544| .0614| 307 | +52 ! 135 | .1030}— 48] +.1520 | + .609 .2580 |

Ig | .0596| .0628} 288 | +52 | 135 |.1044|— 29/ +.1520| + .609 .2613 ||

20 | .0694 | .0656! 274 | +52 | 135 |.1093 | —III| +.1520]|-+ .609 2580 |)

| Mean 89.2683, |!

24 | rr | .4972 | .4884 25 |—5 29 |.4977|— 6) +.0292 | +0.064 8.5271

13, | .4776 | .4791L 26 |—5 32 | .4837|/— 1] +.0292 | + .064 .5136

(75) Mean 8.5204

Sixty-five Stars near 61 Cygni.

TABLE VI.—Resutts or MEASURES OF ANGLE.

( Continued.)

rd Obsemved Position enero. Cor- Paral- eee ea

— orrec- ina or-

= nee tion plus | Refrac. aoe TEODEE dae rected Angle

S East. West. | Preces- ficient.

sion, etc. p T

2 208 44 53 50. 40 13 28 abr 1 28) 41223, +229 209 16 13

IO | 299 12 10/13 43| 13 7 | + 8]26 11/— 9 34|-+202 17 29

II II 45/10 38] 14 13 | + 6}25 30|— 9 38| +1095 16 31

12 8 36] 5 25/15 35 | +11 |22 47|/— 9 38] +195 14 30

13 Io 50} 9 6/13 8 | +19 | 23 25|/— 9 38|-+195 15 21

I5 2I 38|21 3/ 12 13 | + 4 | 33 38)—I15 I1|—158 UF WiC

20 20 40} 20 32| 12 38 | + 5 |33 19|—I5 32|—r108 17 22

Mean 209 16 22.4

2|} 85 15 2/16 8/13 28} + 6]29 9/— 5 22/— 64] 355 24 24

3 1S Ly || UB. BA 1 | Boe | toys 25 2

13 7 0| 7 5/13 428] +10} 20 20|+ 4 14|/— 62 24 36

15 BEACH Se 50 Eee TS Sai) SOi 56) AS. 59 24 35

16 655] 8 Io} Io 58 | —28 1/18 2/+ 652\+ 53 24 44

19 S55 Onis) tu 22) Om 7, 79) “| © 52.1 53 24 19

20 By aS) one diay SON OWT ASH o> © 52)--1158 25 10

Mean 355 24 41.4

tees Oo) 251159145)! 12002) a8 tk 15) — 6) 39))—) 79)|| 356) A ai

2 SOM SAS gue 2On| 1. Ol tO 48)/—— 16) 36,79 4 44

3 57 6/58 2] 13 34] -+-II | Il 19|/— 6 36|— 79 4 20

4 58 US) 58 G5) 28 Se) | aC) || Ore |= Oo ae) 4 54

5 52 30/53 Io] Ir 38 | + 8] 4 36!— 0 14|— 62 3 52

6 5I 37/53 26| 11 38 | +27] 4 37!— 0 14|— 62 4 18

i 48 48| 48 42] 12 52] +15} I 52;—0 6/— 60 4 45

8 AG MIZTAZWAS) 3 9 63h 50159) SO aie 5 | 7S 4 22

9 A5 25/45 34| 14 30] +21 | o 21;+ 5 6!— 78 4 29

To | HG {St ANG BO UG N= hi OO) ee evi 7] 4 32

II 45 10|46 20/ 14 13! + 2] 0 oj;+ 5 13/— 76 415

12 AS) US ANN 27 iS) aS50lai ON S9s 341-5 EBh—— FO 4 31

13 A552) 40 40)|-13 8) | S-10) 59) 34> 5. 13 76 4 44

15 ACP AG AA Wey 2 els sO SON sic Sulit 078 4 27

16 45 271/46 o| 10 58 | —27 156 15|+ 8 27|+ 66 4 37

17 ADAG AACN EL TON\e——Lon WS y a7 3 27ala OO 4 23

18 45 18|45 28} Ir 3 | —25 156 46/+ 8 28'+ 65 4 47

19 AAS AG) Sule 22 se Mon 55) Taalet= © 20) ae 105 4 3

20 ASE US PASS 7a| 2 388 i OUN55) Si iets Oo 2or > 05 bee

Mean 356 4 29.8

II | 62 51 28/55 42| 14 13 |— 3] 7 46; + 6 2/|—852] 333 8 11

13 | 62 5 29| 1 5r| 13 8; — 51/16 43/+ 6 3|—852]} 18 4

| Mean 333 13 7-5

90 Rutherfurd Photographic Measures of

TABLE V.—RESULTS oF MEASURES OF DisTANCE. ( Continued.)

las] g ist. rections for Cor- i

Siar 5 Observed Dist Correctio Ce) rected Seale Proper Parallax Corrected

: © an. | tj 5 j :

ia ; East. | West. | Refrac.| Aberr.| Scale. - tion. Hs apneet12) 0% a fase

27 2 | .2265 | .2096| 118 | —23/ 109 | .2380/-+ 87| +.1228 | --0.222] 38.3724

3 | .2274| .I9I4 | 122 | —23 | I09 | .2298;-+ 64) +.1228 | + .222 .3619

(30) | 10 | .4421 | .4243) I4r | —23 | 308 | .4554 |— 16| —.0969 | + .335 3612

II | .4299 | .4405 | I16 | —23 | 108 | .4549 | — 27|—.0974 | +- .361 3594

12 | .4387 | .4402 | 118 | —23 } 108 | .4593 | — 23) —.0974 | + .361 -3642

13, | .4381 | .4337 | 121 | —23 | -108 | .4561|— 5] —.c974 | + .361 3628

15 | -4898 | .4942 | 114 | +23 | 108 | .5161 |— 40) —.1546 | — .504 «3510

16 | .4972 | .5186|} 129 | +22] 108 | .5334|— 26) —.1579 | — .618 -3650

18 | .5107 | .4993 | 130 | +22] 108 | .5306 |— 21 | —.1582 | — .627 .3622

20 | .4933 | 5113 | I17 | +22 | 108 | .5266 |— 48| —.1582 | — .627 -3555

Mean 38.3616

28 | rr | .8154 | .8118 | 338 | —68 | 112 | .8433 |— 80] —.1002 | +0.381 | 111.7400

I2 | .8212/ .8102] 343 | —68 | 112 | .8459|— 67] —.1002 | + .381 -7439

(60) | 13 | .8050 | .8032] 351 | —68 | 112 | .8351 | — 14] —.Io02/ + .38r -7394.

15 | -8830 | .8616 | 329 | +68 | 112 | .o147 | —117| —.1588 | — .523 °7375

18 | .8925 | .8660] 374 | +65 | 112 | .9258 |— 60) —.1625 | — .645 -7490

19 | .8712| .8688 | 353 | +65 ; If2 | .9145 | — 36) —.1625 | — .645 -7401

Mean III.7415

29 3 | -1795 | -1523| 129 | —21 | 112 |.1876|-+ 60} —.1601 | —0.440] 36.0279

II | .874t | .8697| IIL | —22 | 12 | .8917 | — 26] +.1259 | + .567 .0077

(5) | 13 | .8725 | .8763 | 125 | —22 | 112 | .8956)/— 5) -+.1259| + .567 -O137

Mean 36.0164

e II | .2444 | .2182 60 | —II 78 | .2440 | — 13| +.1536 | —0.793 | 18.3861

69)

a II | .9278 | .9310| 179 | —37 | 102 | .9525 |— 43, —.0820| +0.258] 59.8695

(64

32 I | .8124 | .7994| 227 | —45 | 130 | .8343| +150| +.1095 | +0.100| 76.9601

2 | .8056 | .7947 | 235 | —46 | 130 | .8293 | +175] +.1087 | + .142 -9573

(31) | 3 | -7998| .8035 | 238 | —46 | 130 | .8311 | +128} +.1087 | + .142 -9544

4 | .9032 | .9052| 238 | —47 | 124 | .9329|/— 2] +.0081 | + .378 -9457

5 | -9166 | .9137| 235 | —44 | 124 | -9439|-+ 34] +.0039 | -- -560 .9584

6 | .9144 | .8940] 256 | —44 | 130 | -9356| + 69] +.0039 | + .560 +9536

7 | -9134 | 9000} 245 | —44 | 124 | .9364|+ 7£| +.0035 | + .580 9544

8 | .0047 | .O115 | 235 | -—-46 ! 124 | .0366 !'— 98) —.0842 | + .I91 -9451

9 | .O1IQ | .oo14 | 246 | —46 | 124 | .0363 | — 34] —.0842 | + .1901 -9512

IO | .O117 | .9983 | 232 | —47 | 124 | .033r | — 31 | —.0856 | + .258 9477

II | .0044 | .0053 | 231 | —47 | 124 | .0328 |— 55 | —.0860 | + .284 -9449

I2 | .0090 | .OO10; 233 | —47 | 124 | .0332 |— 46| —.0860| + .284 -9462

TZ | -Q9II | .0017| 236 | —47 | 124 | .0249|— 10] —.0860 | + .284 -9415

I5 | .0522 | .0566| 235 | +47 | 124 | .0922|— 81 | —.1365 | — .430 -9421

16 | .0533 | .0692| 270 | +45 | 125 |.1025 |— 52] —.1394 | — .552 -9508

17 | .0687 | 0591 | 253 | +45 | 124 | .1033 |— 55|—.1394 | — .552 9513

18 | .0672| .0500| 276 | +45 | 124 | .1003 | — 41) —.1396 | — .562 -9494

19 | .0698 | .0420| 254 | +45 | 124 | .0954)— 25) —.1395 | — .562 -Q461

20 | .0621 | .0665} 240 | +45 | 121 | .1025 |— 96| —.1396 | — .562 -9461

Mean 76.9498

TABLE VI.—ReEsuLTS oF MEASURES OF ANGLE.

Siaty-five Stars near 61 Cygni.

fa Observed Hostom Gare Cor-

B com tion plus Refrae,| Wiese | soto.

° East. West. | Preces:

sion, ete. £0

fo) / “i / “ / 4d Vd i ‘a 1) Md

2 | 266 44 0/44 25/13 28 | + 7 157 48) 4-15 21

3 A5 17| 44 12) 13 34 | --12 [58 30) 7-15 21

Io | 267 14 38/13 58| 13 7|— 6]|27 19|/—II 59

II I2 58/13 44] 14 13 | + 2127 37/—12 3

12 ut 6G @ Bll U5 (AS 1 Se © 12 2) 1a 2

13 Tre Bl) ie AB | eS) ae laa A ie

15 22 30| 24 28) 12 13 | — 8 |35 34/—I9 4

16 25 5|26 10} 10 58 | —27 |36 8|—I9 28

18 26 52/25 48| Il 3 | —23 |37 40|—I19 30

20 22 0/24 2] 12 38 | — 9 |35 30|—I19 30

Mean

WUN20S) 23545 12435) 1413 | aa) 21138) 25.— 4-7

12 DiS, 22928) U5 25a Oa 7 saul —— Ae 7

13 23 40)| 24 24) 13 8 | 12137 22|—-4 7

15 28 42|29 56| 12 13 | — 7 |41 25|— 6 31

18 30 20/30 52| II 3 | —25 |4rI 14|— 6 4o

19 30 22|30 00) IL 22 | —I5 |4r 18|— 6 4o

Mean

Gy HOE G 44442 13) 345|, 18) ILO) 35\|——12) 54

II | 100 40 27/38 44] 14 13 | + 5 |53 53] -+10 15

13 42 10,42 40) 13 8 | +17 155 50|-+10 15

Mean

II | II9 16 43/11 55/ 14 13 | + 6] 28 38| +11 41

II | 260 49 18/50 32| 14 13 | + 2] 4 10/— 8 I9

I | 268 18 42!19 55| 12 2} + 6]31r 26|+ 8 Io

2 16 50/17 32} 13 28 | + 6/30 45|+ 8 6

3 17 37|18 22/13 34 | +.9|3t 43;+ 8 6

4 26 12] 26 36) 12 39) + 8]39 11|+ 0 36

5 27, A3\\\27.50)| LL 38) fe 6139 31) + O 18

6 26 38/27 51) Ir 38 | +23 |39 16|+ 0 18

7 22 58123 47| 12 52] +12 |36 26|/+/ 015

8 33 25\/33 30 13 . 3 | -:/8 | 46 38|— 6 15

9 31 55/32 2) 14 30] +18 | 46 46|— 6 15

10 BOHN SS) SSN LS Wee Zone 3040) 40, \——16) 20

| Ai 32 24/33. 5| 14 13 | +.2 | 46 59/— 6 23

12 30 31/31 8| 15 35 | + 5 | 46 30/— 6 23

13 SeeC ONS ONoNa, OF ban OMTAO! (Sila 0) 23

15 38 40/40 8) 12 13 | — 8 |5r 31|—I0 6

16 40 45/41 30] Io 58 | —30 | 51 35|—I0 19

17 42 13/43 27| II 10 | —I19 /53 41|—IO I9

18 | 262 40 53|41 27| II 3 | —27 |52 46|—Io 20

19 40 12/40 58| IL 22 | —r7 |5I 40|—10 20

20 37 53| 38 32| 12 38 | —I0 |50 40/—I0 20

Mean

( Continued).

Paral-

z Fina -

Gone reciear Nagle

jicient. by

ap LOGM NAT a ne uS

+183 Ts

+178 TOMS,

+176 16 6

+176 15 13

+176 TAY 7

—169 I5 10

—I5I Te Oty

—149 16 26

—149 15 20

177 15 24.0

-+ 60] 178 34 9

+ 60 34 0

+ 60 34 1

—> Oy] 34 13

= asi 33 26

yl! 34 19

178 34 1.3

=O Elen OAS

—165 2 38

—165 5 30

GE) BG

—234] 29 38 16

+117] 170 56 2.0

+ 93] 172 40 22

+ 93 40 24

+ 93 40 28

aH 87 39 43

an 0S 40 8

aig iD 40 18

= 978 40 28

+ 92 40 44

+ 92 40 34

ie Ol 40 32

== .99 40 37

+ 90 40 50

+ 90 40 36

— 88 40 34

— 80 4o 18

— 80 40 48

7) ABS

sani) 40 51

==<79 4o 6

172 40 30.0

92 Rutherfurd Photographic Measures of

TaBLE V.—ReEsuLtTs oF Measures oF Distance. (Continued.) 7

Observed Dist. Corrections for Scale Parallax Final |

Varia- | Proper Co- Corrected |

tion, | Motion. | egicient, | Distance.

East. | West. | Refrac.| Aberr. | Scale.

BD 2 | .9723 | .9735| 124 | —2I | 115 | .9944| + 80| —.1815 | —0.587 34.8134 |

3 | .9855 | 9747 | 137 | —2I | 115 | .0029]-+ 58} —.1815 | — .587 .8197 |

(4) | 11 | .6619 | .6613 | rir | —2r | 115 | .6818|— 25] +.1430| — .7or 8133 |

12 | .6594 | .6642) 118 | —2I | 115 | .6827|— 21| +.1430| — .7or 8146 |

13 | .6615 | .6579| 131 | —2I ; 115 |.6819;— 4/|+.1430] — .7or 68155 |

T5 | .5516 | .5545 98 | +2r |] 113 | .5759|— 36| +.2264 | + .815 .8092

18 | .5535 | .5761 99 | +20] 116 | .5880 | — 19] +.2317 | + .887 .8292 |

Mean 34.8164

a4 2 | .4744 | .4310| 106 | —20] 116 |.4726|-+ 78) +.0184 | —0.296] 34.4950 |

II | .4828 | .5022| 105 | —2r | 113 | .5119|— 25] —.o0154 | — .158 -4920

(37) | 13 | .5002| .4982| 106 | —2z | 113 |.5187|— 4|—.0154| — .158 ",5009

Mean 34.4960

30 | II | .5791 | .5869 73 | —I4 | 105 |.5993 | — 16| +.0507 | —0.529| 22.6416

13 | -5724 | .5822 | 79 | —14)| 101 ||.5938 | — 3 | 45-0507 | 2529 6374 |

(66) Mean 22.6395

36 2 | .5805 | .5901 97 | —I3 | I02 | .6039|-+ 51 | —.1805 | —o0.967} 22.4161

3 | .5566| .5800] IT | —13 | 104 | .5884|-+ 38] —.1805 | — .967 -3993

(1) | 10 | .2344 | .2589 84 | —14 | 102 |.2637|— 9] +.1412 | — .952 -3918 |

II | .2540 | .2531 79 | —I4 | I02 | .2702 |— 16| +.1420 | — .945 -3985

I2 | .2634 | .2490 gt | —14 | 102 | .2741 | — 13] +.1420 | — .945 -4027

13 | .2619 | .2501 | 106 | —14| 102 |.2553|— 3| +.1420 | — .945 -4049

15 | .1350 | .1192 63 | +13 98 | .1444 |— 23] +.2249 | + .918 -3788

18 | .1366| .1154| 112 | +13 | to2 | .1487|— 12] +.2301 | + .826 .3882

Mean 22.3977

30 2 | .6800 | .6808 | 146 | —28 | 114 | .7029 | +109) +.0296 | —o0.246| 46.7402

3 | .6756 | .6848 | 145 | —28 | 114 | .7026|-+ 79] +.0296 | — .246 -7369

(35) 4 | .7040 | .6981 | 146 |'—29 | II4 | .7234|— 1, +.0022 | — .007 -7254

5 |.7052|.7086|} 145 | —27 | 114 |.7294|-+ 21/-+.0011 | + .2I10 ee |

6 | .7098 | .6964| 144 | —27 | 118 | .7259/-+ 43] -+.0011 | + .2I10 -7340 |

7 | .7106| .6976| 146 | —27 | 114 |.7267|-+ 44] +.00I0 | + .236 SSE

8 | .7296 | .7294 | I4I | —29 | 114 | .7514 | — 61 | —.0236 | — .200 7191 |

9 | .7345 | -7399| 142 | —29 | 114 |.7592!— 21! —.0236 | — .200 -7309

TO | -7349 | -7305 | 145 | —29 | I14 | .7550 | — 20) —.0239 | — .133 -7274 |

Il | .7333 | -7332| 145 | —29 | I14 | .7556|— 34] —.0241 | — .1c6 -7267 |

T2 | .7322 | .7305| 145 | —29 | 114 | .7537|— 29| —.0241 | — .106 -7253

13 | .7242 | .7366| 345 | —29 | 114 |.7527|— 6|—.0241 | — .106 .7266

I5 | .7390|.7317| 164 | +29 | 118 | .7658 |— 50] —.0383 | — .039 .7220

16 | .7152 | .7370| 232 | +28 | 117 | .763r | — 32|—.0391 | — .184 -7184

LZ | 735° | -7275 | 197: | --28 | 114 1.7648) >— 34 | 0301) od 7199

18 | .7323 | 17253 | 232 | +28 | 114 | .7655 |— 26] —.0392 | — .196 -7212

19 | .7366|.7198|} 195 | +28 | 114 | .7612 |— 16} —.0392) — .196 -7179

20 | .7277 | .7378| 172 | +28 | 116 | .7637 |— 59] —.0392 | — .196 -7161

Mean : 47.7266

Sixty-five Stars near 61 Cygni.

TapLeE VI.—Resutts oF MEAsuRES OF ANGLE. ( Continued.)

= Observed Bosision gece Cor- Paral- he

° East. West. | Preces- ficient.

sion, ete. Dp

2 | 111 10 24 10 52 13 28. +14 | 24 20|—10 22 —165 or 13 59.

3 To 48|1I 30) 13 34 | +20 ]25 3)—I0 22|—165 13 48

II | 110 54 46/55 46| 14 13 |} + 6] 9 35/+ 8 15|—147 I6 26

12 SS aes SES Soest e tlie 2 ats Oy 25) Ay, 14 54

13 5B US| 55 Sh) 1B 9S [aR | 7 AO) ae 8 15 | aay 15 32

15 Ag 1748 43) 12 13 | + 1 | © 14) --13 6 | +126 14 46

18 HOMASNS 2 7 oEL 3) ee 255) 3 29)| a1 23, 25)| ar 1.97 16 39

Mean 21 15 9.1

2M230563 27/13) 69)) 13, 28 7 || 16 49)|-7-20 56-199) 146) 39 57

II Ar)28)| 40° 4| 14 13, | — 4 |54.55|—16 30) --207 39 8

13 40 23140 53| 13 8 | — 8 |53 38|—16 30| +207 38 46

Mean 146 39 17.0

II |213 17 2!'17 24| 14 13 | — 6|31 20/—24 2)-+269]123 8 24

13 17 25|17 40/ 13 8! —17 |30 23|}—24 3)|-+269 8 21

Mean 13 13) DAG

2 |17I 48 14/47 43] 13 28 | — 5] 1 22|+16 30|/-+ 44] 8219 8

3 ADAG) jt n2 ats Saale Onl Ee 5Oh si WO) 30) s1= 4a 18 42

Io | 172 18 12/19 36) 13 7 | — 3/31 58|—13 8/-+ 83 18 59

II 18 17/20 29] 14 13 | — 2 |33 34|/—13 13/-+ 91 20 23

12 18 48/16 43| 15 35 | — 4 133 17|/—13 13/-+ 91 20 48

13 Ig 20/18 4o| 13 8 | — 8 |32 o}]—13 13/-+ 91 Ig 44

15 29 8/29 8] 12 13 /| + 2/41 23/—2r 1/|/—139 I9 13

18 29 55/31 II) 11 3] +27 |42 3|/—21I 30/—183 18 37

Mean 82 19 26.8

2/239 6 5] 655|] 13 28 | — 5 |19 531-15 3)|+146] 149 36 49

3 GW Osh SS UG | eh vl ay tele Te) Sn) Baca) 37 21

4 22 14|22 52] 12 39 | — 7135 4 I 8|-+152 36 32

5 24 14|24 12] Ir 38 | — 6 135 45|+ © 33] +145 37 2

6 PIE ODEs Fi OE KV OE en) Be as 37 47

a IQ 22/20 25| 12 52 | — 8/32 38|-+ 0 29] -+143 37 19

| 8 S525) 5404S) Sr tae O48 42)/——1 0 ai 148 37 46

joo) Sel 1 | ML A) | LAO) |) NN) G5) | a Bi) = acs) 37 21

10 35 18|35 28) 13 7|— 3 |48 28|—11 48| +151 By TR

; 11 B40 18)3452 04 33) i 3/4845, 90 152) a5 37 16

12 BL 5 (82 35) 25 SS | = & ay MA aaah 6 | ope 36 57

13 Ba | BA SE US S| = © di BO Be | aia 36 46

15 AASB 2 VASES 2a aie Li Si El | Oh A E56 a7

16 46 17|47 26) Io 58 | —32 |57 18|—19 I1| —152 26 43

17 48 28'49 4] 11 I0 | —22 |59 34|/—19 11|—152 Ba; QR

18 46 30/47 O| Ir 3 | —29 |57 19/—I9 13|—I51 36 22

19 46 3/46 18| 11 22 | —20 |57 12|—I9 13] —I51 oye:

20 AAS FAAS 5) i238) Snlh7 | 9) 13,| 151 37 8

Mean 149 37 6.6

94 Rutherfurd Photographic Measures of

TABLE V.—ReEsutts oF MEAsuRES OF Distance. ( Continued.)

ry | Observed Dist. Corrections for Cor- | geale Parallax Final

Star pr | PeeM a SER rected | varig- | Proper Co- Corrected

No. o Mean. | tion. | Motion. | eficient, | Distance.

Kast. | West. | Refrac.| Aberr. | Scale.

38 2 | .1008 | .0942| 337 | —66 | 113 | .1274 | +255 | +.0898 | +0.043 | 112.2433

3 | .0889 | -IOII | 340 | —66| 113 | .1252 | +187 | +.0898 | + .043 2343

(32) | 11 | .2728'| .2700 | 336 | —68 | 113 | .3009 |— 80| —.o711 | +- -187 .2242

12 | .2472| .2810| 335 | —68 | 113 | .29035 |— 67|—.o711 ! + .187 .2181

13, | .2560 | .2598 | 336 | —68 | 112 | .2873 | — 14| —.0711 | + .187 .2172

15 | -3051 | .3069| 345 | +68 | 113 | .3500 | —118 | —.1127 | — .335 .2212

18 | .2970 | .28560| 334 | +65 | 113 | .3339 | — 60) —.1154 | — .475 . 2064

Ig | .2952| .2910| 392 ; +65 | 113 | .3415 | — 37 | —.1154 | — -475 .2163

20 | .2980 | .3130] 360 | +65 | 113 | .3507 | —139| —.1154 | — .475 .2153

Mean 112.2206

39 r | .8614 | .8446| 383 | —67 | 130 | .8886 | +222 | —.1662 | —o.433 | 113.7390

2 | .8448 | .8534 | 383 | —68 | 105 | .8822 | +259 | —.1651 | — .473 -7369

(8) 3 | 8484 | .8438 | 415 | —68 | 106 | .8825 | +190| —.1651 | — .473 7303

6 | .7040|.7114 | 506 | —66 | 105 | .7533 | +102 | —.o060 | — .798 -7473

9 | 5794 | -5372| 466 | —69 |. 103 | .5994|— 50| +.1274 | — .517 -7152

Io | .5686 | .5601 | 362 | —69 | 107 | .5955|— 46/ +.1295 | — .575 -7130

II | .5678| .5612| 354 | —7o | 105 |.5945 |— 81/| +.1302 | — .598 .7089

13 | -500% |)-5579) | 4047) ——70 |) 108) "5943) 915) |= aoa) age 7153

15 | .4675 | .4617| 322 | +69 | 108 | .5057 |—119| +.2062|-+ .724 - 7093

16 | .4474| .4601 | 324 | +66! 108 | .4946|— 76| +.2106 | + .809 .7080

17 | .4422|.44c8| 317 | +66 | 108 | .4818 | — 8r| +.2106 | + .809 .6947

18 | .4532 | .4473| 331 | +66] 108 | .4919|— 61| +.2110/ + .816 -7073

19 | .4398 | .4573| 326 | +66] 108 | .4897 | — 37| +.2110| + .816 .7075

20 | .4372 | .4402| 324 | +66 | 108 |.4797 | —141| +.2110 | + .816 .6871

Mean . 113.7157

40 2 |.1750|.1744| 288 | —57 | 138 | .206r | +219| +.0763 | —0.025]| 96.3040

3 | .1687 | .1808 | 290 | —57 | 138 | .2063 | +160] +.0763 | — .025 2983

(33) | Ir | .3050 | -3063 | 287 | —59 | 138 | .3367 | — 69] —.o605 | + .119 .2708

12 | .2842| .3048| 288 | —59 | 138 | .3256|— 58| —.0605 | + .119 .2608

13, | .3034 | .3065 | 289 | —59/ 138 |.3361 |— 12|—.0605|+ .119] ° .2759

15 | 3279 | .3275 | 308 | +59 | 138 | .3726 | —IOI | —.0959 | — .267 .2632

18 | .3268 | .3224| 393 | +56 | 138 | .3777 |— 52| —.c982 | — .414 .2690

Mean 96.2774

41 2 | .O4T4 | .0432| 120 | —20 | 126 | .0646|-+ 78} —.0685 | —0.650]| 33.9956

(38) | 15 | .8546|.8660] 131 | +21 | 126 | .8878 | — 35 | +.0841 | + .426 -9739

Mean 332.9848

42 2 | .2542| .2492| 422 | —73 | 112 | .2864/|-+281 | —.1703 | —o.508 | 123.1377

3 | .2624 | .2463 | 457 | —73 | I07 | .2920 | +205 | —.1703 | — .508 .1357

(7) | 16 |..8572 | .8356| 345 | +72 | 112 | .8879|— 82) +.2172 | 4+ .833 .1076

18 | .8465 | .8353| 356 | +72] I10 | .8833 |— 66| +.2176 | + .839 - 1051

19 | .8395 | .8350| 352 | +72 | 112 | .8794|— 40/ +.2176 | + .839 .1038

Mean 123.1180

Sixty-five Stars near 61 Cygni. 95

TaBLE VI.—REsvuLts ofr MEASURES OF ANGLE. ( Continued.)

HW Observed Position pee Cor- Paral- Ene

East. West. | Preces- ficient.

sion, ete. iD 7

(0) d “i /) “i d 4 a 4 Md 4 Mi {e) / a

2 | 256 27 28| 28 18| 13 28 | + 2 | 41 24/+ 5 53/+ 64| 166 48 4o

3 28 27| 29 48| 13 34 | + 6 | 42 48)+ 5 53/+ 64 49 10

II 89 Al ao 2S wal Tey ae Se BO = 12), Biel a tos 48 44

12 37 BSS7 22 | 25) SS ap SR LOae AU sel see 49 6

13 29 UO! 6 dB us 1S) ae G62 Bi 4 Bsilae 6B 48 48

15 Al U2 | AIS) |) WAS | N09) || G7) 5) || == 7) AO —— Ce 49 34

18 ACTON A gO) Petey) 2OM 5 7a ata 5 48 27

19 HO A2)) Ui) NS) i 2 i al) || iy AS | —— yt SS) 49 55

20 AVAL SG) |) AUR V5) || SSS) | DG ip at 49 22

Mean 166 49 5.1

I |103 812} 9 4/12 2] +14 |20 54|— 3 54/— 56] 13 16 53

2 6 25| 7 13| 13 28 | +12 | 20 29|/— 3 52|— 55 iy 17)

3 TNS) 24) 1S ae sd Wa TO QIAO 3052 | 55 17 34

6 4 30/ 6 2) 11 38 | +38 |17 32/— 0 9|/— 35 Gf AG)

9g | 102 59 56| © 22) 14 30 | +32 /15 1r|+ 3 o]/— 54 17 22

1© | ZOB 2) WSS) 1 F pap Pe dele as ela 5 17 4

Al | 102 59 G2 O Go| awh Ge lise 5 ji Bea ele ko) 16 48

13 |103 00 2] 0 53/13 8 | +18 113 51/+ 3 4|— 50 17 I

I5 | 102 59 47| 0 47] 12 13 | — 2 |]12 28)/+ 4 51)+ 45 17 16

16 |103 I 13] 2 23] 10 58 | —12 |12 34|/+ 4 57/4 38 17 16

17 2 22) 3 13/ 11 Io | — 7 |13 50|\+ 4 57/+ 38 16 56

18 055| 157| If 3 |—I0/12 19|/+ 4 58|+ 37 16 40

19 | 102 59 48/ I 5/11 22 |) — 2 ]/11r 47/+ 4 58|+4 37 16 57

20 59 16/59 44| 12 38 | — 3 [12 5;+ 4 58/+ 37 17 30

Mean 13 17 8.64

2 |252 27 5/26 16| 13 28 o}/4o0 8/+ 7 3/+ 74| 162 48 38

3 BS eis) eis) || Me VL as ae |e Sue Paes a 7/2) 49 27

II 40 35|41 15| 14 13 O55 == See ae 76 49 30

12 39) JE NSS 5) HS) BS || ae © 5S SO | 5 8 eas 50 34

13 40 15) 49 53] 13 an 25S 2 Gy Sh 7s 49 I

15 AGU Alyy AMS || Tie? aig ae | 59) ei tS) 2) | 49 27

18 47 52|47 58|/ I 3 | —30 |58 28; — 9 1);— 69 48 12 f

Mean 162 49 15.6

2|212 1 28) 2 24| 13 28 | —13 ]15 11/ +20 8|-+158]| 122 37 16

15 49 32;51 18| 12 13 | — 6] 2 32|—25 17|—1I99 35 44

Mean 122 36 30.0

2 | 105 25 50| 26 42/ 13 28 | +12 | 39 56|— 3 22|— 50| 15 37 16

3 27 17|27 13/ 13 34 | +18 ]41 7/— 3 22|}/— 50 37 33

16 21 57| 23 13| 10 58 | —10 |33 22|/+ 4 19/+ 33 37 24

18 2I 7/22 12/1 3 —g | 32 46|-+ 4 20|+ 32 36 28

19 21 42/21 17/ 11 22 | — 4/32 47/+ 4 20|+4 32 37 18

Mean I5 37 11.8

96 Rutherfurd Photographic Measures of

TABLE V.—Resutts oF MEAsuRES OF Distance. ( Continued.)

Observed Dist. Corrections for Cor- Parallax Final

rected Proper Cc Corrected

Mean. Motion. ient. | Distance.

East. | West. | Refrac.} Aberr.| Scale.

s o

-1198 | .1144| 199 To8 |} .1423 + .0087 ; 65.1589

.1202 | .1164 | 202 Io5 | .1434 +.0086 : -1624

.1072 | .1286 | 206 Io5 | .1434 +.0086 : .1584

.1334 | .1292 | 201 IO5 | .1562 —.0072 2 -1433

.1330 ; .1302 | 199 To5 | .1563 —.0072 : -1418

HATA |) oeaaal | Bon Io5 | .1597 —.0072 ; -1460

.1285 | -1371 | 204 I05 | .1580 8 | —.0072 : -1474

-I1291 | .I1129}] 231 14 | -1578 —.O116 : -1402

-1065 | .1251 | 339 IIo | .1628 —.0120 - -1453

sO aos |) R27 to8 | .1500 —.0120 F .1332

.1082 | .IOOI | 277 105 | -1445 —.O120 ‘ -1291

-1226 | .1394| 243 To8 | .1682 -—.0120 | — . -1468

Mean 65.1461

44 2 | .12I14].1514| 187 | —34 | 108 | .1614 | +130] —.0286 | --0.496 57.1394

3, | .0957 | .1632|} 194 | —34 | I08 |.1552|-+ 95 | —.0286 | — .496 .1297

(36) | 10 | .1050 | .o813 | 182 | —35 | Io04 | .1172|— 23) +.0219 | — .396 Shey)

II | .1076} .0924| 179 | —35 | 107 | .1240|— 41] +.0221 | — .372 .1372

13, | .0948 | .0884 | I9I | —35 | I04 |.1165/— 7] +.0221 | — .372 -1331

I5 | .OOIL | .0733| 214 | +35 | 107 |.1017 |— 60] +.0347 | + .240 -1335

Mean 57.1341

45 2 | .2294| .1670| 379 | —63 | III | .2336] +253} —.1844 | —0.609 | 106.0667

15 | .7967| .7729 | 300 | +64] 111 | .8250 | —1II! +.2306 | + .832 .0552

(54) Mean 106.0610

@) II | .3643 | -3373 | 157 | —27 | 124 | .3757|— 32] +-1385 | —0.932| 44.4990

4% | 12 | .6216| .5740| 391 | —8o 32 | .6184 | — 78 | —.0516 | +0.063 | 130.5598.

13 | .5923 | -5929| 386 | —8o0 32 | .6127 | — 17| —.0516 | + .063 .5602

(63) | 19 | .6220| .6042] 478 | +76 30 | .6579 | -- 43 | —.0838 | — .362 .5052

Mean 130.5617

48 I | .8930 | .8908 | 202 | —30]| 115 |.9198|-+ 99| —.1233 | —0.849| 50.7955

2 | .8974 | .8948 | 198 | —30 | 114 | .9235 | +116} —.1224 | — .832 .8020

(44) 3 | .8927 | .9083 | 222 | —30 | 114 |.9303|-+ 85) —.1224 | — .832 .8057

4 |.7802|.7702| 214 | —31 | 114 | .8041|— 1] —.cogi | — .686 - 7861

5 | .7692 | .7614| 208 | —29 | 114 |.7938|-+ 33] —.0044 | — .499 .7863

6 | .7539>| -7722 | 265 | —29 | 116 | .7975|-+ 45 | —.0044 | — -499 -7912

7 | -7687 | -7475 | 233 | —29 | 110 | .7887|-+ 47 | —.0039 | — -472 -7834

8 | .6814 | .6796| 213 | —30] 114 | .7093 | — 64] +.0941 | — .809 -7866

9 | .6653 | .6743 | 245 | —30 | 114 |.7019 |— 22] -+.0941 | — .809] .7834

Io | .6770|] .6815 | 18r | —31 | 114 | .7048 | — 21] +.0957 | — .771 -7885

II | .6818 | .6780 | 172 | —3I | 114 |.7046 |— 36| +.0962 | — .755 -7875

I2 | .6745 | .6767| I92 | —31 | 114 | .7023 | — 30] +.0962 | — .755 -7858

13 | 6705 .6747| 215 | —3I | 114 |.7o16;— 7| +.0962 | — .755 7874

I5 | .6026 | .5930|] I99 | +31 | I16 | .6316 | — 53) +.1522 | + .672 -7871

16 | .5727 | .5882| 298 | +30] 116 | .6241 | — 34| +.1555 | + -547 -7832

I7 | .5852| .5900| 251 | +30] 116 | .6265 | — 36) +.1555 | + .547 7854.

18 | .5812 | .5751 | 293 | +29 | 115 | .6211 |— 27}| +.1558 | + .534 -7811

19 | .5778 | .5737 | 246 | +29 | 114 | .6138|— 16] +.1558| + .534 -7749

20 | .5964 | .5919 | 256 | +29 | 116 | .6334)— 63| +.1558| + .534 - 7898

| Mean 50.7880

a at

Sixty-five Stars near 61 Cygni. 97

TaBLE VI.—ReEsouts or MEASURES OF ANGLE. ( Continued.)

Observed Position Zero E

< Angle. Correc- oe, Proper ae Final Cor-

2 tion plus | Refrac. pegied Motion. | Coej- | rected Angle.

° East. West. | Preces- See ficient.

sion. etc. p =

(eo) / 4d / a / Mt “i vi di d td fo} ad

I | 233 26 4/27 20) 12 2) — 9 | 38 35|-+11 13| +101} 143 50 37

2 23 47| 24 40) 13. 28 | — 8 | 37 34|+11 8) +104 50 19

3 2PAAN 2545) 013, 6 34 tOnIB9) SO) = Et 28) 2104 50 59

10 AOR OWAT Oe AN Sey) fin 2 M59) SS) == 440) 1 FS HO 7

II AS eerAN ASRS 2A eT Se eA SOR Gili On 47a. 109 50 58

12 ABW ESAS 33) 15) 50-27 oo 2) 8 474 = Tog 5° 55

13 ASE SOMoN sos) NO ae LLNS 8) Al | 848i) 109 50 56

15 53 28/55 5) 12 3 | —II | 6 19|—13 55|—I114 5I 24

16 55 58/55 13} I0 58 | —29]} 6 5|—I4 13|—II3 50 42

18 54 56/55 52| II 3 | —27 |] 6 48)—14 15|—I12 Bi

19 54 48/56 15| II 22 | —19}] 6 35|—1I4 15|—I12 51 39

20 52 13/52 18|/ 12 38 | —12] 4 42|—14 15|—112 50 I

Mean 143 50 53.3

2 | 223 19 12|16 18] 13 28 | —11 |3r 2|+12 35|-+108] 133 45 16

3 17 30/19 20| 13 34 | —16 | 31 43] +12 35| +108 45 3

Io AES SPAS Ay U3 m ted li=- 67a bS4 DAU 05S) te HHO 45 22

II Ber AB | AN UG aL ag} GN A i 0) Gell Sa 1ey/ 44 23

13 AO) GE AO | eS) Ue || bah AS eG) BO ey) 44 55

15 50 8/50 40| 12 13 | — 9] 2 28)—15 45|—126 45 39

Mean 133 45 6.3

2|II2 43 4/42 ©] 13 28 | +14 156 14|— 3 12/— 53] 22 53 43

15 37 44) 37 40) 12 13 | + 21/49 57|+ 4 I/|+ 40 53 53

Mean 22 53 48.0

II | 174 32 24/32 0] 14 13 | — 2 |46 23;|\— 7 6/-++ 52] 84 39 5.0

12 | 249 19 12| 20 30] 15 35 | — 2 |35 24|— 4 12|/+ 56] 159 31 43

13 22 41|23 17/13 8 | —11/136 6|— 4 12/+ 56 22 38

19 28 15|29 O| IL 22 | —2I | 39 38|;— 6 48|— 53 32 30

Mean 159 32 17.0

I | 195 28 36/29 55| 12 2)|—14 /4t 4/|-+11 41|-+ 68] 105 53 22

2 25 48| 26 26/ 13 28 | —12 | 39 24|)+11 36|+ 74 52 27

3 Dip iy | 2S BIS) Ee mani) | Au Ot eae 6) ea 7h 53 50

4 38 16/39 26] 12 39 | —16]51 15|+ 0 52|-+102 52 9

5 Aly 7,42 (49) (UL 938) ——15 1/53 26\|/-- © 25)) 4-119 54 26

6 40 58) 41 57| It 38 | —39 |52 27) -+ © 25|--1T9 53 52

7 36 23 | 26 53| 12 52 | —25 |49 5|-+ © 22/121 53 32

8 48 38 | 50 Ty | GS) 2 aC) Ola 230 53 24

9 ASh1O)W40)) 1254) 30) 335/12 33i\—— 9, Ol) 180 53 32

10 ABP 5AVAS AG N13 79 —— "Set 49)/-— 9 9)| - 89 52 51

II 47, 2849-7 14 13. = 6 | 2 25 9 12|+ 92 53 15

12 AS Su Aree One N Som lO ali Size On L2i| 792 38) &

13 47 28| 48 43) 13 8 | —18}] 0 56|— 9 12/-+ 92 52 AI

15 SSRN eh eel ou ee hale Os 42h 1435) —— TO 52 58

16 Sea SIe OMS onesie Ole 9 27 )—=14 54) —_r2n 53 20

17 59 30| 0 18| 11 I0 | + 6/11 I11|—14 54|—121 53 28

18 57 5157 12| 11 3/]+ 77] 8 18|—14 56|—122 51 48

19 57 7) 50 45) 22) se 40) © Be | adh Glo | — aie 53 I

20 54h Si | 32 Se | 02 BS jy se 1) 3) ee AU BO) Sich

Mean 105 53 10.6

ANNALS N. Y. ACAD., Sct.

X, August, 1897.—7.

TABLE V.—RESULTS oF MEASURES OF DISTANCE.

Rutherfurd Photographic Measures of

Observed Dist.

Corrections for

( Continued.)

I Cor-_ | Seale Parallax Final

ao = rected | Varia- pnover Co- Corrected

(9) {I | .7198 | .6913 | 191 | —35 | IIo |.731I1 |— 41| +.0740 | —0.648] 57.7927

50 I | .8328 | .8330 | 229 | —34 | 110 | .8622 | +115 | —.1125 | —o.818] 58.7507

2 | .8461 | .8266| 225 | —35 | 108 | .8650 | +134 | —.1117 | — .798 -7565

(43) | 3 | 8240} .8310} 245 | —35 | 108 | .8581 | + 98| —.1117 | — .798 -7460

6 | .7042 | .7006| 292 | —34 | 110 | .7380 | + 52|—.0040 | — .447 -7335

9 | -6356 | .6495 |" 272 | —35 | 108 | .6759 |— 26] +.0858 | — .773 -7492

10 ! .6264 | .6376| 206 | —36 | 106 | .6584 |— 24] +.0872 | — .732 -7339

II | .6362! .6416| 197 | —36 | 108 | .6646 | — 42) +.0877 | — .714 -7389

I2 | .6252 | .6469| 217 | —36 | 108 | .6637 |— 35, +.0877 | — .714 -7387

13 | .6383 | .6366| 239 | —36 | 108 |.6674|— 8] +.0877 | — .714 -7451

15 | 5651 | .5525 | 231 | +36] 110 | .5953 | — 61| +.1389| + .623 -7361

16 | .5421 | .5413 | 350 | +34 | I12 | .5901 | — 39| +-1418 | + .494 7343

17 | .5392 | 5627 | 292 | +34 | II2 | .5935|— 42| +.1418 | + .404 -7374

18 | .5536 | .5380| 341 | 434 | IO | .5931 |— 31| +.142T | + .481 -7393

19 | .5278 | .5230| 285 | +34 | 108 | .5669|— 19] +.1421 | + .481 ABE

20 | .5624 | .5660| 242 | +34 | 108 | .6014 | — 73| +.1421 | + .481 -7424.

Mean 58.7396

ie 2 | .8800 ; .g059| 340 | —63 | 118 | .9249 | +243 | —.0074 | —o.409 | 106.9365

52 I | .3976 | .3860| 312 | —45 | 137 | .4295 | +149 | —.1365 | —0.883] 76.2966

2 | .3822 | .3992 | 306 , —45 | 136 | .4277 | +174| —.1355 | — -869 .2984.

(45) | 3 | -3848|.419r | 339 | —45 | 136 | .4422| +127 | —.1355 | — .869 -3082

Io | .1701 | .1525| 277 | —46 | 136 | .1953 |— 31| +.1061 | — .818 .2878

Ir | .1598 | .1582 | 263 | —47 | 136 |.I915 |— 54)| +.1067 | — .802 2825

12 | .1513 | .1481| 293 | —46 | 136 | .1853 |— 46| +.1067 | — .802 2277

13, | .1288] .1570| 334 | —46 | 136 | .1826 | — Io| +.1067 | — .802 .2780

15 | .0628 | .o610| 299 | +46] 140 | .1077|— 80| +.1689 | + .729 .2780

16 | .0323 | .O501 | 446 | +44 | 136 | .torr |— 51|+.1725 | + .611 .2763

18 | .0378 | .0366| 435 | +44 | 136 | .o960|— 41| +.1729 | + .599 .2725

Mean 76.2855

53 I | .0292 | .0332| 338 | —44 | 136 | .0715 | +148 | —.1840 | —0.969} 75.8899

2 | .0322 | .0274| 326 | —45 | 136 | .0688 | +173 | —.1827 | — .970 .8909 |

(2) 3 | .0089 | .0216| 375 | —45 | 136 | .o592 | +127 | —.1827 | — .970 .8767 —

6 | .8531 | .8279 | 499 | —44 | 140 | .8973 |-+ 68 | —.0066 | — .708 .8873

7 | .8662 | .8756| 41rI | —43 | 136 |.9186|}-+ 70} —.0058 | — .778 -9098

9 | -6960 | .7096| 452 | —45 | 136 | -7544|— 34| +-1411 | — .968 -8797

Io | .7138| .7182| 288 | —46 | 136 | .751I | — 31} +.1433 | — .957 .8790

II | .7125 | .7225 269 | —46 | 136 | .7507 | — 54]/ +.1441 | — .952 .8772

12 | .7044|.7109| 310 | —46 | 136 | .7449|— 45| +.1441 | — .952 8723

I3 | .7131|.7071 | 363 | —46 | 136 | .7527)— Io| +.1441 | — .952 .8836

5 |.5971|.5812| 281 | +46 | 140 | .6332 |— 79| +.2283 | + .927 -8655

16 | .5842 | .5820| 382 | +44 | 140 | .6370|— 51| +.2331 | + .848 .8759

17 | -5973 | -5906| 333 | +44 | 140 | .6430|— 54| +.2331 | + .848 -8816

I8 | .5763 | .5611| 376 | +44 | 138 | .6218 | — 41) +.2336 | + .838 .8621

19 | .5838 | -5694| 333 | +44 | 134 | -6248|— 25 | +.2336| + .838 8667

20 | .5980 | .5938| 292 | +44 | 136 | .6404 | — 94| +.2336 | + .838 8754

Mean 75.8796

Sixty-five Stars near 61 Cygnt. 99

T'ABLE VI.—ReEsutts or MEASURES oF ANGLE. ( Continued.)

= Oe een Ga ane Paral-

— . \ SS Pr ] =

g gn ns ERG ae | le | anes | eset

East. West. | Preces- Jicient.

| sion, ete. p 7

fe) é “d d dd ‘ Md 4d / a / (e) 4 ad

ee 5045, AL ASipi4 1316/54 54) —— 8 534 95 | 114 46 4.0

it |) WG)! © Ass || ae iv) aw —i} UD 37) || j=1O) 3 + 66 109 23 46

2 | 198 58 34/59 32] 13 28 | —13 | 12 18/-++10 28) -+ 71 24 12

3 59 30| I 17| 13 34 | —20| 13 4r)/+10 28/4 71 24 4I

6 |199 12 8/13 4/ Il 38 | —39 | 23 35|+ © 23] +107 24 53

9 18 10/18 50| 14 30 | —33 132 27; — 8 7|-+ 76 24 17

ae) 18 23,18 46) 13 7 ; — 8'}31 34;— 8 14/+ 82 23 29

II 18 7|\18 59| 14 13 | — 6 |32 40|— 8 17|+ 85 24 23

12 TOMES) 55 O) eS. S50 ie E130) 23) Soa O5 23 48

13 I7 48|18 55| 13 8 | —I19 |] 31r 33/— 8 17|-+ 85 24 I1

15 25 28/27 22| 12 13 | — I |38 37|—13 8/|—100 24 34

16 26 21/28 21] 10 58 | + 7 | 38 26|—13 25 |—TIo9 23 53

17 28 37|29 22) Ir 10 | + 2]|40 12|}—13 25|—1I09 Di B

18 2S 2730 el tae pleats e|35) 401-13) 27 || 109 23 44

19 26 53|27 40| Ir 22 | + 2138 41 |—13 27|—I09 24 34

20 24 43|26 12| 12 38 | — 11/38 5]|—13 27|—I09 24 13

Mean | 109 24 10.7

2 |229 I9 12}20 3/13 28 | — 9 |32 57|+ 6 48!-+ 61] 139 41 7.0

Pe KOTM TY IAN 2) 381) 12) 2) |e —=TA) 13 49|-+ 7 20|-+ 39] Ior 21 36

2 | 190 59 52| 0 53] 13 28 | —12 |13 38/+ 7 17/+ 43 22 10

Be Lee Ons ete 21[bi3 349) — 1S (n3, 5A 7 17 43 21 32

10 TAE2S NS OH eTGy) 7a) 7 27) 401) — 5) 44) 1-253 22 0

II MaMa aE 4S ek Aeon O27, SON 5 401 55 21 38

12 AZO) PRS Si T5h 5a OE 2ON 55 (t= FAO a 55 21 4o

13 TSS See UAW ets aS ele 2055) 5240) -f 55 22 53

15 I8 23|19 38) 12 13 | + 2/31 15;|— 9 9|— 68 2I 23

16 20832 (2092351058) |) --14 | 30 42 — 9 21 | 76 21 25

18 18 40/20 4| II 3] +11 |30 36|— 9 22|— 76 19 57

| |Mean| . | IOI 21 31.4

a eZ OAS Te ASIS5 Ite. 25 te OST lict Asay lat y 7). SE p 5) 34

2 AGR22) AGT SOl es 28) p05, 159059), 4.45) LE 5 48

3 AONAS) AS) Is 9345 eS tek ANT A ASH to La 5 59

6 HOR 253) A7alee Ou 2On te Se Silt ONTO) —2/52 5 54

7 AQW St AON 423 gla 520 Ele te 2 3) = OPO) = 54 5 52

9 55 12/56 25; 14 30 | —I7/Io 1|— 3 41|-+ 16 5 56

10 ONION ONS Siu eal 2 Oe 20) 3-45) | 22 5 gE

II Be ROMS ORAS etAS Tap ea) oy T2)|/—— 3546) 125 6 4

12 BROAN EES, 300 ieee 9) 83) 3) AO) 25 5 47

13 BOONSO052 NIG (S709) 30i|— 3) 46) = 25 6 17

15 HOIAAN Oo) 284) 12) 3) to) P2928, 95/59 |—= 39 5 56

16 |171 1 32| 218] 10 58/ +29 ]13 22/— 6 6/— 52 6 28

17 I 52] 3 37/ 11 10 | +20|14 14;— 6 6|— 52 5 44

18 Lae II 3] +27 |12 42;,—6 7)|— 52 5 26

19 © Io} 0 48| 11 22) +17 |12 8|\—6 7|— 52 5 41

20m EONS SRA S59 esl L2= Sonn LE l2) LO — On 7 | 52 5 58

| Mean Sie) by See

100 Rutherfurd Photographic Measures of

TABLE V.—RESULTS OF Measures or Distance. (Continued.)

Observed Dist. Corrections for Cor- | geale Parallax | _ Final

;

uae)

Star | & rected | Varig-| Proper Co- Corrected | —

: @ Mean. | 43 Motion. i i i)

a f East. | West. | Refrac.| Aberr. | Scale. ie HLQa ebieteries ce ‘

54 I | .4460 | .4362| 344 | —45 | 137 | .4820| +151] —.1890 | —0.972| 77.2956

2 | .4637 | .4137) 333 | —46 | 135 | .4806 | +176 | —.1876 | — .975 .2981

(3) | 3 |-4183 | .4360| 385 | —46 | 134 | .4716 | +129] —.1876 | — .975 .2844

9 | .0746 | .0985 | 468 | —46 | 134 | .1393 |— 34] +-1449 | — .975 -2683

10 | .0965 | .1053 | 2904 | —47 | 134 | .1362 |— 31] +.1472 | — .969 .2679

II | .0990 | .0974 | 274 | —47 | 134 | .1315 |— 55/| +.1480 | — .964 .2616

I2 | .0802 | .0902| 316 | —47 | 134 | .1227|— 46) +.1480 | — .964 .2537

13 | -0853 | 0943 | 372 | —47 | 134 | .1329 |— 10] +-.1480 | — .964 -2675

T5 | .QQII | .9729| 227 | +47 | 130 | .o196|— 81| +.2344 | + .946 .2570

16 | .9606 | .9866 | 375 | +45 | 135 |.0263 |— 52/| +.2394 | + .873 eile

17 | .9814 | .9784| 330 | +45 | 135 | -0281 |— 55) +-2394| + .873 .2732

18 | .9590 | .9661 | 373 | +45 | 134 | .o150|— 41/| +.2398 | + .864 .2618

20 | .9690 | .9765 | 293 | +45 | 135 | .0172 |— 96] +.2398 | + .864 -2585

Mean 77.2707

53 =| I2 | .6444 | .6202 |} 416 | —82 17 | .6525 |— 81 | —.co89 | —0.194 | 134.6330

13 | .5973 | .5996| 417 | —82 17 | .6186 | — 17 | —.0089 | — .194 .6055

(59) | 18 | .6110 | .5766| 670 | +79 20 | .6557 | — 72| —.o146 | — .108 .6325

Mean 134.6237

56 2 | .3874 | .3912| 474 | —69 | 130 | .4329 | +267 | —.2077 | —o.833 | 117.2412

3 | .3788 | .3658 | 541 | —69 | 126 | .4222 | +106| —.2077 | — .833 .2234

(6) | I1 | .0598 | .0434| 398 | —71I | 122 | .0867 | — 84| +.1639 | — .908 -2305

15 | .9152| .9fI1 | 354 | +71 | 124 | .9584 | —122| +.2597 | + .979 .2185

16 | .8690 | .8820| 360 | +68 | 124 | .g2I0|— 78] +.2653 | + .993 .1913

18 | 8900 | .8905 | 372 | +68 | 124 | .9368 | — 63] +.2658 | + .993 .2091

19 | .8798 | .8847| 368 | +68 | 124 | .9285 | — 38] +.2658 | + .993 -2033

Mean 117.2168

BY¢ 2 |.7927 | .7629| 445 | —64 | 122 } .8204 | +245 | —.20908 | —c.881 | 107.6238

(53)

ite) 2 | 8308 | .8107| 349 | —53 | 138 | .8597 | +205 | —.1171 | —o.815]| 89.7526

18 | .4881 | .4839| 519 | +52] 135 | .5522|— 48| +.1493 .508 . 7032

20 | .5215.|.5150| 371 | +52] 132 | .5693 | —111] +.1493 -7140

Mean 89.7201

IO | 6051 | .6227| 316 | —55 | 138 | .6493 |— 37| +.0917 | — .752 -7276

(47) | 11 | .6066 | .6086 | 303 | —55 | 134 ! .6414 |— 64] +.0922 | — .735 7178

12 | .5642 | .5797 | 336 | —55 | 134 | .6091 |— 54/ +.0922 | — .735 6865

13 | .6056| .6115 | 374 | —55 | 134 | .6496|— 12] +.0922 | — .735 -7312

15 | -5336|.5150| 353 | +54 | 135 |-5741|— 94| +-1459| + .649 .7189

16/5060) 5177 | 533 | 52) 137 1-577 ee CON LAge ac 521 - 7294,

“TABLE VI.—ReESULTS OF MEASURES OF ANGLE.

Sixty-five Stars near 61 Cygni.

Observed Position

Zero

101

( Continued.)

ry Correc- er P Le Final Cor-

= tions plus| Refrac. nee NOHO. Coef- rected Angle.

° East. West. | Preces- ficient.

sion, ete. iD 7

{o) i a / al i “i Md vi vi “i fe) a Mt

I | 167 59 33/ 0 3) 12 2/]—4]{1r 46;+ 4 18/+ 2] 78 16 18

2 56 40/57 8| 13 28 | — 3 ]I0 19/+ 4 16|/+ 6 15 37

3 57 SO/ 59 Ay | 1g) Bab = © || Mae FO) ae al KS) eS 16 14

9|168 455) 5 15| 14 30 | —14 |19 21/— 3 18|-+ 11 15 37

10 5.29) 2 Ole 7) 2 | 1© So es 2a uy 0G 5

Il 5 12} 6 IO] 14 13 | — I | 19 53|— 3 23|-+ 20 16 6

12 23) 2 5S/ 1S 65) = 3 to Se 2 ea ae an T5 49

13 5 55| 6 20/ 13 8 | — 61/19 I0|— 3 23/-+ 20 16 18

15 8 37/10 20| 12 13 | — 7 |21 34|/— 5 22|— 34 15 AI

16 IO I0|/1II 55| Io 58 | +31 | 22 31|/— 5 28!|— 46 16 17

17 I2 2/13 53] Ir 10; +21 | 24 28|— 5 28|— 46 16 38

18 9 24/10 24) 11 3] +28 ]21 25|— 5 29|— 47 14 49

20 8 30] 9 18! 12 38 | +12 } 21 44|— 5 29|— 47 16 12

Mean 78 15 57.5

12 | 234 16 10/16 58] 15 35 | —7]32 2/— 4 17/+ 52] 144 28 15

13 18 53/20 5/13 8 | — 9 |32.28|— 4 17/+ 52 28 54

18 24 55/25 28/ If 3 | —27 136 36|— 6 56|— 54 28 31

Mean 144 28 33.3

2 | 132 39 28; 40 15| 13 28 | +11 153 31|— 0 52/— 32] 42 53 27

3 40 56/41 2) 13 34 | +16 154 49|— 0 52|— 32 53 St

II 23 U1 gg) 4O|| Wh ey | Se © 5B) aiS |) qe @ ale p= 2S 53 46

15 AS GAS 5B 22 1 | ae © 158 52 ie 2 Hier ue 93 44

16 4l 32/42 5] 10 58) +20]/53 6)/+ 1 6/4+ 7 53 46

18 40 40/41 35| Ir 3 | +20]52 31/+ 1 7/+ 6 52 50

19 40 16}40 50| 11 22 | +14 |52 g/+ 1 7/+ 6 53 17

Mean 42 53 31.6

2 | 138 30 38 | 32 40| 13 28 | +10 | 45 17 — 0 16|— 29| 48 45 51.0

2|197 16 8/16 14| 13 28 | —1r2|29 27|+ 6 45|-+ 44] 107 37 28

10 29 3/30 16/13 7 | — 8|42 39/— 5 18|+ 52 37 19

II 28 26|28 22] 14 13 | — 5 |42 32/-— 5 20|/+ 54 a

12 AS BF | 27 23 | HG 65 | UO a2 Bh |= | ZO ar Fe 37 45

13 29 3/29 25) 13 8/| —I9|42 3/— 5 20/+ 54 37 26

15 Sona este LOA 2) a7 OF: Sil 8)

16 35 5/39 52 10 SS se 7 ay Bi 2 se |= Zo 37 58

18 gh AN BG) I) eB | aE HI dl® Sei S89) | — at 36 33

20 32 46|34 18) 12 38 | + 1 | 46 11|— 8 39|/— 71 37 20

Mean 107 37 24.4 F.

102

Taste V.—ReEsvutts or Measures or Distance. ( Continued.)

Rutherfurd Photographic Measures of

ty | Observed Dist. Corrections for Cor- | geale Parallax Final

Nome Mean, | V2 | srodon. | nC ale ony ees

a9 I | .938r | .9276| 369 | —57 | 148 | .9731 | +189] —.1024 | —0.787] 96.8795

2 | .9478 | .9312 | 364 | —57 | 148 | .9793 | +221 | —.1017 | — .767 .8899

(41) |" 3 )-9384 |-9322 | 394 | —57 | 148 1.9756 | 162) [oreo .8803

TO |'.7559)||-7671 | 337 | 59 || 148) |-7985.| — 39) 0796; nods .8653

II | .7572 | .7653 | 323 | —59 | 148 | .7967 | — 69] +.0800 | — .676 .861T

I2 | .7542 | .7318 | 350 | —59 | 148 ,.7812 | — 58] +.0800 | — .676 .8467

13 | .7580 | .7381 | 388 | —59 | 148 |.7901 | — 12! +.0800 | — .676 .8602

15 | .6890 | .6809 | 380 | +59 | 146 } .7379 |—I01 | +.1266 | + .579 .8618

16 | .6440 | .6572| 581 | +56 | 146 | .7232|— 65|+.1293 | + .446 .8517

17 | .6586 | .6644| 482 | +56 | 147 |.7244|— 69| +.1293 | + .446 8525

18 | .6513 | 6443 | 564 | +56 | 146 | .7188 |— 52| +.1296 | + .433 .8488

19 | .6702; .6610| 471 | +56 | 148 |.7275 | — 32] +.1296| + .433 .8595

20 | .6762 | .6707| 399 | +56 | 146 | .7279 | —120| +.1296 | + .433 8511

Mean 96.8622

60 2 | .7962 | .7690| 422 | —58 | 145 | .8276 | +222 | —.2024 | —0.968} 97.6350

13 | 4324 | .4264| 473 | —60 | 146 | .4795 |— 13] +-.1597 -985 6253

(51) | 15 | .3186 | .3134| 338 | +59 | 146 | .3645 | —102| +.2530| + .998 .6201

Mean 97.6268

61 I | .3070 | .3036| 397 | —63 | 122 | .3432 | -+2r1I | —.0862 | —o.737 | 108.2686

2 | .3178 | .3030 | 389 | —64 | 122 | .3473 | +246) —.0856 | — .712 A272

(40) 3 | .3112|.2954| 423 | —64 | 122 | .3436 | +180} —.0856 | — .712 . 2669

5 | .2298 | .2492 | 408 | —62 | 120 | .2784 | + 48| —.0031 | — .323 .2760

6 | .2046 | .2209 |) 480 |__62 | 122 .2591 | + 97) —.003I1 | — .323 .2616

7 | .2193|.I991 | 442 | —61 } 120 | .2515 | +101 | —.0027 | — .295 .2551

9 | .1560 | .1612| 454 | —65 | 126 | .2024 | — 48) +.0658 | — .681 -2547

IO | .1578 | .1520| 368 | —66 | 126 | .1900| — 44| +.0669 | — .633 -2444

IL | .1635 | .1619| 356 | —66 | 126 | .1966 | — 77| +.0673 | — .613 .2483

I2 | .1466 | .1568|) 383 | —66 | 126 | .1883 | — 65 | +.0673 | — .613 .2412

13 | .1485 | .1453 | 415 | —66 | 126 | .1867 | — 14| +.0673 | — .613 .2447

I5 | .0917 | .0877 | 425 | +66 | 122 | .1433 | —113| +.1064 | + .506 -2449

16 | .0790 | .0780 | 647 | +63 | 122 | .1540|— 72] +.1087 | + .367 .2602

17 | .0733 | 0785 | 537 | +63 | 122 | .1404|— 77!+.1087 , + .367 .2461

18 | .0579 | .o615 | 628 | +63 | 122 | .1333 |— 58] +.1089 | + .354 .2409

19 | .0782 | .0768 | 524 | +63 | 122 |.1407 |— 35] +.1089 | + .354 .2506

20 | .0894 | .0866 | 445 | +63 | 122 | .1433 | —134| +.1089| + .354 .2433

Mean 108.2544

62 2 |.5976| .6115 | 483 | —66 | 125 | .6504 | +265 | —.1918 | —0.977 | 111.4726

3 | .5722 | .5680| 504 | —66 | 124 | .6179 | +186 | —.1918 | — .977 -4322

(57) | 18 | .1430} .1066 | 539 | +65 | 130 |.1899 | — 60| +.2453 | 4- .886 -4406

Mean} ~ ca etimas ELC alo y 111.4485

TABLE VI.—RESULTS oF MEASURES OF ANGLE.

Sixty-five Stars near 61 Cygni.

103

( Continued.)

Observed Position Zero Cor- Paral

I Angle. Cc - : Final Cor-

E a tion plus Refrac.| $050" | srotlon. | hey. [tected Angle.

a East. West.) || Precess Jicient

sion, ete. Pp 7

fe) i “ee 4 ad / 4 dd / Ul 4 4 fo) / ad

I | 202 13 14/14 32] 12 2 | —16 |] 25 39|-+ 6 38|-+ 43] 112 32 45

2 Tit AAS | |) Me AS | AW | 2 AO) G5) || SI 33 32

3 12 44/14 37| 13 34 | —20 | 26 55)+ 6 35|+ 46 33 53

IO 25 8)|25 22) 13 7-| — 8138 14/— 5 to/+ 53 2Z D

II DE UO) Fi WS) WAL WS || Be) py) | el 32 45

12 BM BS ZG) OT MB) bi) | ih SG | ay 33 13

13 By BO) 2A) AL ASS) aS) |S a) Be a 33 24

15 29 20| 30 35| 12 13 |— 2142 9|— 8 15|— 63 33 12

16 30 13/31 50/ 10 58 | + 2})42 2|/— 8 25)— 68 32 44

17 G2 HOSS) Hf) WI HO | a | By eS i — 33 33

18 0) Tis), Bi BO) wi B O | 41 52|— 8 26|— 69 Be) iit

19 30 15|3I 5] II 22 | — 2 | 42 00|— 8 26|— 69 aa)

2c 28 45|29 52| 12 38 | — 3] 41 53|— 8 26|— 69 230 16

Mean 1A 22 75

2 |156 50 25/50 51| 13 28) +2] 4 8|+2 3/— og] 67 7 8

13 5S Bi Seb AN ey re aG || ake re eA aa 1 5

15 56 2/58 2/12 13 | +11 | 9 26/— 2 34|/— 13 6 28

Mean 7 © Bay

I |207 10 48|12 2] 12 2 | —16 | 23 11|/+ 6 12/+ 43] 117 29 51

2 3 43), @ GA) Ug 2s) |) aid! |e) Sie Oye) ta VAs 29 56

3 GO) BAU HO Ne Bb eA) 22) BO) Cae Ne) 30 2

5 18 oO|19 2) 11 38 | —17 |29 52|/+ 0 13/-+ 62 30 19

6 17 4|18 27) 11 38 | —37 |28 46/+ o 13|+ 62 29 38

Ti I2 40/13 33| 12 52 | —26 | 26 33/+ 0 12|+ 62 30 28

9 20 16/21 4| 14 30 | —32 | 34 38|— 4°46|-+- 48 29 39

ae) 2l 2/21 36/13 7 | — 8 }34 18|— 4 50\+ 52 29 26

II HOS 0) 20,50) WARS a0 340 S8 4) 521 53 29 29

12 HS) 13 | US SG NS) gS) |) SS Se) AS | SV GS 29 26

13 2ONZS) 20 7 813) 8) 19) 1/3339) == 4 52) 53 29 30

15 25 2525 3B 12 13 |) == | | GS OW 42 —= Co 29 46

16 26 32/28 16] 10 58 | — 3 138 19/+ 7 52|— 63 29 35

17 28 15|29 31| Ir 10 | — 6/39 57/— 7 52|— 63 Zona

18 26 20| 26 53| 11 3! — 6137 40 7 53|— 63 28 34

19 2GSU5) (20740 Ni 2273 37 AT —— 7) 53am 03 29 30

20 24 26)25 40) 12 38 | — 3 |37 38|— 7 53|— 63 29 36

Mean 117 29 40.1

2 165 20 35 21 26| 13 28 | — 2/34 27,;+ 2 42/+ 17-75 38 9

3 PANS) | 22 P| GB AL | By Bi ae 2 AID Va 38 25

18 30 0/30 27/11 3 | +29 1/41 45|— 3 28|— 30 Bq uO

Mean Ts St Soi

104 Rutherfurd Photographic Measures of

TABLE V.—Resutts or MEAsuRES OF Distance. ( Concluded.)

tg | Observed Dist. Corrections for Cor-_ | seale Parallax Final

Star 2 rected | Varig. | Proper Co- Corrected

No. o Mean. | tion, | Motion. | egicient, | Distance.

East. | West. |Refrac.| Aberr.| Scale. a ms

63 2 |.7541 | .7438| 470 | —65 | 133 | .7946| +250) —.1809 | —0.967 | 109.6263

EI | -4323 |/.4440)| 389 | —67 | 133 | 4757) | 79| a) 24201 eee -5984

(48) | 13 | .4072| .4136| 524 | —67 | 126 | .4607 |— 14| +.1426 | — .946 .5898

I5 | .3026 | .2808) 411 | +66 | 124 | .3438 | —114| +.2259 | + .920 .5701

16 | .2991 | .3042| 555 | +64 | 128 | .3683 |— 73] +.2307 | + .837 .6024

17 | .2860 | .2935 | 488 | +64 | 128 | .3498 | — 78] +.2307 | + .837 5934

18 | .2766 | .2810] 550 | +63 | 126 | .3447 | — 59] +.2312 | + .829 -5806

19 | .3023 | .2725 | 483 | +63 | 126 | .3466 |— 36| +.2312| + .829 .5848

20 | .3147|.2970| 425 | +63 | 134 | .3600 | —136, +.2312; + .829 -5882

Mean 109.5916

64 I | .1776| .1780} 535 | —70O | 123 | .2260 | +234} —.2010 | —o0.965 | 120.0360

2 | .1922|.1778| 520 | —71I | 123 | .2316 | +273 | —.1996 | — .974 .0468

(46) | 3 |.1634 | .1586| 602 | —7I | 123 | .2157 | +200| —.1996 | — .974 .0236

4 | .0126 | .9952| 575 | —73 | 123 |.0558|— 3] —.o0149 | — .971 .0281

5 | 0018 | .9997| 558 | —69 | 123 | .0514|-+ 53!—.0072 | — .889 .0381

6 | .9536 | .9504| 818 | —69 | 123 | .0286 | +107 | —.0072 | — .889 .0207

7 |.9913 | .0029! 664 | —68 | 124 | .0585 | 4-111 | —.0064 | — .874 .0520

g | .8060 | .8200; 741 | —72 | 123 | .8816)— 53] +.1542 | — .981 -O179

Io | .8454 | .8412); 457 | —73 | 123 | .8834|— 49| +.1566 | — .985 .0225

Ir | .8628 | .8512 | 427 | —73 | 123 | .8941 |— 86| +.1575|— .984] .0304

12 | .8466 | .8533 |} 492 | —73 | 123 | .8936|— 72| +.1575 | — -.984 .0313

13, | .8351 , .8323 | 584 | —73 | 323 | .8865 |— 15) +.1575 | — .984 .0299

I5 |.7124|.7110; 422 | +73 | 123 | .7629 | —125| +.2495 | + .989 .0126

£7, \-6883 || -6800)| 9477.) 370) | tea 7450 | Oo) i 254 Oda 0034.

19 | .6955 | 6875 | 481 | —-70; 123 | -7484 |— 39] +.2553 | + -929)19 array

20 | .6944 | .6862 434 | +70 | 126 | .7428 | —149| +.2553 | + -.929 .995:

Mean 120.0250

65 2 | .0835 | .0878| 479 | —76 34 | .1161 | +294 | —.0945 | —0.743 | 129.0415

I5 | .8134 | .8004 | 506 | +78 46 | .8567 | —135| +-1179 | + .547 | 128.9681

(50) | 18 | -7827 | .7731 | 749 \/--75 | (43.'||-8515 | — 69) 1206s) acs +9703

20 | .8129] .8114) 532 | +75 43, | .8641 | —160! +.1206 | + .398 -9738

Mean 128.9884

66 2 | .9326 , .9067 | 523 | —72 | 122 | .9659 | +277| —.1821 | —0.970} 121.7990

II | .6092 | .6052|} 433 | —75 | 123 | .6443 |— 87| +.1437 | — .950 -7671

(49) | 13 | 6028 | .5993 | 585 | —75 | 122 | .6532|— 16| +.1437 | — .950 -7831

18 | .4338 | .4378| 610 | +70 | 128 | .5056|— 65} +.2329| + .836 -7427

Mean 121.7730

Sixty-five Stars near 61 Cygni. 105

Taste VI.—Resuuts or Measures or ANGLE. ( Concluded.)

ry ese ed poate Kae Cor- Paral- rote

as ngle. Trec- ina T-

= < fion plus Refrac. peony OEE! Pie rected signee.

Fast. West. | Preces- ficient.

feed sion, ete. P 7

2 | 171 47 50/48 36 13 28 — 5] 1 36/+ 3 25|+ 8] 82 6 4

II ARASH SD LS LAs ESN sael 20 Oe LO) Sar 2542) 1-1 19 6 4

13 BANG 05 5023) Gy Or) ate iA | 2.42) 19 5 53

15 5 AS | SS) SP U2 US Se SO gh es AE ay 5 Si

16 58 45/00 32| 10 58 | +30 ]10 6/— 4 23|— 37 5 lat

I7 |172 © 50) I 45/ If 10 | +19 | 12 47|— 4 23) — 37 6 6

18 | 171 58 36/59 25/ Ir 3 | +28 | 10 32/— 4 23!— 38 5 5

19 58 36/59 6] II 22 | -+17 | 10 30|/— 4 23|— 38 5 52

20 57 8/58 32] 12 38 | +10 | 10 38|— 4 23|— 38 6 15

Mean 82 5 48.6

i | IGS 29 GS) sO dee py SS be Aes Be) i ae iy | Sie) AL eh

2 AT RS) | Ae Bes we AS |) a= se Ale | a= ae st) 44 40

3 28 30/29 42) 13 34 OR AZTA0) 50) 4 44 41

4 30 58/31 25| 12 39 OAS) Sil an 9 a, LO 43 29

5 32 37|32 45| Ir 38 QU UG) |= © ALlla= 2s) 44 23

6 BM GO) Gs 2) wae Gs | =" dy Asia Cy NS ee) 44 17

7 2 BEN 27 B52 52 |= AD Bae © alla Ay 44 2

9 Bll BQ Ge BGS MAL | eo) —— AIG) Ga ak BIO) pa 44 5

10 BAUS SIIGSr soHous i eae a AOeton=— 8 32) 2 44 23

II 31 37/32 12; 14 13|/ + 1/46 8/—1 32/+ 4 44 6

12 20) AGI FO | us SH a SAG esha ey) wl 44 3

13 ait Bs) 2 32) 1s 8 | qe ie ds Oj Bal ae. A 44 2

15 34 5/35 40| 12 13 | +11 147 16|— 2 26|— 13 44 26

17 BO) Seo) ete LON E2340) 0) | 220) 2 44 18

19 34 50/35 2| Ir 22 | +20 | 46 38|— 2 29|— 22 44 0

20 33 28/34 33| 12 38 | +13 |46 52/— 2 29|— 22 44 29

Mean 69 44 14.7

2 | 204 24 48) 25 48) 13 28 | —14 ]38 32/;+ 5 3)-+ 36,114 44 48

15 39 12140 48] 12 13 | — 3 152 10|— 6 20|— 49 45 13

18 40 5/41 I0/ 1 3 | — 21/51 39|/— 6 28|— 52 44 2

20 28 30/39 Io| 12 38 | — 51 25|— 6 29/— 52 44 51

Mean II4 44 43.5

2a eee (GLO!) 7) 7a) 13) 238) | —— 5 20) Bn 7 Sr 24) 9 4

II II 43|12 37| 14 13 | — 2 | 26 21) — 2 23|+ 16 De BR

13 I2 10/12 34; 13 8 | — 7 |25 23|— 2 23|-++ 16 23 30

18 I5 34\/16 12} 11 3 | +28] 27 24)— 3 52|— 33 22 30

8I 23 24.2

106 Rutherfurd Photographic Measures of

Taste VII.—For Proper Morion.

(See Paragraphs 11-12 and 17-18. )

In Distance. In Position Angle.

Star

No.

S, S> 8s Se Sy

I —.2384 —.0035 —+.9712 .007 43 -+.007 216

2 —-9977 —.0000 -+.0681 .009 17 -+ .000 624

2 —.9997 —.0000 —.0237 .008 75 —.000 207

4 —.9968 —.0000 —.0794 .009 03 —.000 717

5 —.7484 —,.0029 —+.6632 .O12 95 +.008 588

6 —.9997 —,0000 —.0228 O10 53 —.000 240

7 —.9979 —.0000 + .0649 .O12 29 -+.000 798

8 —.3231 —.0073 + .9464 -016 36 +.015 483

9 —.8917 —.0009 —.4526 .008 72 —.003 947

10 -++.1802 —.0049 -++.9836 -O10 09 +.009 925

II --+ 1589 —.0066 ++ .9873 .013 48 -+.013 309

12 —.0319 —.0093 -9995 .018 63 +.018 621

13 + -3395 —.0045 -+.9406 .O10 I7 -+.009 566

I4 —.4216 —.O118 -++.9068 .028 84 +.026 152

15 —.9606 —.0S07 —.2780 .019 16 —.005 326

16 —.9419 —.0019 -+.3360 .033 OI -+.0II O91

19) +.3379 —.0054 -+-.9412 .O12 13 +.01I 417

18 +.2877 —.0065 + .9577 -OI4 30 +.013 695

19 —.7295 —.0018 —.6840 .007 76 —.005 308

20 -++.4677 —.0053 + .8838 .O13 56 -++.01I 984

21 —.9264 —.0032 —.3767 .044 91 —.C16 918

22 +.5569 | —.003I -++.8306 009 04 -+.007 509

23 +.5665 | —.0038 -+.8240 .OII 20 -++.009 229

24 +.1855 | —.0568 -++.9827 -117 38 +.115 349

25 |

27 —.5863 —.0085 —.,8100 .026 06 —.02I 109

28 —.6038 —,0028 —.7971 -008 95 —.007 134

29 +.7608 | —.0058 + .6488 .027 76 +.018 O11

30 +.9269 —.0039 +.3753 -054 36 +.020 401

31 gg | > ease —.8699 .O16 70 —.OI14 527

32 —.5183 —.0048 —.8552 .O13 0O —.o11 118

33 +.8631 —.0037 —-+.5049 .028 72 +.014 501

34 —.0993 —.O144 —.9959 .028 99 —.028 871

35 -+.3090 —.0200 —.9510 .044 16 —.O41 996

36 +.8577 —.0059 —.5I141 -044 64 —.022 941

37 —.1433 -—.0103 —.9897 .020 95 —.020 734

38 —.4283 —.0036 —.9036 .008 QI —.008 O51

39 +.7852 —.O017 +.6192 .008 79 +.005 443

4o —.3641 —.0045 —.9314 | -O10 39 —.009 677

Sixty-five Stars near 61 Cygni. 107

TABLE VII.—For Proper Motion. (Concluded.)

(See Paragraphs 11-12 and 17-18. )

In Distance. In Position Angle.

108.

Rutherfurd Photographic Measures of

Tasue VIII.—For PARALLAX.

(See Paragraphs 14 and 22. )

In Distance. In Position Angle.

OO CONIA UALRW NH

wWunnn

CIES) Cera

NNukRD

|b 144+ +4441

Be BE

C0 COW 10 +H

Sixty-five Stars near 61 Cygni. 109

TasLe VIII.—For Parattax. ( Concluded.)

(See Paragraphs 14 and 22.)

In Distance. In Position Angle.

bt+++

+4+4+44++

110

Star

No.

OO COND NARWDHND H

Distance.

3771.42

3955-97

3202.47

3103.85

2163.15

2660.10

2279.03

1712.84

3213-79

2775.08

2078.41

1§03-97

2754-25

971.48

1462.27

848.59

2308 80

1958.83

3610.25

2066. 13

623.86

3100, 22

2500.62

238.68

19.39

1074.60

3130.15

1008.91

515-04

1677.09

2155-55

975-29

966. 32

634.19

627.41

1336.94

3143.57

3185.45

2696.96

“188

Rutherfurd Photographic Measures of

TasBLe I] X.—MEAN RESULTS.

Position

Angle.

307 44 19.4

235 25 23.3

230 9g 10.8

226 58 31.0

WB 6) AS-(6)

230

235,

302 42

204 35

232 iar

33-1

9.0

34-5

Zone

8.3

213

38.4

43-5

57.0

330

319

341

296

215

16 22.4

355 24 41.4

356 4 29.8

333.13 7.5

61! Cygni

59.6

48.0

5-9

34-5

58.9

251

341

338

349

209

67? Cygni

177 15 24.0

it7fs) GY Te

Durchmusterung.

i ia aden ie

No. Mag.

—3824.94 | +2291.19| Io 38.4318 WP

—3176:65 | 1745; 70))|| | "0 337-4 U5 4a a

—3I01.33 | —2063.32] 5 | 37-4155 | 9.3

—2861.47 | —2127.48 2 37-4157 9.3

—2746.93 | + 108.47] 19 38.4325 6.0

—2581.61 | —1710.30| 19 37.4159 7.5

—2368.76 | —1305.58 2 37.4161 9.5

—1838.55 | + 921.62 6 38.4331 9.3

—1681.35 | —2925.69 6 37.4166 9.1

——1670.41 | +2447.56 6 38.4332 9.2

—1297.85 | +-1812.35| 3 | 38.4333 |) 9:4

1237.16 | 4-1148.44)|" 3 | 38-4334amois

—1127.39 | +2609.07} 17 38.4335 9.0

—II04.18 | + 436.52] II 38.4336 | 8.8

—1070.60 | —1194.04 8 37-4170 8.5

—1I020.22 | — 274.47 8 37-4171 9.4

— 946.63 | +2186.47] 6 | [38.4338] | [9.4]

— 924.37 | +1819.88| 9 | 38.4337 | 9.0

—— 653.13 | 3573-00} 4 | 37-4072 .s\iisag

— 482.39 | +2031.26} 12 38.4339 8.9

— 386.98 | — 544.371 7 | 37.4173 | 88

— 319.06 | +3090.17 G 38.4340 9.1

— 219.69 | +2494.70| 19 38.4341 8.2

— 136.82 | + 213.06 2 38.4342 9.5

38.4343 | 5.0

19 | 38.4344 | 5.3

+ 65.11 | —1073.38} I0 37.4175 9.0

+ 98.35 | —3129.18 6 37.4176 8.7

+ 247.35| + 990.04] 3 | 38.4348 | 9.5

+ 324.32 | + 447.54 I 38.4349 | 9.4

+ 333-84 | 1656.26] 1 | 37-AT77 amos

+ 346.56 | —2138.1I0| 19 37.4178 7-5

= 450:96 |= 908.72) 7 1) 38-435Gms gas

= O73 7h) = 100 72175) wa

+ 674.16 | — 347.24 2 37.4179 8.6

+ 790-67. |= 83-07) 8) 9 38:43 meas

+ 855.80 | —11I54.21 | 18 37.4180 Tel

++ 909.87 | —3061.70 9 37.4181 9.0

+ 941.74 | +3099.16| 14 | 38.4353 | 8.4

+ 1002.82 | —2577.83 7 37.4182 9.4

Sixty-five Stars near 61 Cygni.

TABLE X.—CATALOGUE OF STARS ABOUT 61! CYGENI.

uo}

Star 3 Right Ascension,| Precession,| Sec.Var., Declination,

No. z 1873. 1873.

z Jf iG

hens 8 s Bio

I 20 56 57.333 | +2.3031 | 40.0041 | 38 45 44.59

2 57 40.552 2.3357 0041 | 37 38 27.70

3 57 45-574 2.3384 0041 | 37 33 10.08

4 58 1.564 2.3396 .0041 | 37 32 5.92

5 58 9.200 2.3235 .0042 | 38 09 21.87

6 20 58 20.222 | +2.3375 | +0.0041 | 37 39 3.10

7 58 34.412 2.3353 0042 | 37 45 47.82

8 59 9-759 2.3206 .0042 | 38 22 55.02

9 59 20.239 2.3496 -0042 | 37 18 47.71

Io 59 20.968 2.3097 .0043 | 38 48 20.96

II 20 59 45.806 | +2.3161 | +0.0043 | 38 37 45.75

12 59 49.852 DONT .0043 | 38 26 41.84

13 59 57.170 2.3107 .0043 | 38 51 2.47

14 59 58.717 2.3270 0043 | 38 14 49.92

15 2I 00 0.956 2.3391 -0042 | 37 47 39.36

16 21 00 4.314 | +2.3324 | +0.0043 | 38 02 58.93

17 00 9.220 2.3145 .0043 | 38 43 59.87

18 09 10.704 2.3172 .0044 | 38 37 53.28

19 00 28.787 2.3578 .0043 | 37 08 0.40

20 00 40.170 D.QUD .0044 | 38 41 24.66

21 21 00 46.530 | +2.3369 | +0.0044 | 37 58 29.03

22 OO 51.058 2.3099 .0044 | 38 59 3.57

23 00 57.683 2.3149 .0044 | 38 49 8.10

24 OI 3.208 2.3321 .0044 | 38 II 6.46

25 21 O1 12.329 2.3343 0044 | 38 07 33.40

26 See Contribution No. 13.

27 OI 16.670 | +2.3422 | +0.0044 | 37 49 40.02

28 or 18.886 2.3572 .0044 | 37 15 24.22

29 OL 28.819 2.3276 .0044 | 38 24 3.44

30 OI 33.950 2.3321 .0044 | 38 15 0.94

31 21 OF 34.585 | +2.3387 | +0.0044 | 37 39 57.14

32 Ol 35-433 2.3511 -0044 | 37 31 55-30

33 OI 42.393 2.3290 .0044 | 38 22 42.12

34 OI 57-207 2.3425 0044 | 37 54 5.62

35 OI 57-273 2.3392 .0044 | 38 Of 46.16

26 21 02 5.040 | +2.3364 | +0.0044 | 38 08 56.47

37 02 9.382 2.3458 .0044 | 37 48 19.19

38 02 12.387 2.3597 .0044 | 37 16 31.70

39 02 15.112 2.3147 .0045 | 38 59 12.56

40 02 19.184 2.3565 .0044 | 37 24 35-57

Precession, | Sec. Var.,

L M

Ms yw

13.991 | +-0.235

14.036 237

14.041 2B,

14.058 .237

14.066 236

+14.077 | +0.237

14.092 .236

14.129 234

14.140 5237

14.140 232

14.166 | +0.233

14.170 233

14.178 232

14.179 -234

14,181 -235

+14.185 | +0.234

14.190 "228

14.192 233

14.210 E287

14.222 232

+14.229 | +0.234

14.233 72a

14.240 232

I4 246 233

14.260 233

+14.259 | 0.234

14.262 -235

14.272 232

14.277 -233

--14.278 | +0.234

14.279 235

14.286 232

_ 14.301 234

14.301 233

+ 14.309 | +-0.233 |

14.313 -234

14.316 235

14.319 230

14.324 .234

112 Rutherfurd Photographic Measures of

Taste [X.—MeEan ReEsutts. ( Concluded.)

Durchmusterung.

No. | Distance.| Fonaen ae Bh ited

No. Mag.

AI 952.00 122 36. 30.0 1017.45 -—— 514.25 2 37.4183 95

A2 | 3448.83 | 15 37 11.6 | 4-1195.67 | 1-3319:791)| 5 |) 36.4850 mmo

43 | 1824.90 | 143 50 53.3 | +1360.90 | —1475.72| 12 | 37.4185 | 9.0

44 | 1600.46 | 133 45 6.3 | +1463.45 | —II09.29 6 37.4186 9.5

45 | 2971.02] 22 53 48.0 | +1484.97 | +-2734.35 2 38.4357 | 9.3

46 | 1246.52) 84 39 5.0| +1578.37 | + 113.27 if 38.4358 9.5

A7 | 3657.35 | 159 32 17-0 | +1604.53 | —3429.64 3 37-4187 | 9.0

48 | 1422.69 | 105 53 10.6) +1736.87 | — 392.98 19 37-4189 7.9

49 | 1618.91 | 114 46 4.0) +1863.84 | — 682.32 I 37.4191 9.4

50 | 1645.44 | 109 24 10.7 | +1968.78 | — 551.20 15 37.4192 9.0

Bl 2995-55 394 WON 244225) || Se Orly IT 37-4195 | 9-5

52 | 2136.94 | IOI 21 31.4 | +2658.96 | — 429.20] 10 37.4197 9.1

53 | 2125.57] 81 5 52-2] +2672.78 | + 320.52 16 38.4362 7.8

54 | 2164.54] 78 15 57.5 | +2698.53 | + 431-63] 13 38.4363 | 9.1

55 | 3771-13 | 144 28 33-3 | +2753-46 , —3078.19|] 3 | 37-4198 | 8.7

56 | 3283.52 | 42 53 31.6 | +2867.24 | +2396.00 7 38.4364 9.0

57 | 3014.80) 48 45 51.0 | +-2903.97 | --1977.36 I 38.4365 | 9.3

58 | 2513.28 | 107 37 24.4 | +3036.08 | — 771.78 9 37-4201 9.3

59 | 2713.34 | 112 33 7.5 | +3172.80 | —1052.51 13 37.4202 8.8

60 | 2734.76| 67 6 33.7) +3215.61 | +1051.59 3 38.4367 9.0

6I | 3032.47 | 117 29 40.1 | +3401.30 | —1413.65 07) 37.4203 8.3

62) 3121-94 | 75) 37 50-7 | an3e55-72 | 757-20 3 38.4369 | 9.3

63 | 3069.92) 82 5 48.6} +387@.48 | + 404.48 9 38.4370 9.0

64 | 3362.19) 69 44 14.7 | +4027.23 | +1145.36] 16 38.4372 7.8

65 | 3613.27 | 114 44 43.5 | +-4147.41 | —1532.77 4 | 37.4200) eas:

66 | 3411.15 | 81 23 24.2 | +4295.50| + 488.97 4 38.4375 8.4

Siaty-five Stars neur 61 Cygni. 113

TABLE X.—CATALOGUE OF STaRs ABOUT 611 Cra@ni. ( Concluded.)

No. | ¢ 1873. 1873.

i Si K ib, M

h m 3. s © 2: 10 “

AI 21 02 20.159 | +2.3415 | +0.0045 | 37 58 59.15 | +14.325 | +0.233

42 02 32.040 2.3140 -0045 | 39 2 53.19 14.336 .230

43 02 43.056 2.3498 .0045 | 37 42 57.68 14-348 -234

44 02 49.892 2.3476 -0045 | 37 49 4.11 14.355 233

45 02 51.327 2.3194 0045 | 38 53 7-75 14.356 -230

46 2I 02 57.554 | +2.3391 | +0.0045 138 9 26.67) +14.362 | +0.232

47 02 59.298 2.3648 .0045 | 37 10 23.76 14.364 -235

48 03 8.120 2.3434 .0045 |38 I 0.42 14.373 .232

49 03 16.585 2.3459 .0045 | 37 56 11.08 14.382 .232

50 03 23.581 2.3453 -0045 | 37 58 22.20 14.389 5232

51 2I 03 55.164 | +2.3595 | --0.0045 | 37 29 22.23 | +14.421 | +0.233

52 04 9.593 2.3470 .0046 | 38 O 24.20 14.435 .231

53 04 10.514 2.3415 .0046 | 38 12 53.92 14.436 A220

54 04 12.231 2.3409 -0046 | 38 14 45.03 14.438 P22

55 04 15.893 2.3662 .0045 | 37 16 15.21 14.442 7232

56 21 04 23.478 | + 2.3272 | +0.0046 | 38 47 29.40 | +14.450 | +0.229

57 O04 25.927 2.3302 .0046 | 38 4o 30.76 14.452 .230

58 04 34.734 2.3508 .0046 | 37 54 41.62 14.461 232

59 04 43.849 2.3532 .co46 | 37 50 0.89 14.470 .232

60 04 46.703 2.3382 .0046 | 38 25 4.99 14.473 .230

61 21 04 59.082 | +2.3567 | +0.0046 | 37 43 59-75 | 14.486 | +0.231

62 | 05 29.376 2.3427 .0047 | 38 20 10.60 14.516 -230

63 05 30.428 2.3454 .0047 | 38 14 17.88 14.517 .230

64. 05 40.811 2.3406 .0048 | 38 26 38.76 14.527 .229

65 05 48.823 2.3603 .0047 | 37 42 0.63 14.536 .231

| 66 05 58.696 2.3463 .0048 | 38 15 42.37 14.546 .229

114 Rutherfurd Photographic Measures of

TABLE XI.—LIMITING VALUES OF PARALLAX Conretcmiaiy

FOR I= + 0."3597.

In DISTANCE.

Use Parallax Coefficient S; P; -- S, P, as the argument in the body of table.

In Postt1ion—ANGLE.

Use Parallax Coefficient S, P; + S, P, as the argument in the body of table.

dé Ml 4 Vt ‘4 4d 4d Ua dé Mt

00’ | 10°| 20°) 30°! 40° | 50 | 60 | wo | 80 | 90 | 100

Sixty-five Stars near 61 Cygni. 115

The Position of 61? Cygni.

26. When we correct the measured coordinates of 612 Cygni

with respect to 611 Cygni, it is, of course, necessary to take into

account the very considerable proper motion of the measured

star as well as of the central star.

On account of the shortness of time over which the RuTHER-

FURD plates extend, a value of the relative motion deduced from

them alone would have very small weight. On the other hand,

the mean of the measured distances and of the measured angles

is entitled to great ,weight as representing the true value of the

distance and angle of these stars at the mean of the dates of ob-

servation, 1873.546. I have, accordingly, with the latter as a

basis, deduced trigonometrically a set of formulz which represent

the motion of either of these stars relative to the other; assuming

the motion of each to be uniform and on the arc of a great circle.

In these formulz have then been substituted constants derived

from the proper motion of each star separately, as determined

from meridian observations in the manner used in my “ Declina-

tions and Proper Motions of Fifty-six Stars,”* to which reference

is made for an explanation of the method.

27. For 61! Cygni I have used Auwers’ values as previously

quoted on page 62; but for 617 Cygni the results given here have

been derived from the data of Table XII.

Gn! Oye P= 5.20528 YS oyyue”’ t= usoy,

Om OUGG /V =F URIOQ2 FSS 5 S47 VIS

By the usual formuley these become:

61! Cygni Pp = 5.20521 Yy =51°42/13/’ 1873.546.

61? Cygni po’ = 5. 15192 %' —=53 3437 1873.546.

We have also:

611 Cygni 6) = 38°7/35/!

and from the RUTHERFURD measures :

For 61? Cygni, relative to 611, o),=19.''3823 7) == 114°41'30" at 1873.546.

* Contribution from the Observatory of Columbia College, New York.—No. 8.

{ Chauvenet : Manual of Spherical and Practical Astronomy, Vol. I, 2380.

116 Rutherfurd Photographic Measures of

AB = o)= True distance at 1873.546 from the

mean of all the measured distances.

MN = Distance measured on plate of the

date, 4, corrected except for proper

motion.

Po, Po’ = The proper motions of 611 and 612

Cygni at the epoch 1873.546.

AM, BN= Arcs traveled over in the time

7 =t—1873.546.

Aoo= The change in op due to the proper

motion of only 611 from A to M.

A’oy= The change in (o)— Aap) due to the

proper motion of only 617 from Bto XW: |

PAB=7)= True angle at 1873.546 from the

mean of all the measured angles.

PMN = Position-angle measured on plate

of the date, t, corrected except for

proper motion.

Xo Xo = The position-angles of the proper

motion of 611 and 61? at 1873.546.

PBA =d)/, also y, 2,A are auxiliary angles

having the significance shown above.

Am) = The change in 7) due to the proper

motion of only 611 from A to M.

Aly = The change in (m—Az7p) due to the

proper motion of 61? from Bto NV.

ty ie a hl ee

Siaty-five Stars near 61 Cygni. 117

28, Let the angles and arcs have the significance attached to

them in the figure; where P is the Pole; PA and PB hour-

circles through 611 and 6/? respectively at 1873.546,and M’M

and N’N the paths of proper motion. Then,as the arc AB joining

611 and 61? is the mean of all the measures of distance, it may be

assumed as the true distance at the mean date of observation.

In like manner PAB is assumed as the true position-angle at the

same date. The problem before us is to (1) determine the distance

MN at the end of the interval t years; (2) determine the angle

PMN at the end'of the same interval. In both these cases evi-

dently we regard the only cause of motion of the stars to be that

known as proper motion, 7.e., uniform motion on the are of a

great circle.

Let all angles count from the hour circle positively towards the

east, 7.e., counter-clockwise in the figure; or else from the are

AB, but always likewise positive when counter-clockwise, as

shown by the direction of the arrows in the figure.

29. Let us first suppose that 672 remains motionless while 671

advances from A to M during the time 7; then the change in dis-

tance is given by the formula:

Ao = (7P9) c08(™ — Xo)

“+ (*Po)? | ae (7% — Ao) }

+ (7Po)8 | a 35,35 (7% — Xo) COS (%™|— Xo) }

+ (00)! | 355 LE sin* (9 — xp) —sin® (=> — 40) 008° (=> — xo)] }

When the proper constants have been substituted in this we have:

Aoy = [9.657224] (79) +[8.311234n] (79)? +[6.68105n] (79 )®+[3-6310n] (7 )*-

Thus is obtained the auxiliary distance BM agreeing of course

with the formula of paragraph 11, as far as terms in 7?.

30. Now during the same interval of time +, suppose 61! to re-

main still and 61? to be in motion. Then the change of distance

is given by the formula:

lo) = (zp!) 008 (44! — 2)

+ (7Po”)? | aren sin? (%’ — 2) }

+ (7p)”)* | arene [2 sin? (7)’ — 2) — sin? (%’ —2) eos? (%’ — 2) ] \

118 Rutherfurd Photographic Measures of

which may be computed for each plate separately after 4c, has

been computed by the preceding formula; and where the value:of:

z is obtained from the following relations :*

== 7

Z2=1—id,/.

A)’ = 180° — 7) — 9) sin 7, tan 4,

I o

cot A = - 4 — cot (7% — x).

Py Sin (|) — Ao)

By substitution of the constants for these stars these become:

Ao’ = 65°18/16/7.5

cot A) = 21.75560 a — 0.509789

hence

2 = 1 — 65°18/16/".5

which may be computed for each plate.

Thus the variation in distance due solely to the proper motions

of 611 and 612 Cygni in the assumed direction at the assumed

rate may be expressed by

Ao, + A7oy

as computed for each value of ct, and printed in columns nine and

ten of Table XIII. This quantity is additive to the observed

distance on each plate to reduce to the mean epoch.

31. By the formula of paragraph 17 may be computed values

of K or 4y, applicable to the new mean epoch adopted, thus:

Axo = [9.7895] 7P

where the number in brackets is a logarithm as usual.

We also have, as in paragraph 30,

I o — Ao,

cot A’z, = “=

9) tp)? sin'( x’ — 2)

— cot (%’ — z)

and

I T ;

cot y = Po — cot (7 — %)

G sin (%)— X%)

* Jordan : Handbuch der Vermessungskunde, 4te Auflage. Bd. III, 2 359, 342-

Sixty-five Stars near 61 Cygni. 119

whence is obtained by substitution of the constants and from the

figure:

Amy= 62959717’ + (y— AX) before epoch,

= — 117° 0/43/’ + (y— Ax) after epoch,

and thus the total change of angle is

Ar, + A’

additive to the observed position-angle. These quantities are

printed in columns seven and eight of Table XIII.

When these corrections for proper motion have been applied to

the preceding columns of Table XIII we get in the next-to-the-

last column of the Table the distance and angle of 6/7 good for

1873.546 corrected for all known motions of either star, except

for difference of parallax if there be any such difference. This

oint will be considered in the following Contribution, No. 13.

120 Rutherfurd Photographic Measures of

TABLE XIJ.—Proper Motion or 612 Cygni.

Epoch .

Date of eps Reduction

f No. of | Position at

F Observa-| . to 1875-+Syst. | Reduced C.—O.

Authority. : Cata- | Obs. Epoch-of ae sir Wet.

tion. Gane Catalogue. Correction. | Position. ,

t T n . A! B R

RIGHT ASCENSION.

208 2 7™-+- |

m Ss m tS} SS}

Br. 2745 | 1753-8 | 1755 2 | 55 57:40 | 5 | 25.767) e077 OS one

Pi. xx:476 | 1806.2 | 1800 17 | 57 57.80 |-+3 21.497 | 19.297 | 0.3 | —.089

Abo 482 | 1828. 1830 62 | 59 18.34 |+2 0.805] 19.145 | 4.0 | +.089

Pond 946 | 1830. 1830 16 | 59 18.73 +2 0.737] 19.467 | I.o | —.230

Tay. 9785 | 1835. 1835 5 | 59 32.24 | +1 47.368] 19.608 | 0.4 | —.365

12 Yr, 1887 | 1830. 1840 30 | 59 45.14 | +1 34.086] 19.226 | 3.0 | +.022

12 Yr, 1887 | 1845. 1845 40 | 59 58.61 |-+1 20.598] 19.208 | 3.0 | +.047

6 Yr. 1358 | 1850.8 | 1850 45 | 60 12.11 ;+1 7.153] 19.263 | 3.0 | —.oor

Rad, 5107 | 1853.0 | 1845 Ig | 59 58.76 |-+1 20.550} 19.310 | 3.0 | —.046

Yarn. 09477 | 1854.8 | 1860 23 | 60 37.08 |+0 42.174] 19.254 | 2.0 | -+.o12

Rad, 2059 | 1856.4 | 1860 Ir | 60 38.93 |-+0 40.377] 19.307 | 2.0 | —.039

7 Yr. 1743 | 1856.9 | 1860 48 | 60 38.95 |-+0 40.308, 19.258 | 3.0 | +.011

Quet. 9276 | 1861.6 | 1865 18 | 60 51.11 |-+0 28.134] 19.244 | 3.0 | +.031

N. 7 Yr. 2394 | 1864.0 | 1864 17 | 60 49.70 |-+0 29.569 | 19.269 | 3.0 | +.009

Poulk. 1866.2 | 1865 27 | 60 52.448 |; +0 26.839| 19.287 | 8.0 | —.007

9 Yr. 1976 | 1872.3 | 1872 13 | 64 11.185 | +0 8.091 | 19.276 | 3.0 | +.011

Romb. 4784 | 1877.9 | 1875 7 | 61 19.37 |-+0 0.002 |°19.372 | 4.0 | —.078

IO Yr. 3532 | 1883.6 | 1880 I4 | 61 32.656 |—o 13.394] 19.262 | 3.0 | +.039

Green. Yearly | 1893.7 | 1893 Io | 62 7.565 |—o 48.294] 19.271 | 2.4 | +-.042

m iS)

Results. 1858.58 | 1875 | 424 | 61 19.291 51.4 |

DECLINATION.

Biraty 38° 7 aie

d 4d d Mf Md Md

Br. 2745 | 1753-8 | 1755 T3321 340 +34 13.76) 57-60) |¢Q:25))——Onge

Pi. xx:476 | 1805.8 | 1800 13 | 46 34.0 +21 26.49} 60.49 | 0.3 | —2.21

Abo 482 | 1828. 1830 BR WBS | ally +12 54.11} 58.81 | 4.0 | +0.07

Tay. 9785 | 1835. 1835 9 | 56 30.47 | +11 29.19] 59.66 | 0.5 | —0.59

12 Yr, 1887 | 1839. 1840 3I | 57 55-7L |+10 3.00] 58.71 | 3.0 | +0.47

12 Yr, 1887 | 1844. 1845 36 | 59 22.02 |+ 8 36.89] 58.91 | 3.0 | +0.40f

6 Yr. 1358 | 1851.2 | 1850 35 | 60 48.67 |+ 7 10.90] 59.57 | 3.0 | —0.06

Rad, 5107 | 1853.2 | 1845 18 | 59 23.2 + 8 36.32| 59.52 | 3.0 | +0.04

Yarn. 9477 | 1854.0 | 1860 | 113 | 63 22.6 + 4 37.25) 59.85 | 3.0 | —0.27

Of ties 1743 | 1857.0 | 1860 44 | 63 40.53 | + 4 19.02); 59.55 | 3.0 | +0.12 |

Rad, 2059 | 1858.8 | 1860 Io | 63 41.8 + 4 18.51| 60.31 | 2.0 | —o.60

N. 7 Yr. 2394 | 1864.2 | 1864 Ig | 64 49.69 }+ 3 9.90] 59.59 | 3.0 | +0.27

@) VaR. 1976 | 1871.9 | 1872 14 | 67 8.90 |+ 0 51.16| 60.06 | 3.0 .0O

Romb. 4784 | 1877.9 | 1875 a Osh O39 +0 0.02] 60.72 | 4.0 | —0.50

10 Yr. 3532 | 1883.6 | 1880 I5 | 69 26.61 |— I 26.54] 60.07 | 3.0 | +0.31

Green. Yearly | 1893.7 | 1893 IO | 73 12.43 |— 5 11.81] 60.62 | 2.4: | -+0.03

Results. 1857.69 | 1875 | 408 68 0.150 40.4

Probably an error of 5’’ in Quetelet’s declination, hence it has been discarded.

Sixty-five Stars near 61 Cygni.

TABLE XIII.—Posrrion or 612 Cygni.

Corrections

Observed Dist. for Cor-

rected

East. West. /|Refr.| Scale. aie

0.6843 | 0.6716/ 3 | + 5 | 0.6788

-6900 | .6866| 3 oO | .6886

.6968 | .6846/} 3 o| .6910

.6918 | .6916| 3 o | .6920

.6877 | .6865| 3 Oo} .6874

.6834 | .701I2; 3 | — 2] .6924

.6968 | .6864|; 3 | + 3 | .6922

-6934 | .6935| 3 oO | .6937

.6852 | .6910| 3 Oo} .6883

.6951 | .6940]| 2 0 | .6947 |

B7O22) | 7016} 2 | -- © | .7023

-6955 | -6951| 3 | + 1] .6958

FG963)) .6992 | 3 | = 1 | .6982

.6966 | .6987/ 3 | — 6] .6974

-6839 | .7047| 4 oO | .6947

-6935 | -6958| 3 | + 3] .6953

-6774| .6957| 4 | + 3 | -6873

.6868 | .6846| 4 Oo} .6861

6905 | .6889| 3 | +10] .6910

Means

Seale

Varia-

tion.

iad Bee

HOOO00

12]

: Correction for

Wisten ge at Proper Motion of Distance | Parallax

ee a a

28'!.0124(s-+0') 611 Cygni | 612 Cygni 1873.546 efficient

19.0176 —5.2484 | +5.4774 | 19.2466 | —o.767

2949 | —5.2191 | +5.4468 5226 | — .745

B5049) 0 -5-20OK | (5-440 bog tf h5

3846 | —1.6956 | +1.7739| -.4629 | — .572

2557 —I.5652 | +1.6381 .3286 | — .369

-3986 —I.5652 | +-1.6381 -4715 | — .369

-3930 —I.5505 | +1.6229 -4654 | — .341

4294 | +0.7173 | —0.7583 | 3884 | — .715

2809 | +0.7173 | —0.7583| -2399 ;— -715§

.4602 +0.7448 | —o.7877 -4173, | — .670

.6731 ++0.7546 | —0.7981 .6296 | — .650

-4910 +0.7546 | —o.7981 -4475 | — .650

-5583 +0.7546 | —o.7981 .5148 | — .650

-5330 | +1.5946|—I.7030| .4246 | + .550

.4602 +1.6312 | —1.7433 -3481 | + .415

4779 | +1.6312 | —1.7433| .3649 | + .415

.2529 +1.6348 | —1I.7471 .1406 | + .401

.2193 +1.6348 | —1.7471 .1070 | + .4o1

3538 +1.6348 | —1.7471 | 19.2415 | +0.401

19.3823 19.3868

122 Rutherfurd Photographic Measures of

TarLE XITI, Concluded.—Position oF 612 Cygnt.

Observed Position oT Correction for 7

as) Angle EERO Moun Anes prope Maden of Angle Paral

= tion plus |Refrac.) ‘at Date of at Coef-

East. West. | ston cies ee ate.) 611 Cygni 612 Cygni 1873.546 | ficient.

| | =

fe) / “i fo) 4 4/| v] “i Ml (eo) / 4 fo) 4 “ ° / “a [o) ‘ Mi

I | 203 25 46| 203 43 17| 12 2 | —16 | 113-46 30/ +18 31 4 | —17 53 47 | 114 23 47 -Osne

2BZOA O26) 203) 7.26) 39 23) |r 5 LO)) =-18. 127900 |i 7aeonrat 28 19] +6732

3/203 20 I1 | 203 31 18] 13 34 || —20 39 5| +18 27 0 | —17 49 51 16 14| +6732

4 | 203 44 56| 203 47 23; 12 39 | —18 i SO ar te SO a Ala 37 12 9| +8536

5 | 203 30 8| 204 48 33] 11 38 | —17 |114 18 4| + 7 28 2! — 7 14 49 31 17| +9464

6 | 204 45 51 | 204 36 21} 11 38 | —39 AQVS2I\ se 720.2 |e 63 5} +9464

7 | 203 30 28/204 I 21) 12 52 | —26 led || Gein ee | > a ile Zul I4 49} +9533

8 | 204 15 3/204 9 3/13 3 | —20 2432) —— 4 4anitwal Aug aeeG 17 47| +7149

Q | 205 21 46| 203 56 36) 14 30 | —33 52130 4) 42 ae gone 45 53| +7149

EO | 204 AI 33| 205 2 20/13 7.|— 8/115 4 34] — 4 54 37 | + 4 46 55 56 52| +7689

Mag 204, 13 57)| 205) 29.54) 14) 134 9 OB 21 ANS Oni lt etm ao ae 52 43| +7889

I2 | 204 49 18| 204 22 36| 15 35 | —II | 114 51 32/ — 459 5|+ 4 51 16 43 43) +7889

13 | 204 34 43 | 203 57 12| 13 8:| —I9 A) Ti | Vi SIs) SP ae ak SE 21 22| +7889

MOA SANS 2050 (0A 2 Baa Aa LS a9 One 8 31 | +12 49 9 53 29 | —9045

16 | 204 58 47| 204 47 40) Io 58} —1 3042 | 13) 37, 52) | else 43 32] —9677

17 |206 5 42/205 55 25| II Io | — 2116 9 37| —13 37 52 | +13 17 42 10g 27| —9677

18 | 204 39 30| 204 36 40/ Ir 3 | — 2 ]|114 48 17} —13 4o 49 | +13 20 34 28 2| —9715

Ig | 204 55 18} 204 58 48| 11 22 | — 3 ]115 8 20; —13 40 49 | +13 20 34 48 5] —9715

20 | 205 II 40| 205 39 o| 12 38 | — 2 38 10; —I3 40 49 | +13 20 34 | 114 77 55] —9715

Means II4 AI 30 II4 4 30

IV.—The Parallax of 61+ Cygni, deduced from the Rutherfurd

Photographic Measures.

By HERMAN S. DAVIS.

Read May 3d, 1897.

32. For the purpose of determining the parallax of 621 Cygni

the measures of both distance and position-angle have been used

as recorded in the preceding catalogue of sixty-five stars. The

method adopted for getting the parallax from the measures of

distance is the same as has been used in previous investigations at

this Observatory.* Briefly stated this consists of correcting the

observed distances for refraction, aberration, errors of the scale,

proper motion of 611 Cygni, etc. These distances so corrected

may be obtained from Table V by taking the sums of the quan-

tities in columns eight, nine and ten. These sums are printed in

columns two and three of Table XVI.

33. Then particular pairs of comparison stars were so chosen

that their components should be as nearly as possible equally

distant from 61! Cygni and differing 180° in position-angle.

‘Table XIV contains a catalogue of these stars with memorandum

of some other observers who have used the same stars for de-

termining the parallax of 61 Cygnt.

In the equations of condition of Table X VII have been intro-

duced an unknown y varying with the time, as a correction of the

assumed proper motion; and another unknown w, as the correc-

tion of the assumed mean of the distances. The coeflicients of the

parallax have been obtained as follows: Using the symbols of

paragraph 14, the quantities of column eleven, Table V are

S3 Ps - Sy Py

Denoting by primed letters all symbols belonging to the less

distant of the two comparison stars of each pair, we have as the

coefiicient of the parallax

(8, P; + Sz Py) —- (83! P3 + 81! Pr)

when the absolute term of the equations is the difference of the

distance of the comparison stars from 61! Cygni, after these dif-

* The Parallax of « and @ Cassiopeie, by HAROLD JACOBY.

The Parallax of 7 Cassiopeix, by HERMAN 8. DAVIS.

124 Parallax of 611 Cygni, deduced from

ferences have been corrected by their proportional part of the

variation of distance. This variation is deduced from the devia-

tion of the sum of the distances on the various plates from the

mean of all the plates. See Table X VI, columns four to seven

inclusive.

Equations of condition thus formed are in Table XVII. At the

foot of each page of this table will be found the normal equa-

tions, the deduced values of the unknowns, with their probable

errors and the probable error of one equation of unit weight.

Hight different stars combined in five pairs were used for the

determination of the parallax by measures of distance.

34, Whereas heretofore only measures of distance were used

for parallax, in the present research measures of angle have also

been used. For it has been recently shown* in the case of eight.

stars among the Pleiades whose average distance is 2160’, rang-

ing from 631’’ to 3160’, that the displacement on the are of a

great circle by reason of the probable error of observation is but.

little larger in measures of angle than of distance. This re-

search on the measures of 611 Cygni has shown in addition that,

for the seven stars whose measurement of position-angle I have

used, the probable error for one plate of unit weight is +o’’.149

in angle, whereas for the eight stars used in distance it is +o’’.191.

The average distance of these stars is only 1956/’, ranging from

1075/’ to 2754’’.. This fully justifies the use of position-angle for

parallax determination from the RutHERFuRD photographic plates

in the present and in future reductions.

30. In the use of measures of position-angle the seven stars

were selected irrespective of distance but as equally distributed

in angle as possible.

Several methods of reduction suggested themselves, but the

following was adopted. The observed angles were corrected as

described in paragraphs 16-21. The “reduced angles,” obtained

from adding together columns six and seven of Table VI and the

“variation” of paragraph 21, are printed in Table X VIII.

If x’ and y’ be introduced for error of the adopted mean of

the angles and of proper motion respectively, and the parallax

coefficient

Ss Ps + Sp Py

* On the Permanence of the Rutherfurd Photographic Plates, by HAROLD J A-

COBY. Page 282.

1 a

—?.

The Rutherfurd Photographic Measures. 125

from column eight, Table VI, be used, the equations of condi-

tion can be formed as in Table XVIII. The solution of these

equations is given at the bottom of each page; where also will be

found the probable errors of the unknowns; likewise the prob-

able error of one equation of unit weight expressed as change of

position-angle and also as reduced to the arc of a great circle by

aid of the

“* Factor ’? = 28/’.0124 -o-sin 1/’ = [6.1329] o

36. The values of parallax given by the measures of distance

of the various pairs of stars are collected in the first part of Table

XV, with their weights, p, deduced from the least-square solu-

tion, and the corresponding probable errors, 7r,. As the stars 5

and 6 enter respectively into each of two pairs, the “ combining

weights ” of those pairs, (p), were used in computing the mean

of the five determinations. The (7,) is the probable error of the

parallax when (p) is regarded as the weight. Hence

Parallax = + 0/7.3999 - 0’’.0230.

In the second part of Table XV are given the values of

parallax deduced from the measures of position-angle, with their

probable errors 7,. Hence

Parallax = + 0/7.3326 + 0’/.0189.

When these two values are combined with weights which are

the reciprocals of the squares of their respective probable errors

there results the

Mean relative parallax of 61! Cygni = + 0’’.360 + 0/’.0146

126 Parallax of 611 Cygni, deduced from

TABLE XI V.—CoMPARISON STARS.

Comp. | Approximate position

ee referred to 61+ Cygni. DELS AIEEE

Remarks.

No. Distance. Angle. Number. | Mag.

64 3362 69.74 | 38:4372. | 7.8

6 2660 230.21 37:4159 7.5

39 3185 13-29 | 38:4353 | 8.4

5 2163 CPA aust 38:4325 | 6.0 | Johnson.

53 2126 81.10 38:4362 oe)

54 2165 One BSR MAO IG) 1

48 1423 105.89 327:4189 7.9 | Johnson : [Pritchard]: Wilsing.

14 971 296.79 884830) | ore [Pritchard].

2y 1337 149.62 37:4180 Weg [Pritchard].

27 1075 177.26 Rape ALG) = 9.0 Johnson : [Pritchard].

48 1423 105.89 37:4189 7-9

43 1825 143.85 | 37:4185 | 9.0

32 2156 172.68 37:4178 5

2 2501 356.08 38:4341 nz

13 2754 341-41 | 38:4335 | 9.0

Comp.

Stars.

The Rutherfurd Photographic Measures. 127

Relative

| Parallax

TABLE X V.—RESULTS.

FRoM MEASURES OF DISTANCE.

Probable Error. Relative

Weights. | :

Weights.

| of

| 611 Cygni |

64— 6

39- 6

Sys)

48-14

Results |

ieee 4497 |

ts, 3733 |

|--o.2431 |

Fa gee)

Es 0. 3999

21.8784/14.5856| .1576) .o409 .0500)

, |

De Oye | te (1)

26. 2675. |17-5117|+E0. 1641, ees 037 3| 6.0457

19. 8822 13 -2548| .2562| -0429) .0525|

|22. a 15.2147 le .2020 +0.0400 0.0490)

8.4314| 8.4314/+ .1840\0.0658|+0.0658|

eras

68.9982 cto. one

From MEASURES OF PosITION-ANGLE.

Relative — Weights. | Probable Error. | Relative

Comp. Parallax | Weight.

Stars. of Nl if

61! Cygni Pp o2 | (ape | T4 i ze | ao

| | | g

37 |e, 3028) 196 129.40) leans: tis 7°, Eo, ‘Tor8 a5 55 354, 796.9

Bi SSO STIG) Uy 7h OeVe G2inagal 2o527\) lamseis| 030ml) O41. 2

A bee 2794| 10 142. 84 2580. | 25-49} -1758) .0473) 447-5

43 +0.3299) 79 259.74/4245., 18.52 .1638) .0557| 322.6

32 |+0.3442| 63 960.30/5921.| peste, 37) 22208) | 4-0620) 250-9

23 |+0.3334| 44 572-46/7968.| 12.33) .1496| ~ .0743] 181.0

13 lage A4o7| 36 689. 52) 9667. Ere. 32|=Eo. a =E0.0819| 149.0

Results| to. 3326 688 588. 88

sto. 7488 +o, .0189, 2797-5

128

Parallax of 611 Cygni, deduced from

TABLE X VI.—OBSERVATIONAL DATA.

CoMPARISON STARS 64 AND 6.

C ted Dist b :

Plate ieee yt a eed | ou Mean Didereuce | Seale Corr,| Corrected

No mala Starg | Distances minus oe Distamces | Difference

I | 120.0484 | 94.9562 | 215.0046 | —.0152 | 25.0922 | —.0018 | 25.0904

2 .0593 | .9648 -O24T | —.0347 -0945 | —.0041 -0904,

3 .0361 .9600 | 214.9961 | —.0067 .0761 | —.0008 -0753

4 .0406| .9519) 9925 | —.0031 .0887 | —.0004 .0883

| -0495 -9559 | 215.0054 | —.0160 .0936 | —.0019 -O917

6 .0321 .9487 | 214.9808 | +-.0086 .0834 | -+-.0010 .0844

7 .0632 .9609 | 215.0241 | —.0347 .1023 | —.OO41 -0982

9 .0305 | .9480 | 214.9785 | -+.0109 .0825 | +.0013 .0838

ae) .0351 .9526 | -9877 | -+.0017 .0825 | +.0002 .0827

ies 0430 | .9487 | -9917 | —.0023 |. .0943 | —.0003 .0940

12 0439-9499 .9938,- —.0044 -0940 | —.0005 -0935

13 .0425 -9357 | .9782 | +.0112 .1068 | +.0013 .1081

15 | 119.9999 .9668 | .9667 | +.0227 .0331 | +.0027 .0358

a -9914| .9781 -9695 | +.0199 .0133 | +.0023 -O156.

7 |

19 -9998 .9805 .9803 | +.0091 .0193 | +.0011 .0204

20 .9832 .9701 -9533 | +.0361 .O13I | +.0042 -O173

Adopted mean, 214.9894

Assumed value, 25.0730

(6)

HH RH |

® NH

bo HOH H

(O) Wey Sap feat

1.00%

I.00

1.00

I.00

-I1.00

1.00

I.00

—I.14y

—I.13

—o.08

—0.04

+0.88

0.89

-+-0.90 —

0.90

-++0.90

+1.42

apes 5

+1.45

SPAS

The Rutherfurd Photographic Measures. 129

TABLE X VIJ.—PARALLAX EQUATIONS.

CoMPARISON STARS 64 AND 6.

Residuals.

E Seale. Are.

—1.841l +1.74=0 +0.46 +0//.13

ley +1.74=0 ++0.39 ae piapate

—1.87 SO.223 = © —I,12 = at

—1.94 +1.53=0 ~—0.23 — .06

—1.85 +1.87 =o +0.27 + .08

—1.85 S111 = © —o.46 — .13

—1.83 +2.52—0 0.96 + .27

—1I.90 +1.08 =o —o.86 —— 42)

—1.93 -++0.97 =o —1.03 — .29

SOR +2.10 =o 0.10 + .03

—I1.93 +2.05 =o +0.05 + .o1

—1.93 +3.51=0 +1.51 + .42

+1.99 —3.72=0 +1.42 +. .40

+1.94 —5.74=0 —o.69 — .19

+1.93 —5.26=0 —0.23 — .06

+1.93 HH = © —0.54 == yk

[vv] = 9.81

Normal Equations.

-+ 16.0000x + 6.6400y — 14.8800II+ 0.1900 =o

- + 16.1850 + 9.3353 — 25.1545 =o

+ 58.0200 — 78.1820 =o

In units of 2d dec. place of scale.

Solution.

Il = + 1.8602 + 0.1143

y = — 0.2695 = 0.2073

x = + 1.8299 + 0.2276

In Are.

Tl = + 0//.5211 + 0/7,0320

y=—O .0755+0 .0581

2=+0 .5126+0 .0638

Seale. AAR.

Probable error of one equation = + 0/7.5859 = + 0/’.1641

130 Parallax of 611 Cygni, deduced from

TABLE X VI.—OBSERVATIONAL DATA.

Comparison STARS 39 AND 6,

Corrected Distance. Sum

Star 39 Stare | Distances

Corrected

Difference

f Difference

Mean

minus Sum

(0)

Distances

113.7446 | 94.9562 | 208.7008 | —.0261 | 18.7884 ; 18.7861

.7430 .9648 .7078 | —.0331 .7782 : -7752

.7364 .9600 .6964 | —.0217 .7764 b -7744

7575 .9487 .7062 | —.0315 .8088 : .8060

7218 .9480 .6698 | +.0049 .7738 : 7742

.7204 .9526 .6730 | +-.0017 .7678 : -7680

-7166| .9487 .6653 | ++-.0094 .7679 ‘ .7687

.7230 -9357 .6587 | -+-.o160 .7873 : .7887

.7000 .9668 .6668 | -+-.0079 72RD : -7339

.6976 -9552 .6528 | +.0219 .7A24 : -7444

.6843 .9781 .6624 | +.0123 .7062 : .7073

.6968 -9650 .6618 | +.0129 .7318 : -7330

.6970 -9805 -6775 | —.0028 .7165 : .7162

.6766 .9701 .6467 | +-.0280 .7065 : -7090

Adopted mean, 208.6747 Assumed value, 18.7560

The Rutherfurd Photographic Measures.

131

TABLE XVII.—PARALLAX EQUATIONS.

CoMPARISON STARS 39 AND 6

, Residuals

, Seale. Are.

I.00X —I.14y —1.30lI +3.01 =o +0.52 +//.15

1.00 —I1.13 —1.37 -++1.92 =o —0.68 — .19

1.00 —I.13 —1.37 +1.84=0 —0.76 = ait

I.00 —0.04 —1.76 +5.00=0 +2.10 + .59

1.00 -++0.88 —1.43 +1.82 =o —0o.29 .— .08

1.00 0.89 —I1.52 +1.20=o0 —I1.05 — .29

1.00 -++0.90 —1.55 +1.27 Oo —I.03 — .29

1.00 +0.90 —I1.55 +3.27 =0 +0.97 a Gay

1.00 +1.42 + 1.73 —2.21 =o +o.92 + .26

1.00 +1.45 +1.81 —I.16=0 -+2.09 + .59

I.00 +1.45 +1.81 —4.87 =0 —1.61 — .45

1.00 +1.45 +1.81 —2.30=0 0.96 + .27

1.00 +1.45 +1.81 —3.98 =0 —0.72 — .20

1.00 +1.45 +1.81 —4.70 =0 —I.44 — .4o

[vv] = 20.23

Normal Equations.

+14.0000% + 8.8000y — 1.0700I1 + 0.1100 =o

+19.5704 +14.8265 —28.9273 =o

+37.0751 —63.9392 = 0

Solution.

Tn units of 2d dec. place of scale. In Are.

Il =+1.6054 0.2051 IL=-+0/’.4497 -£0’’.0575

y = 0.2941 0.3330 y=-+o .082I +0 .0933

x = —0.0694 =£0.3291 %Z=—O .O194 0 .0922

Seale. Arc.

Probable error of one equation = 0.9145 = -£0’’.2562

132

Parallax of 611 Cygni, deduced from

TABLE X VI.—OBSERVATIONAL DATA.

CoMPARISON STARS 5 AND 53.

Corrected Distance.

Star 5

Star 53

Distances

Mean

minus Sum

Difference

of | Seale Corr.

Distances

Corrected

Difference

77-2195

.2144

ANE

2135

.2180

.2093

.2058

.2092

.2103

.2093

.2244

.2169

.2201

.2254

Bay

-2199

75-9023

9034

.8892

.8975

9198 |

.8921

.8913

.8894

.8845

.8958

.8536

.8650

.8707

.8513

-8559

.8646

153-1218

.1178

.1023

-IIIO

.1378

-1014

.0971

.0986

.0948

-1051

.0780

.OS19

.0908

.0767

.0876

-0845

Adopted mean, 153.0993

—.0225

—.O185

—.0030

—.OII7

—.0385

—.002T

+ .0022

++ .0007

+.0045

—.0058

+ .0213

+.0174

+.0085

+-.0226

+.o117

+.0148

2172

.3110

3239

-3160 |

.2982

RIG * ||

-3145

.3198

3258

+3135

.3708

3519

-3494

-3741

-3758

3553

1.3170

.3108

Befaos)

-3159

-2979

sue

-3145

.3198

3258

-3134

.3710

3521

-3495

-3743

-3759

+3554

Assumed value, 1.3330

———

i. a oe

I.00X

I.00

1.00

I.00

1.00

I.00

1.00

I.00

1.00

I.00

The Rutherfurd Photographic Measures.

—I.14y

—I.13

—0.04

+0.88

0.89

0.90

-++0.90

+0.90

+1.42

EAS

+1.45

1.45

+1.45

133

TABLE X VIIT.—PARALLAX EQUATIONS.

CoMPARISON STARS 5 AND 53.

Residuals.

Scale. Arc.

+1.9011 —1.60=0 +0.41 +0/. 11

-+1.90 —2.22=0 —0.21 — .06

-++1.90 —o.9I = 0 +1.10 + .31

+1.47 —1.7I1=0 —0.4I ==) ik

+1.42 —3.51=0 —2.28 — .64

+1.88 —I.58=0 +0.16 + .04

+1.85 —1.85=0 —o.15 — .04

+1.83 —1.32=0 +0.35 + .I0

+1.83 —0.72=0 +0.95 + .27

+1.83 —1.96 = 0 —0.29 — .08

—1.75 +3.80=0 +0.64 + .18

—1.57 +1.91=0 —1I.02 — .29

—I1.57 +1.65=0 —1.28 — .36

—1.55 +4.13=0 +1.22 + .34

—I1.55 +4.29 = 0 +1.38 = 30

—1.55 +2.24=0 —0.67 — .19

[vv] = 14.87

Normal Equations.

+ 16.0000%-++ 9.6600y-++ 8.2700II-+ 0.6400 = 0

+ 20.3820 —12.1142 - 24.9478=0

+ 47.2107 —58.9600 =o

Solution.

In units of 2d dec. place of scale.

I= -+ 1.3326 + 0.1510

y = — 0.1213 + 0.2593

®% =— 0.6556 + 0.2826

In Are.

TT = + 0/7.3733 + 0/7.0423

y=—O .0340+0 +0726

x=—o .1836+0 .0792

Seale. Arc.

Probable error of one equation = + 0.7211 = + 0’’.2020

134

| Corrected Distance

Parallax of 611 Cygni, deduced from

TABLE X VI.—OBSERVATIONAL DATA.

CoMPANION STARS 54 AND 5.

Star 54

Star 5

Sum

Distances

Mean

minus Sum

Diiereuce

(0)

Distances

Scale Corr.

Corrected

Difference

77.3081

.3106

-2969

.2808

.2803

.2740

.2661

-2799

-2449

.2605

.2620

.2507

.2474.

77-2195

.2144

2131

.2093

.2058 |

.2092

.2103

2093 |

2244 |

.2169

.2201

2254

.2199

154.5276

.5250

.5 100

.4901 |

.4861

.4832

4764

.4892

-4693

-4774

.4821

.4761

.4673

Adopted mean, 154.4893

—.0383

Sine 7

—.0207

0.0886

.0962

.0838

.0558

.0706

.0205

.0436

.0419

.0253

.0275

.O715 |

-0745 |

.0648 |

CUS ROVOROROROMONC)

0.0886

.0962

.0838

.0715

-0745

.0648

.0558

.0706

.0205

.0436

.O419

.0253

0.0275

Assumed value, 0.0590

ee 2s

The Rutherfurd Photographic Measures.

Taste X VII.—ParaLnax EQUATIONS.

COMPARISON STARS 54 AND 5.

135

Residuals.

Plate. Seale. Are.

I 1.00% —I.14y —r.91Il -+2.96=0 —0.10 —0’/.03

2 1.00 —I.13 —1I.90 +3.72=0 0.68 + .19

B 1.00 —I.13 —I.90 +2.48=0 —0.56 — .16

9 I.00 +0.88 —1.89 +1.25 =o +0.34 + .10

m0) I.00 +0.89 —1.86 +1.55 =o +0.68 + .19

II 1.00 -++o.90 —1.84 +0.58 =o —0.27 — .08

12 1.00 +0.90 —1.84 —0.32 =0 =I. 17 — 33

1 1.00 +o.90 —1.84 +1.16=o 0.31 + .09

15 1.00 +1.42 +1.77 —3.85 =o —I.01 — .28

16 1.00 +1.45 +1.59 —1.54=0 +1.17 a | 488

7 1.00 +1.45 +1.59 1.7 == © +1.00 + .28

18 1.00 +1.45 +1.57 3.37 =O —o.68 — .19

20 I.00 +1.45 +1.57 —3.15 =o —0o.46 — .13

[vv] = 6.96

Normal Equations.

-+13.0000% + 8.2900y — 6.8g00II1 — 0.2400 =o

+18.2763 + 9.8622 —26.2564 =o

+41.1755 —47.5103 =o

Solution.

In units of 2d dec. place of scale. In Are.

Tl = +0.8680 0.1203 IL-0’ 2431 -£0/.0337

y = -+1.0570 0.2044 y=+o .2961 +O .0573

% = —0.1955 0.2369 Z=—O .0548 oO .0664

Seale. Are.

Probable error of one equation = -£0.5626 = -+-0/’.1576.

136

Parallax of 61: Cygni, deduced from

TABLE X VI.—OBSERVATIONAL DATA.

CoMPARISON STARS 48 AND I4.

Corrected Distance

Star 48

Star 14

Sum

Distances

Mean

|minus Sum

Difference

| Distances

Seale Corr.

Corrected

Difference

50.8127

.8164

-7984

-7972

-7955

-7971

-7785

-7762

-7742

.7680

.7829

| 34.6771

.6853

.6690

.6765

.6742

.6601

.6805

-6744

.6928

.6859

| 6834

85.4898

.5017

.4674

4737

.4697

-4572

-4590

-4506

-4670

-4539

4663

Adopted mean, 85.4688

16.1356

BuO

.1294

.1207

“WAI?

.1370

.0980

.1018

-O814

.O82I

-0995

-+-.0003

—.0009

—.0002

-+.0022

+.oo018

+.0034

+.0003

+.0028

+-.0005

16.1317

' 1249

.1297

.1198

AIT

.1392

.0998 J

1052

.0817

.0849

. 1000

Assumed value, 16.1130

The Rutherfurd Photographic Measures. 137

TABLE X VII.—PARALLAX EQUATIONS.

COMPARISON STARS 48 AND 14. (

Residuals.

Plate. Seale. Are.

2 1.00% —I.13y —r.551l +1.87—=0 0.32 -+0/7.09

2 1.00 —I.13 —1.55 +1.19=0 —0.36 —— LO

IO 1.00 0.89 —1.42 +1.67=0 +0.23 + .06

igh I.00 0.90 —1.38 +0.68 =o —o.71 — .20

12 I.00 -+-o.90 —1.38 -++o.81 =o —0o.58 — .16

13 I.00 -++0.90 —1.38 +2.62=0 +1.23 + .34

15 I.00 +1.42 +1.19 —1I.32—=0 +0.84 + .24

16 I.00 +1.45 +0.93 —o.78=0 +1.02 + .29

18 1.00 +1.45 —++0.90 —3.13—0 —1.37 — .38

19) - | -.00 seas +0.90 —28i==O SIO = ae

20 1.00 +1.45 0.90 —I.30=0 +o.46 + .13

[ov] =7.58

Normal Equations.

+11.00007 + 8.5500y — 3.8400II — 0.5000 =0

+16.2023 + 5.4665 —1II.7759=0

+17.2456 —21.5984 =o

Solution.

In units of 2d dec. place of scale. In Are.

Il =-+1.3880 0.2261 II = + 077.3888 -0’’.0634

y = —0.0359 0.2918 y=—O .O10I +0 .0818

% = +0.5579 0.3485 x=-+0o .1563 +0 .0976

Seale. Arc.

Probable error of one equation -+0.6568 = -0/’.1840

138 Parallax of 611 Cygni, deduced from

TABLE X VIII.—PARALLAX EQUATIONS.

PosITION-ANGLE. STAR 37.

Residuals

in are of

Plate. Reduced Angle. great circle.

2 149°35/56/ 1.0027 —1.13y +146. —54’//—=o — 11

3 36 28 1.00 —1.13 +146. —22 =0 + .I0

4 25 37 1.00 —o.08 +152. 72, =O — .25

5 36 Io I.00 —0.04 +145. —40 = — .05 ;

6 36 55 1.00 —0.04 +145. +5 = + .24

7 36 28 1.00 —0.04 +143. —22 = + .07

8 26 53 I.00 +0.88 +148. qo 3 =—© + .21

9 36 28 1.00 +0.88 +148. = = © + .05

ace) 36 19 1.00 +0.89 +151. =f = = Co

II 36 22 T.00 -++o.90 +151. —28 = + .02

12 AGB 1.00 ++o.90 +151. 47 = — .10

13 35 52 1.00 -+o.90 +151. —5s8 = — .18

15 38 5 1.00 +1.42 —I156. +75 =o + .07

16 37 38 1.00 +1.45 —I152. +48 =o = 10

Ie, 38 18 1.00 +1.45 —I152. +88 =o + .16

18 37 16 1.00 +1.45 —I5I. +26 = — .24

19 37 58 1.00 +1.45 —I5I. +68 = + .03

20 BSD 1.00 +1.45 —I5I. +72 =o +- .06

149 36 50 = Adopted Mean.

Normal Equations.

+18.00x”/ + 11.56y’ + 864.001] — 12.00 =0

+ 19.86 — 876.04 + 474.39=0

+ 402194.00 —115427.00 =o

Solution.

TI =+ 0/.3028 + 0//.0355 [ov] — S12 78

y’ =— 3 .g189+6 .039 o =1336/’.94

¢/ ——- Tl .3531 == 6 -368 Factor = .00648

In Angle. Arc of great circle.

Probable error of one equation = + 15’’.70= + 0’”. 1018

The Rutherfurd Photographic Measures. 139

TasLtE XVIII.—PaAraAtLax EQuaTIONs.

PosITION-ANGLE. STAR 27.

Residuals

in are of

Plate. Reduced Angle. great circle.

2 E7714’ of” 1.0027 —1.13y/ +183.11 — 59./”7=0 +7/.03

2 13 57 1.00 —I.13 +183. — 71. =O — .03

ae) 1459 1.00 +0.89 +178. —— O50) fer

II 1s) I.00 -++o.90 +176. ea ON eo

12 I4 10 I.00 +0.90 +176. —= 5, =O = OF

13 12 a T.00 ++o.90 +176. —I124. =o — .39

15 16 It 1.00 +1.42 —169. + 63. =o — .12

16 16 II 1.00 +1.45° —I5I. a> (Ge ==@> <= O's:

18 17 20 1.00 +1.45 —149. +132. =o + .28

20 16 14 I.00 +1.45 —149. 6, =O. — 7

177 15 8.0o= Adopted Mean.

~ Normal Equations.

+10.0007 + 7.10y’-+ 454.ooll— ZOO 10)

+14.1I0 — 670.99 + 438.500

+287354.00 —1I07966.00 =o

Solution.

I ess OM 2767 3s OY C727) fev], —=Ta187-

Of === F W257 SEND SOR CG) —1O7477.60

a/=—II .8966+14 .69 Factor = .00521

In Angle. Are of great circle.

Probable error of one equation = + 20//.27 = + 0/.1525

140 Parallax of 611 Cygni, deduced from

TABLE X VIII.—PARALLAX EQUATIONS.

PosiTIoN-ANGLE. STAR 48.

Residuals ‘

in arc of q

Plate. Reduced Angle. great circle.

I 105°52/58// I.002/ —I.14y’ + 68.11 — 3//=.0 +//.03

2 52 0 T.00 —I1.13 + 74. —6I =.0 — .35

3 53 23 I.00 —I.13 + 74. +22 =.0 + 4.22

4 51 32 1.00 —o.08 +102. —89 =.0 — .48

5 53 43 I.00 —0.04 +119. +42 =.0 + .46

6 53 9 1.00 —0.04 +119. so 3) ==. + .22

7 52 48 1.00 —0.04 +121. —I3 =.0 + .08

8) 5255 T.00 +0.88 + 80. = (5 = + .06

9 a @ I.00 +0.88 + 8o. = 2 = + .12

ae) ' 52 19 I.00 +0.89 + 89. —42 =.0 — .16

II 52 42 I.00 -+0.90 + 92. —I9 =.0 — .00

I2 52 36 1.00 +0.90 + 92. —25 =.0 — .o4

13 52 8 1.00 -++0.90 + 92. —53 =.0 — .24

15 53 38 I.00 +1.42 —II0. ae =O + .00

16 54 4 I.00 +1.45 —I2I. +63 =.0 + .16

17 54 12 1.00 +1.45 —121. sj == © + .22

18 52 32 1.00 +1.45 —I22. —29 =.0 — .47

19 5355 1.00 +1.45 —I122. +54 =.0 + °.10

20 53 51 1.00 +1.45 —122. +50 =.0 + .07

105 53 1.0 Adopted Mean.

Normal Equations.

+ 19.002/+10.42y’ + 484.0011 + 9.00 =0

+21.16 — 836.67 + 280.52=0

-+201090.00 —50207.00=0

Solution.

TI =-+0/’.2794 -0/’.0766 [vv] = 22847.

y’ =+2 .0965 +8 .487 On 122/269

a/=—8 .7418 +8 - .453 Factor = .00690

In Angle. Arc of great circle.

Probable error of one equation = +25/’.49 = -£0’’.1758

The Rutherfurd Photographic Measures. 141

TABLE X VIII.—PARALLAX EQUATIONS.

Posrrion-ANGLE. STAR 43.

Residuals

in are of

Plate. Reduced Angle. great circle.

I 143°50/ 1// T.00x/ —I.14y’ +tor.II —48.//=o0 —//,01

2 49 42 1.00 —I.13 +104. —67. =0 — .17

2 50 22 1.00 SS) +104. 270 On - 18

ito) 50 28 I.00 0.89 +108. 21% —=10 tO

II 50 19 1.00 -++0.90 +109. —30. =O0O — .o1

I2 50 16 1.00 -++0.90 +109. —33. —9O — .03

13 50 17 1.00 +0.90 +109. —32. =O — .02

15 52 5 I.00 +1.42 —Il4. +76. =o + .23

16 51 23 I.00 +1.45 —II3. +34. =o — .I4

18 51 43 1.00 +1.45 —II2. +54. = + .04

19 52 19 I.00 +1.45 —Ii2. +90. = + .36

20 50 4I I.00 +1.45 —II2. = § = — .51

143 50 49.0 = Adopted Mean.

Normal Equations.

+12.00%/+ 7.41y/-+ 181.00II— 12.000

SEI —= Fy) SS alien == ©

+-142537.00 —54985.00 =o

Solution.

TI = +40’’.3299 -0//.0658 [vv] =6788.

y/ =—9 .8126 +6 .845 o == 1824//.90

a/=--2 .0830 7 .280 Factor = .00885

In Angle. Arc of great circle,

Probable error of one equation = +18//.52 = +0/’.1638

142 Parallax of 611 Cygni, deduced from

TABLE X VIII.—PARALLAX EQUATIONS.

POSITION-ANGLE. STAR 32.

Residuals

: in arc of

Plate. Reduced Angle. : great circle.

I 172°39/40// 1.00x/ —I.14y’ +93.11 —30./’=0 -+0//.08

2 39 51 1.00 —I1.13 +93. —28. =o + .10

3 39 55 I.00 —I1.13 +93. —24. =o + .14

4 BoM2 I.00 —0.08 +87. —67. =o — .43

5 39 41 1.00 —0.04 +75. —38. =o — .18

6 39 51 I.00 —0.04 +75. —28. =o — .07

7 4o 2 I.00 —0.04 +73. —I7. =o + .03

8 40 II 1.00 +0.88 +02. — 8 =o + .I0

9 4o 1 1.00 +0.88 +92. —18. —o — .00

a0) 39 59 1.00 0.89 or. —20. =O — .03

iit 40 5 1.00 -+c.90 +90. —I4. =o + .03

I2 4o 18 1.00 -+0.90 +90. = 1, =o faa,

13 4o 4 I.00 0.90 +90. —I5. =o + .02

15 Ar 6 T.00 +1.42 —S88. +47. =o — .02

16 40 47 T.00 +1.45 —S8o. +28. =o — .I9

I7 A KF 1.00 +1.45 —8o. +58. = + 12

18 AI 36 1.00 +1.45 ==76). SRife == rE

19 4I 19 I.00 +1.45 —79. +60. = St iaillral

20 4O 34 I.00 +1.45 —79. +15. =9 — .33

172°40 19.0 = Adopted Mean.

Normal Equations.

+19.00%’-+10.42y/+ 649.0011— 23.000

+21.16 — 546.78 + 445.800

-++138871.00 —49582.00 =o

Solution.

II =+0//.3442 + 0/’.0489 [vv] =5382.

Of ==—=©) 562 SE 4) 251 oO = 2155.//55

u/=—5 .3013 +4 .638 Factor = .01045

In Ang'e. Arc of great circle.

Probable error of one equation = --12./”37 = -—0.//1293

Plate. Reduced Angle.

oO MON ANH WN

NY HH HH HR HAR Ra

OO ON AM WN H

356°4/49//

5 12

4 49

5 20

4 14

4 40

5 F

4 50

4 57

5 0

4 42

458

5 11

Ant

413

359

4 24

3 40

PositTIon-A NGLE.

The Rutherfurd Photographic Measures. 148

TABLE X VIII.—-PARALLAX EQUATIONS.

STAR 23.

Residuals

in arc of

great circle.

_—T.14y —79.I1 + 8.”=0 —0o/’.08

—I.13 —79 +31. = + .20

—I.13 —79 +8. = — .08

—0.08 18 “ok =o Ais PES

—0.04 —62. —27. =o — .45

—0.04 —62. —il= ee

—0.04 —60 +26. =o + .20

0.88 —78. +9. =o OS

+0.88 —78. +16. =o + .00

+0.89 —77. +19. =o + .0o4

-++0.90 —76. + 1. =o = Gf

-++0.90 —76. 7g 6) So How

-++0.90 —76. +30. =o + .18

+1.42 +73. —40. =o = 07

+1.45 +66. —28. = + .05

+1.45 +66. —42. =o — .I2

+1.45 +65. —I7. =0 ee Gil)

+1.45 +65. —61. = — .36

+1.45 +65. — 2. =o + .36

4 39

1.00

356 4 41.0= Adopted Mean.

Normal Equations.

+19.00%/ +10.42y’ — 555.001!1I— 14.000

+21.16 -+ 448.60 — 248.42—0

-+97481.00 —26185.00 =o

Solution.

T= -+ 0/7.3334 0/7.0584 [vv] 5349.

y/ =— 0 .6676 +4 .237 o = 2500/’.62

a/—=+10 .8423 +4 .652

Factor = .01213

In Angle. Arc of great circle.

Probable error of one equation = 127.33 = -£0’’.1496

144

Parallax of 611 Cygni, deduced from

TABLE X VIII.—PaARALLAX EQUATIONS.

PosITION-ANGLE. STAR 13.

Plate. Reduced Angle.

BAT 257167 1.00%

24 30 1.00

25 10 1.00

25 40 1.00

25 0 1.00

24 55 1.00

25 6 1.00

25 14 1.00

25 13 1.00

24 59 1.00

25 4 1.00

23 54 1.00

24 13 1.00

24 19 1.00

24 47 I.00

23, 52 1.00

23, 59 1.00

—I.14y

—I.13

—o.08

—0.04

+0.89

—++0.90

0.90

-++0.90

+1.42

+1.45

SoA

Sleds)

+1.45

Sls)

341 24 46.0= Adopted Mean.

_Normal Equations.

+17.002/ + 8.66y’ —

365.0011 +- 2.00 =O

+19.62 + 601.51 — 270.020

-+85293.00 —30221.00 =o

Solution.

I+ 0/7.4401 +0/’.0643 [vv] = 4672.

Yl 4 GO y= A) 5 Om C2 5A

#/—=+11 .8592 +4 .582 Factor = .01336

Residuals

in arc of

é : great circle.

—73.11 +23.//—=0 0/7. 11

—73. —I6. =" — AI

—73. +24. = + .12

72. > --54.: 10 es

—66. +14. = — .04

—66 +9 = — II

—65 +20. = + .05

I, +28. = Bie os

Fa +27, = == 82

ial +13. = a

—74 +18. =o eS

+74. —52. = ===) 228

69. +33. (= 0 ees

+69. —27,. = + «II

+69. +r = + .48

+69. —54. = — .26

+69. —47. =0 — A16

In Angle. Arc of great circle.

Probable error of one equation = +12/’.32 = -£0’7.1646

The Rutherfurd Photographic Measures. 145

The Parallax of 61° Cygni.

o¢. If the coefficients for parallax of 617 Cygni be computed by

the formule of paragraphs 14 and 22, we have:

. 8) 01206 Ss = +9777-

S, = —o 822 8, = —I1120.

With these, and the values of P, and P, of paragraph 14, have

been obtained the quantities printed in the last column of Table

XIII.

38. The measured distances duly corrected for proper motions

of both stars are given in the last-but-one column of Table XIII.

Table XIX contains the equations of condition of the form:

x + (t—1873.546)y + (SP; + &,P,) I+ ¢—o,’=0

from which are derived the values of the unknowns given on the

same page.

39. In column nine of Table XIII are given in like manner the

corrected position-angles from which the equations of condition

of Table XX have been formed after the manner of paragraph 35.

They are of the form

a’ + (t—1873.546)y’ + o-sin 1’/’- (SP; -+ SyP,) I+ o-sin 1/’- (7 —7,/) =o.

The resulting values of the unknowns will be found on the same

page. ;

40. In both these cases, however, we cannot assume the parallax

of the reference star to be nil. Its value has been shown to be

+ 0./’360 +/..015. The mean by weight of the values of parallax of

61+ with respect to 617 obtained from distance and from angle is

++ o!’.072 +’’.028, wherefore the concluded value of the

Parallax of 612 Cygni = 0//.288 + ’/.031

referred indirectly to all the comparison stars given in Table XIV.

146

HHH ee y eo

MIAN WNHOWMNAUMSEA

NO H

(oe)

Parallax of 61% Cygni, deduced from

TABLE XIX.—PARALLAX HQUATIONS IN DISTANCE.

I.00%

I.00

1.00

31,00

1.00

I.00

CoMPARISON STAR, 611 Cygni.

—I.60y —o.77II

—1.68 —o.74

—1.68 —0.74

—0.63 —0.57

—0.59 —0.37

—o.58 —0.34

0.33 —Oo.71

0.33 —0o.71

+0.34 —0.67

+0.35 —0.65

0.87 0.55

-+0.90 +0.42

0.91 +0.40

--0.91 +0.40

0.91 +0.40

Normal Equations.

—0o/’,140=0 —o/’,248

+ .136=0 + .032

+ .200—0 + .096

+ .076=0 + .022

— .058=o0 — .085

+ .085=0 + .058

4-. 1.0780 == Cee

+ .ocoI= — .045

et AO oS

+ .030—0 = Oo

+ 243-0 = .205

+ .06I=o0 + .023

+ .128= + .o90

+ .038= + .168

ee ORI a 2O75

022—= + .092

— .246=0 — «134

— ,.280—0 — .168

— .146=0 =) 023

-+-19.000 oo0r + 0.010 000y —5.350 oo0oII —o’’.002 000 =0

+15.492 500 +5.728200 —O .957070—0

6.262 300 —o .691 430=—o0

Probable error of one equation = -£0’’.0865.

Solution.

x= -0’.0362 -£0/’.0249

y=-bo .0272 +0 .0295

T=-bo .1282 £0 .0533

Weights.

I2.08

8.59

2.64

[vv] = 0.2634

OO ON AN KR HN

ND oH HH HH HH HH

OO ON DUN WN H

The Ruther furd Photographic Measures.

TABLE X X.—PARALLAX EQUATIONS IN ANGLE.

CoMPARISON STAR, 61! Cygnt.

1.002/ —1.69y/ +0.59711 —// 1000

1.00 —1.68 + .633 — .074=0

I.00 —1.68 + .633 — .142=0

I.00 —0.63 + .802 — .165=0

1.00 —0.59 + .890 — .058:=0

I.00 —0.59 + .890 + .122—o0

1.00 —0.58 + .896 — .150=0

I.00 +0.33 + .672 — .134—0

I.00 +c.33 + .672 + .025=0

I.00 +0.34 + .723 + .087—0

I.00 +0.35 + .742 + .063—0

1.00 +0.35 + .742 + .o13=0

I.00 +0.35 + .742 — .II3=0

I.00 +0.87 — .850 + .068—o

1.00 0.90 — .gI0 + .o12=0

I.00 -++o.90 — .9gI10 + .383=0

I.00 -+o.91 — .9I3 — .076—0

I.00 -+0.91 — .9I3 + .037=0

1.00 0.91 — .9I3 + .205=0

Normal Equations.

-++-19.000 ooor + 0.010 000y-+ 4.225 oooll +-0’”.003 000 = 0

+15.492 500 — 8.612500 +1 .231 4500

+12.145003 —I .0o12 807 =o

Solution.

Weights.

x’ —=—0’7,0115 + /’/.0200 16.57

y’ =—O .0510 + .0273 =—O°.15I £0°.081 8.87

II +0 .0512 + .0321 6.42

Probable error of one equation = -£0’’.0813 [vv] = 0.2326

147

Vv.

+/7.005

.033

.065

.103

.006

.186

.086

.128

.031

+095

.072

.022

.104

| ear |

[+++ |

.031

— .092

-279

.181

.068

.100

ae |

148 Parallax of 617 Cygni, deduced from

Incidentally it should be noticed that the assumed annual

change in distance of 61? from 611 was —o’’.128, the negative

sign being used to indicate separation. From the value of y in

Table XIX the correction to this is o’’.027. Thus the RurHer-

FURD plates for an interval of only 2.6 years give:

Annual increase of distance = 0/’.Io1 -+’/.030.

In like manner, the assumed increase of position-angle being

0°.370 and Table XX, giving as a correction a further increase

of 0°.151, there results :

Annual increase of angle — 0°,521 --°.081.

But what is of greater significance, there is also a difference of

parallax :

(61' Cygni— 61° Cygni) = + 0”.072 + ”’.028

41. This result is so surprising and yet the difference of paral-

lax obtained from angles and from distances is so accordant

within the limits of their respective probable errors that I have

deemed it advisable to use the very excellent series of measures

of the distance of these two stars given by WILSING in Sitzungs-

berichten* der Konigl. Preuss. Akademie der Wissenschaften,

1893, Bd. 40, to see what value of the difference of parallax, if

any, might be deduced from them.

42, Using Auwers’ values of the right ascension and declina-

tion of 61! Cygni for 1875.0 and his constants of precession we

have:

tee RN Gee } for 1891.0

O33 821248726

I have taken p= 114°.692 for 1873 with an annual variation of

0°.50 which gives p = 123°.5 for 1891.0 quite accurately enough ;

as an error of a whole degree would, demonstrably, have no sen-

sible effect upon the deduced value of parallax. Therefore :

&, = [9.9849] sin 350°.8 = — 0.154

S, = [9 9181] sin 271°.3 = — 0.828

With these and the values of P,; and P, computed for each date

of Wixstna’s plates} were formed the parallax coefficients

SPs > Si Px

which are found in the equations of condition of Table XXI.

*Since given more fully in Publicationen des Astrophysikalischen Observator-

iums zu Potsdam, Nr. 36, Bd. XI, 1897.

+Sitzungsberichten, etc., pages 883-4.

The Rutherfurd Photographic Measures.

Date.

TABLE X XI.—WiItsING’s MEASURES.

Meas.

Dist.

Equations of Condition.

Cor-

rected -

Distance.

149

Distance

Minus

Mean.

NO oH

HOW CONIO MN eS (os)

1890 Oct.

Nov.

Dee.

1891 Feb.

May

June

Sept.

14.43

22.43,

5.32

17.24

4.29

5.48

8.49

I1.46

I1.47

TOA,

29.46

9-49

16.44

17.47

17.49

. 18.40

18.41

18.43

22.42

23.44

27.41

27.42

28.45

28.46

29.38

31.37

31.39

6.44

6.45

7.42

7-43

9.46

11.38

23.41

23-43

24.35

24.36

30.37

30.38

“dl

21.04

20.90

20.89

20.95

20.99

21.04

20.97

21.04

20.87

20.81

20.94

20.91

20.85

20.81

20.76

21.12

21.11

21.10

21.01

21.03

21.06

21.20

21.04

21.16

21.02

21.03

21.06

21.02

21.12

21.16

20.95

20.97

21.03

21.14

20.87

21.22

20.90

21.04

I.2—O.22y gall o4-—=0

I —0.1I9 —.79 —.IO

i —O} 16) ——+70 | ——. ©

I —0.04 —.2I —.05=0

tI +o.10 +.48 —.oI=o

rt +0.34 +.70 +.04=0

I +0.35 +.68 —.03

rt +0.36 +.65 +.04

I +0.36 +.65 —.13

I +0.36 +.64 —.19

I +0.40 +.46 —.06

I +0.42 +.37 —.09=0

rt +0.46 +.22 —.15

rt +0.46 +.21 —.19

rt +0.46 +.21 —.24

1 +0.63 —.60 +.12=o0

I +0.63 —.60 +.11

I +0.63 —.60 +.10

I +0.64 —.64 +.01

I +0.64 —.65 -+.03

I +0.66 —.69 -+.06

I +0.66 —.69 +.20

I +0.66 —.69 +.04

I +0.66 —.69 +.16

I +0.66 —.70 +.02

I +0.67 —.72 +.03

I +0.67 —.72 -+.06

I +0.69 —.76 -+.02=0

I +0.69 —.76 +.12

I +0.69 —.77 +.16

I +0.69 —.78 —.05

1 +0.69 —.79 —.03

I +0.72 —.83 +.03

I +0.72 —.83 +.14

tI +0.72 —.83 —.13

I +0.72 —.83 +.22

I +0.75 —.84 —.I0

I +0.75 —.84 +.04

20.986

20.847

20.842

20.935

21.024

21.073

21.001

21.071

20.901

20.837

20.947

20.907

20.831

20.790

20.740

21.017

21.005

20.995

20.901

20.920

20.946

21.086

20.926

21.046

20.905

20.912

20.942

20.896

20.996

21.036

20.825

20.844

20.898

21.008

20.738

21.088

20.764

20.904

+004

—.135

—.140

—.047

+.042

-++-.091

-+.019

+.089

—.o81

—-145

=:039

—.075

—.I151

—.192

—.242

+-.035

150 Parallax of 61% Cygni, deduced from

TABLE XXI.—Witsinea’s MEAsurEs, ( Continued).

Cor-

No. Date. Meas. Equations of Condition. rected

Dist. Distance.

20.864

1.a+0.75y —,.84II-+o0o=o

‘ I +0.75 —.84 +.07 20.934

42 6.35 | 21.01]I -+0.77 —.84 +.o1 20.873

43 pave | Biante || 1 EOL —seul ee 20.993

44 9.36 | 21.32/11 +0.78 —.84 +.32 21.182

45 10.30 | 21.31 |I -++0.78 —.84 +.31 21.172

46 20.43 | 21.13|1 +0.80 —.80 +.13 20.994

47 23.42 | 21.21}1 +0.81 —.79 +.21 21.074

48 23.43 | 21.08}/1 +0.81 —.79 +.08 20.944

49 28.36 | 21.1I0/1 +0.82 —.76 -+.10 20.965

50 Oct. 29.32 | 21.17|1 +0.82 —.75 +.17=o] 21.036

51 Nov. 3.32 | 21.13|1 +0.84 —.72 +.13 20.998

52 3.33 | 21.11|1I +0.84 —.72 +.11 20.978

53 5.41 | 21.06}1 -+0.84 —.70 +.06 20.930

54 5.42 | 21.03|/1 +0.84 —.70 +.03 20.900

55 19.30 | 21.34]1 -++0.88 —.57 +.34 21.217

56 29.33 | 21.23 ,;1 +0.91 —.46 +.23 21.115

57 29.34 | 21.41|I +0.91 —.46 +.41 21.295

21.202

+0.94 —.30 +.25 21.147

+0.95 —.29 +.18 21.077

+0.95 —.29 +.26 21.157

: 21.033

+0.96 —.21 +.07 20.973

+o0.98 —.10 +.32 21.230

+o.98 —.10 +.11 21.020

+0.98 —.10 -+.09 21.000

HHHHHHH HA

Ne)

ics)

67 | 1892 Jan. 7.24 | 21.07/1 +1.02 +.09 +.07=0] 20.994

68 7.26 | 21.12]1 +1.02 +.09 +.12 21.044

69 17.29 | 21.14]1 +1.04 +.24 +.14 21.075

70 17.30 | 21.T0]/1 -+1.04 +.24 +.10 21.035

ail 20.25 | 21.26}1 +1.05 +.28 +.26 21.198

72 20.27 | 21.18}/1 +1.05 +.28 +.18 21.118

73 - 20.28 | 21.09]/1 +1.05 +.28 +.09 21.028

74 May 8.53 | 21.08

75 II.52 | 21.08

76 II.53 | 21.07

77 26.54 | 21.05

+1.35 +.67 +.08=o0] 21.028

+1.36 +.64 +.08 21.024

21.014

+1.40 +.48 -++.05 20.977

HHHHH

iilaete

-b

fe)

78 26.56 | 21.10 +1.40 +.48 +.10 21.027

79 June 8.49} 21.05}/1 +1.43 +.32 +.05=o] 20.960

80 8.51 | 21.07}1 +1.43 +.32 +.07 20.980 | —.002

8I 17.55 | 21.17/11 +1.46 +.20 +.17 21.068 | +.086

82 28.48 | 21.16]1 +1.49 +.04 +.16 21.041 | +.059

The Rutherfurd Photographic Measures. 151

TABLE XXI—Wustne’s Measures, (Concluded).

Gon Distance

Date. Meee Equations of Condition. rected | “Wear,

ist. Distance. Fae

1892 Dec. 22.36 | 21.12 | I.a+1.97y —.13II1+.12=0] 20.947 | —.035

1893 Jan. 7.24 | 21.16 +2.02 +.10 +.16 21.003 | +.021

7.28 | 21.12 +2.02 +.10 +.12 20.963 | —.O19

I1.25 | 21.15 +2.03 +.16 +.15 20.997 | +.015

28.26 | 21.10 +2.08 +.40 +.10 20.964 | —.018

Feb. 4.26 | 21.19 +2.10 +.49 +.19 21.060 | +.078

Mar. 23.61 | 20.98]1 +2.23 +.83 —.02=o] 20.869 | —.113

j 23.64 | 21.00/1 +2.23 +.83 .0O 20.889 | —.093

27.62 | 21.06{1 +2.24 +.84 +.06 20.949 | —.033

HHA RAR

Apr. 6.57 | 20.95]1 +2.27 +.84 —.05=0| 20.837 | —.145

18.59 | 21.02|1 +2.30 +.80 +.02 20.900 | —.082

21.50 | 21.05|1 +2.31 +.79 +.05 20.929 | —.053

May 9.55|21.11/1 +2.36 +.66 +.11=o0]| 20.974 | —.008

IO.51 | 21.11 }1 -+2.36 +.65 -+.11 20.973, | —.009

15.56 | 21.10 +2.37 +.60 +.10 20.958 | —.024

23.57 | 21.09 +2.39 +.52 +.09 20.939 | —.043

June 1.50|21.12}1 +2.41 +.41 +.12=0] 20.957 | —.025

7.49 | 21.15|/1 +2.43 +.34 +.15 20.980 | —.002

14.49 | 21.16}1 +2.45 +.24 +.16 20.979 | —.003

24.44 | 21.13/1 +2.48 +.10 +.13 20.935 | —.047

July 4.44) 21.22|1 +2.51 —.04 +.22=0] 21.009 | +.027

15.41 | 21.2T}1 +2.54 —.19 +.21 20.984 | +.002

Aug. 3.41 | 21.24]/1 +2.59 —.44 +.24 20.988 | +.006

Aug. 4.41 | 21.23|/1 +2.59 —.46 -+.23=0] 20.977 | —.005

10.39 | 21.17|1I -+2.61 —.52 +.17 20.909 | —.073

31.45 | 21.26|1 +2.67 —.72 +.26 20.977 | —.005

Sept. 1.49 | 21.27}1 +2.67 —.73 +.27=0] 20.986 | +.004

15.48 | 21.22/14 +2.71 —.81 +.22 20.926 | —.056

21.00 = Assumed Mean. Luv = 1.1032

Mean = 20.982

152 Parallax of 612 Cygni, deduced from

43. From these equations are obtained the following normal

equations and values of the unknowns :

Normal Equations.

-+I10.0000x +-129.0300y —19.1300II +10.3300 =0

+215.2083 — 3.9695 -+15.7599=0

+39.4805 — 3.4429 =0

Solution.

Weights.

x=-+ 0’’.0180 + 0’’.0014 25.49

y¥=—O .0824 =O .0003 54.42

M=-+0 .0876+0 .0123 30.81

Probable error of one equation = + 0/’.0684

fevi|i== 1/7 71006

44, It will be noticed that this difference of parallax between

6r: and 67? is in very close agreement with the + 0o/’.072 + .’’028

derived from the RUTHERFURD measures. Its probable error and

the sum of the squares of the residuals when compared with simi-

lar quantities* in WILsING’s determination of the parallax of 61?

Cygni would indicate that it has as real an existence in the meas-

ures as his own values of the parallax of 67? itself; while at the

same time bearing testimony to the excellent quality of his meas-

ures.

45, Yet this difference cf parallax does not preclude the possi-

bility of orbital motion of either 6z1 or 677 about a dark com-

panion, as has been suggested by WILsING to account for the sys-

tematic irregularity of his measures—a suggestion which the

outstanding residuals, after corrections for this difference of paral-

lax have been applied to the measures, would in a degree confirm.

And yet it is greatly to be regretted that points numbered 1, 2, 3,

and 4 of his curvef are determined by only 4, 2, 2, and 2, ex-

posures on 2,1, 1, and 1 plates respeetively, in contrast with the

other points which are determined by the means of from 11 to 4o

exposures ; and that the most critical portion of the curve (that

from January 15th, 1892, to January 13th, 1893) is determined by

two points only, from 15 and 11 exposures on only 5 and 4 plates

respectively. Moreover, for the reasons stated on page 160 of this

paper, the testimony of the PrircHaRD measures, adduced by

* [vv] = 2.691 ; 2.390 and 1.681 on pages I09, 114 and 120 respectively,

Publicationen, etc.

+ Sitzungsberichten, etc., pages 884-5.

The Rutherfurd Photographic Measures. 153

J AcoBy* to corroborate WILSING, should be given no weight at the

present time.

On the other hand, it is stillan open question whether or not

the parallaxes obtained from RUTHERFURD measures may not be

affected by systematic errors, the nature and origin as well as ex-

istence of which are at present unknown. The case of f Cygnit

as well as Mrs. Davis’ deduction of a similarly large parallax

from the measures] of “ Bradley 3077 ” give room for this suspi-

cion. It is for this reason that the confirmation of difference of

parallax by WILsInG’s measures is all the more instructive.

46. It should be stated in this connection also, that even if

such orbital motion exist, its amplitude is so greatly diminished

by this difference of parallax of the two stars as to reduce the

sum of the squares of the residuals formed in means for the 22

groups of Wiusina’s Table on page 885§ from 0.1708 to 0.1052 or

by nearly forty per cent.

In the following Table, are reproduced, in column two, these

twenty-two mean residuals{ and in column three are given also the

mean of the residuals for the same plates from the last column of

Table XXI, whereby to facilitate their comparison as to the ef-

fect produced by the introduction of the parallax into the equa-

tions.

I have also made a second solution of these 110 equations on

the assumption that there might be a term whose coéflicient is]||

tan ¢ cos (p — q)

to account for the unequal effect on the two stars of the at-

mospheric dispersion. The solution of the equations and the re-

sulting residuals are not contradictory of WiILsine’s conclusions

(from the similarity of the spectra of 6z1 and 672) that there is

no reason for the introduction of this term. In column four are

given, however, the means of the residuals resulting from this so-

lution.

*Monthly Notices, Vol. LIV, page 117. See also, Vierteljahrsschrift, for 1891,

Vol. 26, p. 146.

t Astronomical Journal, No. 287: On the Probable Large Parallax of

Cygni, by Harold Jacoby.

{ Contribution from the Observatory of Columbia University, New York,

No. 14.

¢ Sitzungsberichten, etc.

|| Publicationen des Astrophysikalischen Observatoriums zu Potsdam, No 36,

page 144.

{| Monthly Notices, Vol. LV, page 123. But see also Vol. LVIII, page 83.

154 Parallax of 61? Cygni, deduced from

TABLE X XIT.—WiItstna’s MEASURES.

(See Paragraph 46. )

Mean of Residuals. Weight.

oak with | With Paral. Mean Date.

Wilsing. it and Atmos. | Plates. | Expos.

Parallax. | Dispersion.

oat — 066 —'073 1890 Oct.

—.039 —.140 —.142 Nov.

+.0oo1 —.047 —.084 Dec.

+.031 +.042 —.O41 . 1891 Feb.

—.039 —.O1O +.052 May

—.179 —.165 —.145 June

-+.071 —.O15 —,003 Aug.

+.031 —.063 —.047 Sept.

+.111 +.018 +.026 Oct.

+.131 +.077 +.066 Nov.

+.I51 +.111 +.069 Dec.

-+.091 +.088 +.018 1892 Jan.

—.009 +.032 +.043 May

-+.o11 +.030 +.038 June

—.009 +.007 —.o61 1893 Jan.

—.159 —.080 —.043 Mar.

—.169 —.093 —.054 | April 15

—.089 —.021 —.O14 May 14

—.049 —.019 +.004 June II

+.021 +.o012 +.026 ~ July 18

+.o1r —.028 —.002 Aug. 15

+.031 —.026 —.022 Sept. 8

47, Several astronomers have investigated the parallax of

these stars by measures with reference to the point mid-way be-

tween 6z1 and 672; others with reference to either star indepen-

dently of the other. In Table XXIII are gathered many of the

results of such investigations where the stars were individually

observed. Whenthe same measures have been reduced in several

different ways or by different persons, that result which is re-

garded as definitive has been printed in heavy type, the lightface

type being used in other cases. The numbers in the last column

refer to the list of reference books given on pages 159-160.

The Rutherfurd Photographic Measures.

TABLE X XIIJ.—VAaARiIouS VALUES OF PARALLAX OF 61! CYGNI.

Method.

Star

Comparison.

Parallax

(0)

611 Cygni.

Probable

error

Authority.

Photography

Absclute

38°4351

Absolute (? )

Ten Stars

10.349

.4654

.400

.50

AeA

.30

-£0.080

-0497

-055

:094

.03

Peters

Ball

Ramb. Ball

Belopolsky

Flint

Kapteyn

Distance.

Photography

37°4189

38°4336

37°4175

38°4348

38°4372—37°4159

38°4353—37° 4159

38°4325—38° 4362

38°4363—38° 4325

37°4189—38° 4336

37° 4189

[0.4294]

[ .4414]

[ .4448]

[ .4193]

5211

4497

+3733

2431

.3888

.405

+6.0162

.0222

.O212

.O182

-0373

.0429

.0400

-0409

.0658

.026

Pritchard

Davis

Wilsing

ition Angle.

Photography

37°4180

37°4175

37°4189

37° 4185

37°4178

38°43.41

38° 4335

0.3028

3779

-2794

-3299

3442

3334

4401

+6.0354

-0395

-0473

-0557

.0620

-0743

.0819

156

Parallax of 61? Cygni, deduced from

TasBLE X XIII.—Various VALUES OF PARALLAX OF 612 OYGNI.

Parallax | Probable

Method. 4 Star of oO error Authority.

omparison. §12 Cygni. r

Ad, Microm. 38°4351 +0.4676 0.0321 Ball 9

SS 38° 4345 .2698 .0130 | A. Hall II

oe 38°4345 .3217 .0213 | A. Hall 6k

(a Aa = —63°.5 x

Ad =—34// . 2005; .0246 | A. Hall II

Aa Absolute (?) 55 .o91 | Belopolsky ae)

Photography Ten Stars. 36 .034 | Kapteyn 7

Distance.

Micrometer 38°4345 0.5092 +0.03 55 | O. Struve 3

oe y .5179 .0328 | Lamp’s Struve 6

Micrometer 38°4345 4365 .0738 | Socolofi’s Schweizer 5

is as .4885 .0824 | Socoloft’s Schweizer 5

e os .4388 .0654 | Lamp’s Socoloff’s Schweizer | 6

rs ws .5220 .0770 | Lamp’s Socoloft’s Schweizer | 6

ss ae -4594 .0637 | Lamp’s Schweizer 6

oe s 4715 .0684 | Lamp’s Schweizer 6

Photography 37°4189 |[ .4250]| .0176| Pritchard 12

& 38°4336 [ .4508] .OIgI | Pritchard 12

& 37°AI75 [ .4320]| .o1go | Pritchard I2

es 38°4348 [ .4303]| .o178 | Pritchard 12 |

Photography 61! Cygni .288 .031 | Davis 13

Photography 37°4189 .357 .o17 | Wilsing 14 |

Position-Angle.

Micrometer 28°4345 +0.5008 +.0.0466 O. Struve 3

o “ 4913 .0371 | Lamp’s Struve 6

Micrometer 38°4345 -3761 -0439 | Socoloff’s Schweizer 5

es ue .4926 .0546 | Socoloff’s Schweizer 5

Hs Se 3925 .0438 | Lamp’s Socolofi’s Schweizer | 6

KD oe .4957 .0512 | Lamp’s Socoloft’s Schweizer | 6

“3 ie .3818 .0457 | Lamp’s Schweizer 6

Gh a 4824 .0517 | Lamp’s Schweizer 6

The Rutherfurd Photographic Measures. 157

48. While there is some dependence of one result on another

in those instances where the same star of comparison was used,

yet, as the measures were made by independent observers and dis-

similar methods, and show in themselves no indication of a paral-

lax of the comparison-star, it is not improper to combine all these

individual results into means by weights proportional to the re-

ciprocal of the square of the probable error. Thus we have the

mean of previous determinations of the

Parallax of 61! Cygni = 0./”417 + 0/’.0216

and, in like manner excluding my own determinations:

Parallax of 61? Cygni = 0’7.335 ++ 0’”.0076

which give:

671 — 61? = +0.//082 =0/’.023 [-+0’’.054 +0’’.o10]

and if the RuTHERFURD results be included as given in Table

XXIII, this becomes:

61! — 67? = +0/’.048 + 0’’.014 [-+0/7.035 +0’’,009]

The numbers placed in the brackets are what these values would

have been had PRITCHARD’ results not been discarded.

49. Let us now tabulate these differences of parallax of the

two stars under consideration :

Davis’ Rutherfurd,—direct measures of distance +-0’’.128 +-77.053

Davis’ Rutherfurd,—direct measures of angles -++ .051 .032

Adopted Mean = +. 0//,072 + //,028

Davis’ Wilsing,—direct measures of distance + 088 .O12

Wilsing’s (61! — 6) — (612 — 6)* + .048 .031

Mean of all determinations{ previous to Rutherfurd = + 082 .O13

Mean of all determinations including Rutherfurd = + .048 .O14

The magnitude and accordance of these values when considered

in connection with their respective probable errors leave little

room for doubt as to the reality of the difference of parallax de-

tected by the measures of the RuTHERFURD plates, and discarding

PRITCHARD’s results in no respect lessens the force of the argu-

ment. So that if 611 Cygni be really a binary system of which

*Publicationen des Astrophysikalischen Observatoriums zu Potsdam: Nr. 36.

page 148.

As determined from Table X XIII on pages 155-6, using only the values in

bold type. :

158 Parallax of 612 Cygni, deduced from

one member is a dark body* it is nevertheless far removed from

the influence of 617 Cygni, which would account for the as yet

unproved} orbital motion of 671 and 6z* around a centre of

gravity common to the two. The probabilities in favor of the

existence of such orbital motion, if they really have the same

parallax, are fully as strong as are those against the juxtaposition

in line of sight of two stars having so nearly the same large ap-

parent motion, if they are really separated in space by the dis-

tance which this difference of parallax indicates.

This presents to us therefore one of those cases where the ex-

ceedingly strong probability against an event happening is per-

haps overruled by its actual occurrence.

The evidence here presented as to a difference of parallax is at

any rate of sufficient weight to demand a more extended series of

photographic measures of the same degree of precision as WIL-

sING’s and extending over more than two years. Perhaps Prof,

Wilsing would himself be willing to continue his series of plates.

It is also highly desirable to reinforce the evidence of a variable

proper motion of 671 by independent methods, such as is afforded ,

by the spectroscope, for example.

* Publications of the Lick Observatory, Vol. II, 1894. Page 122. BURNHAM

records his inability to see at 1889.463 and 1889.502 a companion to either

star, though using the 36-inch telescope with powers up to 1000.

+ Monthly Notices, Vol. XX XV, page 323. Ast. Nach., Vol. 132, pages 87 and

199. BURNHAM in The Sideral Messenger, Vol. X, page 1,and MANN, ibid.

page 13.

The Rutherfurd Photographic Measures. 159

Reference Books.—(See Taste XXIII.)

(1.) BesseEt—Astronomische Nachrichten, No. 365-6, and Vol.

XVII.

(2.) Pevers—Recherches sur la Parallaxe des Htoiles Fixes.

Recueil de Mémoires présentés a1’ Académie des Sciences par

_les Astronomes de Poulkova. Vol. I, page 136.

(8.) Struve—Nouvelle Détermination de la Parallaxe an-

nuelle des Etoiles a Lyre et 61 Cygni. Memoires de |’ Académie

Impériale des Sciences de St.-Pétersbourg, VII Série. Vol. I,

No. 1, page 44.

(4.) Auwers—Untersuchungen itiber die Beobachtungen von

Bessel und Schliiter am Konigsberger Heliometer zur Bestim-

mung der Parallaxe von 61 Cygni. Abhandlungen der Academie

zu Berlin, 1868: page 113.

(5.) Socotorr —Parallaxes des Etoiles observées par G.

Schweizer. Annales de 1’ Observatoire de Moscou, Vol. VIII, 2,

pages 89-90.

- (6.) Lamp—Neue Berechnung der Parallaxe von 61 Cygni aus

den Beobachtungen von Schweizer in Moskau 1863-1866, Kiel,

1883, pages 52-0.

(7.) Jounson — Introduction to the Observations with the

Heliometer. Part II of Astronomical Observations made at the

Radcliffe Observatory in the year 1853. Vol. XIV, page xxxix.

(8.) Batt—On a new Determination of the Parallax of the

Preceding Star of 61 Cygni by the Method of Differences of

Declination. Astronomical Observations and Researches made

at Dunsink. Part III, page 27.

(9.) Batu—Further Researches on the Parallax of 61 Cygni.

Astronomical Observations and Researches made at Dunsink.

Part V, page 166.

(10.) BrLopotsky—Astronomische Nachrichten, No. 2888.

These values of parallax are computed from discordances in right ascension

between observations made six months apart on the transit instrument by

WAGNER at Poulkova in 1862-1870.

(11.) Hatt—Observations for Stellar Parallax. Washington

Observations for 1883, Appendix II, pages 54 and 67.

160 Parallax of 61% Cygni, deduced from

(12.) Pritcearp—Researches in Stellar Parallax by the aid of

Photography, from Observations made at the Oxford University

Observatory, Oxford, 1889.

In the formation of Table X XIII, giving the various values of the parallax

of 61 Cygni hitherto published, I have not placed Pritchard’s values in bold

type, because they cannot be regarded as trustworthy. They have been dis-

carded in taking the means of the determinations for 67! and 67%. I have ex-

amined the eight sets of normal equations given in the work on 61 Cygni

(pages 17-63) and among the eight sets have not found one which is correct in

every quantity. The set on page 30 first attracted my attention and so it may

be used for illustration. As given there the quantities are :

— 1/’,3140 = + 88.0000 # — 6.7889 du — 2.5442 7

+ 4 .3827=— 6.7889 + 8.4762 + 9.7965

+17 .1716 =— 2.5442 + 9.7965 -+38.7724

These should be :

— 1//,2180 = + 88.0000 x — 6.7889 du — 0.9281 7

+ 4 .3853=— 6.7889 + 8.4783 + 9.7854

+17 .1967 = — 0.9281 + 9.7854 +38.7849

This criticism applies not only to the normals for 61 Cygni but for many

of the other stars as well. No attempt has been made to verify all the num-

bers in each set of normals, nor indeed to extend the test to all sets of normals

given in the book, but it can be stated that at least one number is wrong in

each of the fourteen sets given on pages 17, 23, 30, 36, 47, 52, 58, 73, 75, 875

104, 106, 107 and 113.

(13.) Davis—Contributions from the Observatory of Columbia

University, New York, No. 13.

(14.) Witstnc—Untersuchungen uber die Parallaxe und die

Higenbewegung von 61 Cygni nach Photographischen Aufnahmen.

Publicationen des Astrophysikalischen Observatoriums zu Pots-

dam, No. 36, pages 152 and 148.

(15.) RamBpaut—On the Effects of Atmospheric Dispersion on

the Position of a Star. Monthly Notices, Vol. LV, page 123.

(16.) Fuint—Research Work at the Washburn Observatory.

The Astrophysical Journal, Vol. VI, page 420.

A preliminary announcement of results now in process of computation.

(17.) Kapreyn—Bestimmung von 250 Parallaxen. Astronom-

ische Nachrichten, Bd. 145, S. 300.

V.—The Rutherfurd Photographie Measures of Thirty-four

Stars near “Bradley 3077.”

BY HERMAN §&. DAVIS.

Read May, 1897.

I. The methods of reduction employed in the formation of this

catalogue are the same as have been described in my paper on

Sixty-five Stars near 61 Cygnt, except that no corrections for

parallax were applied. The computations have been almost en-

tirely performed by Mrs. Davis, who has also rendered consider-

able assistance in the computations connected with all my other

papers on the Rutherfurd Measures.

In this presentation of results the Tables have been given num-

bers to correspond with the similar tables in the paper on 61

Cygni, reference to which will make clear any matter not sufti-

ciently intelligible from the captions to the various columns.

2. Nearly the mean date of observation, 1874.0, was selected as

the epoch to which the observations were reduced. Thus we have:

Ap,3 = — 8’ + [0.919] A + [0.246n] B+ [0.1672] C + [9.537] D

Ap,.—= 0 + [0.919] A + [0.2462] B+ [0.1671] C+ [9-537] D

as the correction for precession, nutation and aberration in posi-

tion-angle; and, for all years, to correct for aberration in dis-

tance :

As = }[4.058]C + [4.416n]D}s

3. The logarithms of the Besselian day-numbers, taken from the

American Ephemeris, are:

Plates. log A. log B. log C. log D.

Tee (25038 9.786 0.808n 1.053 1.213

4, 5, 96, 9.805 0.80In 0.958 1.253

FH. Sh 9.336 O85 On'77On —Uwsaelyin

9, 10, 9.411 0.854n 0.418) 1.306n

iit, 1A, 9.417 0.854n 0.364n 1.307n

( 161 )

162 Ruther furd Photographic Measures of

4, ARGELANDER’S position and proper motion of this star as

given in Mittlere Positionen von 160 Sternen have been adopted.

For 1874.0 they are:

C— 22 o7 IB a50 = +0%.24867

0 = 56° 28/ 21/.95 pe’ = + 0/7.2685

From these are derived :

p = 2//.07765 = 04.07416 V— (920 347g

The values of P,, P,, P;,and K, depending hereon, are in

Table VII on page 184; and S,,S;, S,,and S,,are in Table VIII.

5. For determining the correction for scale-variation, stars

numbered 3, 9, 19, 20, 31 and 33 have been used. These are so

distributed that

Xss= 4284.6222, LZcosp=—o.o1, and 2sinp = —o.I0o

Therefore the

2ss— (83 + S9 + 819 + S90 + S31 +E 833 ) 5

Dss é

This factor of s will be found on page 184.

Seale variation ==

6. The correction for orientation variation on page 184 has been

deduced in the same manner as described in paragraphs 19-21 of

the paper on 61 Cygni, except that Mrs. Davis has reduced the

orientation to the mean of all the plates excluding that numbered

six, regarding for very obvious reasons the mean of the remaining

eleven as nearer the truth than the mean of the entire twelve.

Thus the corrections actually applied reduces the orientation to

the mean of the remaining eleven plates. The nine stars whose

numbers are 8, 9, 10, II, 14, 16, 17, 20 and 33 after correction for

proper motion have been used as standards. They give:

o2S, Xo28,

a =+6.0 and Sain

“. For calculating the difference of right ascension and of dec-

lination the following constants have been used :

log P = 0.257799 log R = 9.5094n log T= 4.5633n

log Q = 5.1221 log S = 0.0458 log U = 9.4870n

Also, by paragraph 24 of Catalogue of Sixty-five Stars near 61

Cygni.

n =osint

m =o cost

a’ — a = Pn+ Qnm + Rn? + Snm?

6’ — 9) = m —+- Tn? +- Un?m

163

Thirty-four Stars near “Bradley 3077.”

69hh'9 | 16°16 — | oS-ZE loeps| 2:2 09 HS 6S | oofof | oc gz oz | £¢ Ce 6r | Cr oung cI

z1tv'g9 | SL:bg — | 6o'zP | 68'8h | vo oL 69 IZ | 08662 | tb ¢S 61 | Zr o O61 | zr oung OI

obby'9 | 99°€6 — | oo'9f | CLZ°VS | LZ 09 cS 09 | vg6'6c | o1 LE oz | $e by 61 | I une g

L¢eby'9 | 60°98 — | Srv) irvS | LZ 09 cs o9 | vg66c | VS 68 6r | LZ ZL Gr) 1 sung Per L

6L9r'9 | cog + | Lo-zv | 0685 | QZ gt ce gt | givot | fr 11 v | te gr € | ce “aon ¢

LoLl¥’9 | of V6 + | ¢Z2°SC | €L°f9 | og of Sz 6z Zer-of | €S 0% £ XG VI “AON Zz

60LP 9 | zv-zor-+ | 60°1¢ | 09°85 | og of QZ 6z | zt1‘oe | €S oh e | € PS | vr ‘aon CZer I

(oe) ‘ ° {eo} {e) te) ‘Sen 7 s w T

» SOT “3B 5 ‘oraz | ‘snooy eee ieee Wavene “MOIR ee rescanta ‘ayn ‘a1BId

M 729';:9SuSSyv = ‘su0'T “Bv <b ov = 9eT

"YIOK MON Spanjsoyyny "PL “T Jo A10zvA1esqQ—VIV(, IWAINTH—] WAV,

164 Rutherfurd Photographic Measures of

TABLE IJ.—CoRRECTIONS FOR REFRACTION.

Position Angle, <= >< 108 Ae, Position Angle, ox 103 pal

PLATE 1. PLATE 2.

O22 2820 +.410 0.0 94° 274° +.456 0.0

1A BoD -406 — 3.9 104 284 -451 — 5.5

2 2eO2 -397 — 7.2 II4 2094 438 —I10.4

BQ BUS 383 — 9.7 124 304 417 —13.9

I42 322 3605 —IlI.1 134 314 392 —15.8

15 Bao 345 —IlI.I 144 324 -305 —15.8

162 342 .328 Shy] 154 334 -339 —13.9

7A Bs -314 — 7.2 164 344 319 —10.4

182 2 -304 = 29 174 354 -306 = 5.5

192 I2 -301 0.0 184 A 301 0.0

202 22 304 + 3.9 194 I4 306 + 5.5

212 32 .314 + 7.2 204 24 319 +10.4

222) AZ .328 ae One eat 4 Sy «339 +13.9

232 Ba 345 +11.1 224 44 365 +15.8

242 62 305 III 234 54 -392 +15.8

252) 72 -383 ap Gui 244 64 417 13.9

262 82 .397 + 7.2 254 7A .438 +10.4

272) 92 -406 + 3.9 264 84 -451 a 525

282 102 .410 0.0 274 94 -456 0.0

PLATE 3. PLATE 4.

Sy AS77© +.521 0.0 Olu +.483 0.0

OW) Da -515 — 7.8 IOI 281 477 — 6.5

Oy = DSi .496 —I14.7 Hiei = QOL -462 —I12.2

SL ee O7) .466 —19.8 12 Teg 437 —16.4

127s O7, -430 —22.5 Ug - Qiit -407 —18.7

UR ai -391 —22.5 I4I 321 0375 —18.7

WA Be -355 —19.8 USE nS 344 —16.4

Sy Belay .326 —I4.7 I6I 341 -320 —I2.2

Woy) YG .306 — 7.8 17s Si -305 — 6.5

WG Bey .300 0.0 181 I :299 0.0

187 7 .306 + 7.8 191 II -305 + 6.5

197 17 326 +14.7 201 21 -320 +12.2

207 By 2355 +19.8 211 31 344 +16.4

217 Ba 2301 +22.5 221 AI 0 B75 +18.7

DD Az -430 +22.5 231 51 -407 +18.7

237 57 .466 +19.8 241 61 :437 +16.4

247 67 .496 +14.7 251 7 .462 +12.2

2575 Hawi -515 + 7.8 261 81 -477 + 6:5

267 87 6521 0.0 271 91 -483 0.0

Thirty-four Stars near “Bradley 3077.” 165

TaBLE II.—CorrReEcTIons FoR REFRACTION. (Continued.)

Position Angle, | ¢—5 \ 103 Position Angle,

pe | moe 2 P

PLATE 5. PLATE 6.

+.552 +-644

-544 -634

523 .603

.489 S551

-448 .502

403 441

361 385

«328 -339

.307 309

.299 © |I .299

PaO 309

328 8 ©339

361 385

-403 j -A4I

.448 .502

.489 -557

523 .603

+544 634

+552 -644

PLATE 7. PLATE 8.

Dr elo +.498 0.0 2600 SO +.432 0.0

284 104 -491 — 7.6 276 96 427 — 5.3

294 II4 -473 —14.3 286 106 -414 — 9.8

304 124 -444 —I19.3 296 116 394 13:3

314 134 -409 —21.9 306 126 .370 —I5.1

324 144 -372 —21.9 Ail 196) 344 SSF

334 154 -336 =a19.3 326 146 -320 —13.3

344 164 -308 —I4.3 336 156 .300 — 9.8

354 174 .288 — 7.6 346 166 .286 — 5.3

4 184 .282 0.0 356 176 .282 0.0

14 104 .288 + 7.6 6 186 .286 + 5.3

24 204 308 +14.3 16 196 -300 + 9.8

Be pital 330 +10.3 26 206 -320 +13.3

44 224 a2 +21.9 36 ©6216 -344 +15.1

54 234 -409 21.9 46 226 -370 +15.1

64 244 -444 +19.3 56 236 -394 +13.3

74 254 473 +14.3 66 246 -414 + 9.8

84 264 -491 sre ZOvm 250 -427 Sees)

94 274 -498 0.0 86 266 432 0.0

166 Rutherfurd Photographic Measures of

TABLE IJ.—CoRRECTIONS FOR REFRACTION. (Concluded.)

Hee Angle, — < 103 a ee Angle, 7 x 108 at

PLATE 9. PLATE 10.

281° 101° +.580 0.0 2750 NOS a + .498 0.0

201) en | oBy7/at —10.8 285 105 491 — 7.9

30I 121 544 —20.2 2905 115 -471 —14.8

Aue WATE .504 —27.2 305 125 -442 —20.0

321 IAL 454 —31.0 BiG AG -405 —=22.7 ©

Bau Ge .400 —3I1.0 325 145 307 —22.7

341 I6f -350 —27.2 335 155 330 —20.0

351 I71 .310 —20.2 345 165 301 —14.8

| Sit 283 —I0.8 355 175 .280 — 7.9

II Io91 .274 0.0 5 185 -274 0.0

2I 201 .283 +10.8 15 195 .280 + 7.9

Bw Bree -310 20.2 25 205 301 +14.8

Ae E22 -350 +27.2 85s 330 -++20.0

Sey 2 ak -400 -+31.0 45 225 .307 +22.7

61 241 -454 +31.0 55 285 -405 22.7

Git Bisit -504 +27.2 65 245 -442 20.0

8I 261 544 20.2 75 255 471 +14.8

Oi Ay 571 +10.8 85 265 491 + 7.9

IOI 281 .580 0.0 OG 275 498 0.0

PLATE 11. PLATE 12.

DIG OR +.518 0.0 268° 88° +.452 0.0

285 105 .511 — 8.2 278 98 447 — 5.9

2905 115 .490 —15.4 288 108 -432 —II.I

305 125 -459 —20.7 298 118 -409 —I14.9

Bis | as 421 —23.6 308 128 383 —17.0

325 145 .381 —23.6 218) 13s 353 —17.0

335 155 .342 —20.7 328 148 -326 —I4.9

345 165 312 —I15.4 338 158 304 —II.1

355 175 .291 — 8.2 348 168 .289 — 5.9

005) .284 0.0 358 178 284 oko)

I5 195 .291 + 8.2 8 188 .289 + 5.9

25 205 ean +15.4 18 198 304 +II.1

Bee ns .342 + 20.7 28 208 -326 -+14.9

45 225 391 +23.6 23) 2S -353 +17.0-

55 235 421 +23.6 48 228 383 -+17.0

65 245 -459 +20.7 58 238 -409 +14.9

75 255 -490 +15.4 68 248 -432 +II.1

85 265 -511 + 8.2 78 258 -447 + 5.9

95 275 .518 0.0 88 268 452 0.0

Thirty-four Stars near “Bradley 3077.” 167

TABLE III].—CorreEcrions FoR PRECESSION, ETC., TO 1874 AND

ZERO CORRECTIONS.

Precession, etc. < ve

Plate Zero Correction Bele

No. |position Angle| Distance | “2\Hast + West) ie Salas

Correction. Factor < 103

4) 4 Mt Vd / ad

I — 2.9 —.0297 +20 31 —35 +19 56

2 — 2.9 —.0297 22 23 —38 21 45

3 — 2.9 —.0297 20 50 —3I 20 19

4 + 1.0 —.0363 19 16 —54 18 22

5 + I.0 —.0363 20 52 —4A 20 8

6 Se ee —.0363 14 39 35 14 4

7 +16.6 +.0437 I9 18 —AI 18 37

8 +16.6 +.0437 “19 36 —42 18 54

9 + 11.5 —+.0497 19 5 —52 18 13

ne) +11.5 +-.0497 17 22 -—52 16 30

II +11.2 —++.0502 19 14 —36 18 38

12 +I1.2 +.0502 +19 21 —AI +18 4o

TABLE IT V.—TANGENT CORRECTION.

This correction is always negative, and is here expressed in terms of the fourth

decimal place of the micrometer readings.

Distance. 0. il, 2. 3. 4 e D. 6. Ue 8. 9,

20. | — o|— o|— of— o|j— o|— I\— If I\— I1\— 1

30. 2 2 2 2 2 3 B B 3 3

40. 4 4 4 5 5 6 6 6 7 7

50. 8 8 8 9 9 se) 10 II II 12

60. 13 13 14 15 16 17 17 18 19 20

70. 21 22 23 24 25 26 27 28 ZO || Bie

11°, 81 83 85 87 90 93 95 98| 100] 103

120. NOG) | MLOON Nee) LL aa 2ON 22a E26) 26) ans 2

130. |—135 |—138 |—141 |—145 |—148 |—151 |—155 |—158 |—162 |—165

168 Rutherfurd Photographic Measures of

TABLE V.—RESULTS OF MEASURES OF DISTANCE.

Observed Dist. Corrections for Cor- Final

Star = : a i rected eee Proper | Corrected

No. = Mean.} tion, | Motion. | Distance.

: East. | West. | Refrac.) Aberr. | Scale. a

1 II | .g218|.9o90| 625 | +62 80 | .9802 | — 46| —.0334 | 123.9422

(2) | 12 | .8604 | .9280| 557 | +62 94. | .9536 | — 52] —.0334 -9150

Mean 123.9286

) I | .0565 | .0314| 426 | —35 | 118 | .o851 |— 11] +.0088 | 117.0928

(5) 2 | .0288 | .o212| 480 | —35 | 118 | .0715|-+ 31] +.0088 .0834

4 | .0233 | .of22|} 512 | —42 | 108 | .0658 | +135] +.0073 .0866

5 | O19I | .0307] 603 | —35 | 112 | .c831 21 | +.0073 .0925

7 | .0681 | .0718| 508 | +5r | 118 |.1278|— 8}| —.o290 -0980

8 | .0672 | .0506| 473 | +5r | 118 |.1134/+ 8] —.0290 .0852

II + .0588 | .0687) 518 | +59 | 118 | .1234 | — 44 | —.0312 .0878

I2 | .0788 | .0600} 490 | +59 | 118 | .1263 | — 49} —.0312 .0902

Mean 117.0896

3 I | .8405 | .8320] 308 | —23 | 126 |.8747;/— 7|-+.0092] 75.8832

@7Z) | 2 | .8343-| .8318 | 345 | —23 | r26 (.8751 | -— 201/---ecg2 .8863

3 | .8370 | .8265 | 393 | —23 | 126 |.8787|-+ 3] +.0092 .8882

4 | .8290 | .8253 | 365 | —28 | 119 | .8700]-+ 87] +.0077 .8864.

5 | 8246 | .8268} 414 | —28 | 120 | .8736| + 14] +.0077 .8827

6 | .8246 | .8302| 470 | —28 | 126 | .8815 | — 39] +.0077 8853

7 | 8677 | .8751 | 377 | +33 | 125 | .9222/— 5] —.0305 .8Q12

8 | .8702 | .8771 | 326 | +33 | 125 |.9193|/-+ 5) —.0305 .8893

Q | 8731 | 8745 | 434 | 4-38 | 418 || 9301 |— 30) — 0327 -8944

Io | .8802 | .86:8| 376 | +38 | I19 | .9221 |} + II} —.0327 .8905

II | .8722] .8724| 392 | +38 | 126 | .925r | — 28 | —.0329 .8894

I2 | .8680 | .8923| 342 | +38 | 120 | .9275 |— 32] —.0329 .8914

Mean 75.8882

4 I | .6812 | .6768 | 297 | —24 | 125 |.7156/— 8|+.0090| 79.7238

(A) 2 | .6670 | .6668 | 336 | —24 | 126 |.7075|-+ 21| +.0090 .7186

3 | .6482 | .6546] 393 | —24 | 125 |.6976|+ 3)} +.0090 .7069

4 | .6526 | .6361 | 357 | —29 | 122 | .686r | + 92] +.0075 .7028

5 | 6528] .6540) 42r | —29 |] 2 |.7015 | -+ 15|] +.0075 -7105

6 | .6520| .6515 | 500 | —29 | 125 | .7082|— 4I1| +.0075 .7116

7 | .7078 | .7126} 359 | +35 | 126 |.7590|/— 5|—.0207 -7288

8 | .7097 | -7233.| 330 | +35 | 126 |.7624|/-+ 5|—.0297 -7332

9 | .7018 | .7226| 382 | +40 | 122 | .7634 | — 31 | —.0319 BG/ Zeus -

IO | .7171; .7008| 355 | +40 | 122 |.7575|-+ 312|-—.0319 .7268

IL | .7009 | .7205 | 368 | +40 | 126 | .7609|— 30) —.0321 7258

I2 | .7038|.7110| 340 | +48 | 126 | .7548 | — 34] —.032I | -7193

Mean 79.7197

3 I | .4787 | .5182| 383 | —36 | 112 | .5337|}— 12| +.0062] 120.5387

(7) 2 | .4734|.4791 | 408 | —36 | 108 | .5136|/+ 32; 4-.0062 .5230

4 | .4728 | .4666 | 425 | —44 | 108 | .5079 | +139] +.0052 .5270

7 | .5138|.5006} 406 | +53 | I09 | .5533!— 8]|—.0206 -5319

9 | .5070| .5259] 389 | +60] I09 |} .5615 |— 47| —.0220 5348

Mean 120.5311

Thirty-four Stars near “Bradley 3077.” 169

TasLeE VI.—ReEsSULTS oF MEASURES OF ANGLE.

rg pasty ee 7 osition Pee Cariccted :

= : tion plus |Refrac. eae UGE. Sc eananns

East. West. | Preces- i

eEOk sion, ete. ie T

°o ‘ “ i di ‘ “i di (eo) / Mi ‘ Md ad

II | 351 38 20/39 25| 18 38 | +10 | 261 57 41| —o 2 | 261 57 53

12 40 50|41 45| 18 4o | + 4]|262 0 2| —o 2 57 22

Mean | 261 58 52 261 57 38

I | 331 22 50| 23 32| 19 56] +11 | 241 43 18] +0 6 | 241 43 58

2 19 8/21 30] 20 45 | +15 42 20/ +0 6 43, 33

4 Di Pe Gs Gil ats) Be | Sas) 42 22)) = O15 43, 56

5 BAS | Oo RI 20) On e-t i7 42 53| +0 5 44 1

7 23 43|25 45| 18 37 | +20 AGWA a | = Or 2 44 23

8 24°50|27 3) 18 54 | +12 45 3 O 21 44 23

Ts 24 58) 25 45| 18 38 | +22 44 22| — 0 22 44 14

I2 27 10|28 17| 18 40 | +13 AGE2 70122 43, 37

Mean | 241 43 57 241 44 I

I 2E2ONAS| | ies ero Soni Any 272) 50) Ann| ——sON Au 272) 5h 0E

2 27 40) 28 38| 21 45 | + 2 AQUSO) 10) A. 59° 59

3 BE BI S2) CW A2o ae BTS Ol | On 5E 25

4 B57 S4 or tor e225 | —— 12 51 22} —o 4 51 47

5 30 6/3050] 20 8/|—6 50 30 —o 4 51 29

6 SiO 2 SS es | iy Aull 650) —— (| ah 51 42

vi 30 26) 31 32| 18 37 | + 2 He) 2h8:|) == @) ied 50 55

8 BAAS 3 Sr 1Si) 1S 540 | —— 3 51 22| + 0 14 SISL?

9 33) 2533140 | 18) 13, | 9 554 Ors 5I 13

ae) Be) M2 || BS 917] || 1K) BX) | Sew 51 6| +015 Fit (6)

II Bit AD |G evil || aes} Bie} aw 50 40| + 015 5I 9

12 34 28| 34 54) 18 4o | — 3 5310) a OMES 50 55

Mean | 272 50 35 272 51 16

S350 07) FO) S27 | 192050) tO 1246 17, 241) Oh 7 IN 2AG 18 15

2 BAN 3355421) 26 945) ns i? Siar Oey 18 19

2 57 25|58 13| 20 19 | +16 Hite) PL) Sey Os Y/ I8 Io

4 58 8/00 o| 18 22] +17 17 43} +0 6 18 18

5 56 1/57 2/20 8] +15 1655} +0 6 ins) il

6 SONS 59) 5)) IA 4th a4 HAS On 6 18 56

7 57 48|59 20/ 18 37 | +18 I7 29} —o 24 ies) (8)

8 59 23) 00 38/ 18 54 | +10 TO 5) == One) 18 22

9 |336 00 2] 1 50| 18 13 | +29 19 38} — 0 26 18 16

age) . I 38| 2 42/ 16 30 | +19 18 59| — 0 26 18 18

II 1335 58 39/59 45| 18 38 | +20 18 10| — o 26 17 58

WA || Bete) it By || By Sil awe) Al) | See TsO} —— On? O 18 6

Mean | 246 17 49 246 18 15

I | 303 48 8] 49 33/ 19 56] + 8|214 8 54| +012 | 214 9 4o

2 45 14|46 12; 21 45 | +14 7 AL| == © 12 9 0

4 48 57/51 5| 18 22] +17 8 40} + 0 Io 9 19

7 49 6|50 40] 18 37 | +19 S549) — OF 45 9 II

9 51 40/54 I0| 18 13 | +22 II 30| — oO 44 9 50

Mean|214 9 7 214 9 24

170 Rutherfurd Photographic Measures of

TABLE V.—ReEsutts or MEAsuRES OF Distance. (Continued.)

ty | Observed Dist. Corrections for Cor-_ | geale

Star = rected | Varia-

NOoen es Mean. | tion

5 East. | West. |Refrac.| Aberr.| Scale. 8

6 I | .6300 | .6668 | 206 | —18 | 108 |] .6767|— 6

(6) | 7 | 6482) 6756) 237 | --27 | 104 | .6974|— 4

8 | .6311 | .6802| 229 | +27 104 | .6903|+ 4

II | .6501 | .6848 | 242 | +30] 104 !.7037|— 23

I2 | .6314 | .7006| 234 | +30] 104 |.7015 |— 26

Mean

7 I | .4126|.4174| 280 | —27 | 132] .a491|— 9

(8) | 2 | .4182|.4170| 297 | —27 | 132 | -4534|-++ 24

3 | 4091 | .4190 | 329 | —27 | 135 |.4533|+ 3

4 | .4038 | .3977 | 307 | —32 | 132 | -4371 | +103

7 | 4462 | .4322 | 292 | +39 | 135 |-4814|— 6

9 | .4520, .4428! 276 | +44 | 132 | .4882 |— 35

II | .4362 | .4448| 291 | +45 | 135 | -4832|— 33

12 | .4324!.4485 | 297 | +45 |_ 135 | .4838|— 38

: Mean

8 I | .4792| .4746| 226 | —17 98 | .5063|}— 6

(36) | 2 | .4758|.4712| 235 | —17| 96 | .5037| + 16

3 || -4737 | 4681) 245 | —17 98 | .5023|+ 2

4 | .4762 | .4686 | 240 | —2r g2 | .5023 | -+ 67

5 | -4792| .4766| 246 | —21 95 | .5087|-+ 11

6 | .4765 | .4783 | 253 | —21 98 | .5092 | — 30

7 | -4964 | .4917| 249 | +26 95 | -5298|— 4

8 | .5143 | 5112 | 209 | +26 95 |-5446;/+ 4

9 | .4998 | .5047 | 297 | +29 94 | -5430 | — 23

TO | .5128| .5015 | 248 | +29 90 |.5427;/+ 8

II | .4968 | .5012| 257 | +29 95 | -5359 | — 22

12 | .4998 | .4960| 221 , +29 95 | -5312|— 25

Mean

9 I | .6254 | .6327] I20 | — 9 | —12 |; .6387/— 3

(1) 2 | .6082 | .6068 | 134 | —9|—9].6189;+ 8

3 | .6143 | .6124 | 154 | — 9 | —12].6264/+ 1

4 | .6158 | .5907| 143 | —II ; —16 | .6147|-+ 34

5 | 6198 | .6114 | 162 | —1r | —13 |.6292|/-+ 5

6 | .5928 | .6051 | 185 | —II | —1I2 | .6149|— 15

fr) 0 5924) 0030) 147.9513 ae O) iO OAN me

8 | .6626 | .6476| 128 | +13 | — 9 |.668r|+ 2

9 | .6701 | .6652|} 169 | +15 | —15 | .6844|— 12

IO | .6486 | .6434 | 347 | +15 | —16]|.6604|+ 4

II | .6690 | .6858 | 153 | +15 | — 9 | .6931 | — II

12 | .6680 | .6870| 134 | +15 | —13 | .6909 | — 13

Mean

Proper

Motion.

-F.0079

—.0260

—.0280

+.0058

+.0049

—.0193

—.0207

—.0208

-+.0063

-++ .0063

+ .0063

+ .0052

+.0052

—.0208

—.0223

—.0224

+-.0093

---0093

+.0093

+.0077

+.€077

++ .0077

—.0307

—.0329

—.0331

Final

Corrected

Distance.

60.6840

.6710

.6647

-6734

.6709

60.6728

89.4540

.4616

-4594

-4523

-4615

.4640

-4591

-4592

89.4589

58.5120

-5116

.5088

.5142

.5150

.5114

.5086

5242

.5184

.5212

-5113

.5063

58.5136

29.6477

.6290

-6358

.6258

-6374

.6211

6455

.6376

.6503

-6279

.6589

-6565

29 6394

Thirty-four Stars near “ Bradley 3077.” 171

TaBLeE VI.—Resutts or MEAsuRES OF ANGLE. (Continued.)

NRONHRW DH

Hae eS

NH OW CONI DAUNBRW NH

Cn Au B® NH

Observed Position Gay Corrected

Angle. “A on plas Refrac.} Mean.

East. West. | Preces-

sion, ete. LB

319 8 16/10 5] 19 56| +11 |229 29 17

Ti AO) 1) teh) eS 2h | ee 30 46

T2013) 26) nS.) 54) | eas St 33

II 43/12 58, 18 38 | +-24 31 23

I2 53/15 58| 18 4o| +16 33 22

Mean | 229 31 16

300 40 20/41 54| 19 56| + 6 |211 I 9

38 36/38 53| 2t 45 | +12 ae

AI 35|41 28! 20 19 | +21 2 12

At 25|43 31| 18 22 | +16 ee

43 42/44 35| 18 37 | +18 a3

45 50) 46 45) 18 13 | +19 ae)

43 47|44 37| 18 38| +18 ae

46 12 47 45| 18 40] +15 3 53

Mean|21Ir 2 45

39 59 28, 00 26! 19 56 | — 9 ]3I0 I9 45

56 38/57 52| 28 45 | —15 18 45

40 0 35| 2 8| 20 19 | —23 21 18

1 48/ 3 2| 18 22 |—18 20 29

39 59 44/59 48) 20 8 | —26 19.28

59 30/00 51) 14 4 | —34 13 41

58 3/59 55| 18 37 | —20 17 16

50) W256) GO! ne Gn || 2ne 18 Io

ACT 20 AAS) 03) |) 27 EOS

I 30| 3 46) 16 30 | —ar 18 47

39 59 5/159 40| 18 38 | —22 17 38

AS) Te Bs) B) Fe) aS Ao) yp 7 20 31

Mean | 310 I8 45

2A 22/25 12| 2r 45 | + 3 46 35

PS} 2) || D7 All| GS) iG) |} == @ 48

27 45|27 18| 18 22/4 1 45 55

27 47|24 28| 20 8|—5 46 II

26 40/27 42| 14 4 | —15 ab 8

28 26| 28 50| 18 37 | + 3 47 18

23 alae Col us Gal | se 48 22

30 8132 55| 18 13 | +12 49 57

29 28|32 32| 16 30! + 4 47 34

Bay S| Gy) Be ws) 28 + 4 46 22

30 48,31 5| 18 4o |] — 2 49 35

Mean | 270 46 56

Pp Final Cor-

Motlon. rected Angle

+ o 18 229 30 9

—= © 9 39 50

== © SY) 39 15

re Sens) 30 34

—I 3 29 41

229 30 18

+ 017 21th 25 1O)

+ O17 2 6

+ 017 28

a= @ Wl I 49

cay 3 9

—IiI 2 52

—I 2 2 20

—I1I 2 2yet)

A 2D AO

—— 0 24 310 19 55

— 0 24 Ig 28

— 0 24 20 33

— 0 20 20 38

— 0 20 20 II

— 0 20 20 28

ap) ee 19 39

-+- I 20 19 II

ae 8 25 19 38

+ I 25 19 57

+ 1 26 19 18

+ I 26 I9 19

310 19 51

—0o 9 270 46 38

ap Con) 47 33

ong 47 38

Sa Oey. 46 17

FO Wf 47 7

—o 7 48 0

+ 0 29 48 50

+ © 29 48 32

a> @ $2 49 33

+ © 32 47 5t

+ © 32 47 8

ain ©. 32 47 2

270 47 43

172

Rutherfurd Photographic Measures of

TABLE V.—REsULTS OF MEASURES OF DisTANCE. ( Continued.)

Observed Dist.

Corrections for

Cor-

Seale

Final

ac)

Star | & rected | Varig. | Proper | Corrected

No. @ Mean. | tion, | Motion. | Distance.

East. | West. |Refrac.| Aberr.| Scale. si

10 I | .5694 | .5805 71 | — 6 82 |.5897|— 2|-+.0092] 18.5987

(ay) 2 | .5719 | .5707 80 | — 6 82 | .5869}-+ 5] +.0092 -5966

3 | .5054 | .5760 93 | — 6 82 | .5876|-+ 1] +.0092 -5969

4 | .5708 | .5648 86 | — 7 80 | .5837 | + 21] +.0076 5934

5 | -5722|.5796| I00 | — 7 79 |.5931|+ 3) -+.0076 .6010

6 | .5602 | .5624| 118 | — 7 82 | .5806|— 9| -+.0076 5873

7 | .6199 | .6315 86 | + 8 84 | .6435|— 1]| —.0303 .6131

8 | .6193 | .6273 78 | + 8 83 | .6402|/+ 1) —.0303 .6100

Q | -6193 | 6354 | 93 | 9) |) 80 126455 | 7 ages 6123

IO | .6271 | .6077 85 | +9] 80 |.6348) + 3] —.0325 .6026

Ir | .6221 | .6370 88 | + 9 83 | .6476|— 7 | —.0327 .6142

I2 | .6156 | .6302 8r | +9 79 |.6397|— 8| —.0327 .6062

Mean 18.6027

11 T | 8040 | .8069| 321 | —31I | 114 | .8386|}— Io} +.0022] 105.8398

(13) | 2 |.7998| .7846| 320 | —31 | 113 | .8251 | + 28] +.0022 - 8301

3 | -8079 | -7994| 323 | —31 | 114 | .8369/+ 4] +.0022 -8395

4 | -7984.| .7982} 319 | —38 | 113 | .8304 | +122] +.0018 .8444

5 | .7858 | .8043 | 329 | —38 | 114 | .8283 | -+ 19/ +.0018 .8320

6 | .8105 | .7979 | 35r | —38 | 114 | .8396|— 54] +.0018 .8360

7 | .8096 | .8005 | 300 | +46 | 111 | .8434!— 7} —.0072 8355

8 | .8069 | .7925 | 302 | +46] rir | .8383/-+ 7] —.0072 .8318

9g | .8170 | .8218} 295 | +53 | 115 | .8584|— 41 | —.0077 .8466

Io | .8217|.7905| 292 | +53 | 113 | .8446|-+ 15 | —.0077 .8384

II | .8097 | .8067| 302 | +53 | 114 | .8478 | — 39| —.0077 .8362

12 | .8047 | .7993| 304 | +53 | 114 | .8418 | — 45 | —.0077 .8296

Mean 105.8366

12 3 | .0888 | .0700| 43 | —4 48 | .o881 o| +.0053} 12.0934

(9) 6 | .0682 | .0690 52 |—4 48 | .0782|}— 6} +.0044 .0820

7 | .0909 | .1093 38 | + 5 48 | .Io9g2 |— 1] —.o176 -O916

IL | .1478 | .1806 39 | + 6 48 | .1735|/— 5|—.O190 .1540

Mean 12.1052

13 I | .0319 | .0384| 73 | — 7] T12 |.0529|— 2|+.0024| 24.0551

(10) 2 | .0380 | .0307 72 |— 71] I1r |.0518|+ 6) +.0024 .0584

3 | .0364 | .0349 73 |— 7 | 112 |.0533|/+ 1] +.co24 -0558

4 | .0286 | .0345 72 |— 9] III | .0489|+ 28] +.0020 -0537

5 | .0258 | .0495 75 |— 9] 112 |.0554|/+ 4] +.0020 0578

6 | .0384 | .0380 80 | — 9} I12 | .0564|— 12] +.0020 .0572

7 | .0418 | .0258 68 | +11 | rrr |.0527|— 2)|—.0078 .0447

8 | .0542 | .0408 69 | +11 | Ir |.0665|+ 2) —.0078 .0589

9 | .0473 | .0495 67 | +12} 111 | .0673|— 9) —.0084 .0580

IO | .0457 | .0405 66 | +12 | rrr |.o62r|}+ 3) —.0084 .0540

II | .0405 | .0475 69 | +12 | 112 | .0632|— 9} —.0085 -0538

12 | .0508 | .0479 69 | +12 | I10 } .0684 |— 10) —.0085 .0589

Mean 24.0552

Thirty-four Stars near “Bradley 3077.”

Observed Position

Taste VI.—ReEsocuts oF MEASURES OF ANGLE,

173

( Continued.)

las) Cor- A

= rected ] Final Cor-

o Soe teat Meo Motion. a oa

I 340 10 45, 9 22 --I0 | 250 30 + 0 22 | 250 3r. 5

2 GE59)| 7 55 29 a) 22 30 52

3 IO 50/10 13 31 = © 22 Bit G

4 9 37| 12 42 29 43; + 0 18 30 30

5 8 42]11 48 30 +o 18 31 56

6 ir 7 | tO Si 25 + 018 32 38

A 14 I10| 12 28 22 —I1 13 Qi Gg

8 15 52|18 55 36 Bates 34 53

9 15 36) 14 45 33 50 118 31 36

18 27/19 15 35S ale 34 5

13, 54| 13 57 BB 31 46

T5 35/17 13 35 ey ah) 31 17

250 31 250 31 59

275 37 43 | 39 10 ree 58 a= © US) || WSh Gis) ee

35 33 | 36 32 ahaa Gy Ais | ap @ ae 59 13

38 0] 39 25 Seas) 59 Sip OMLO 50°33

38 55 | 40 35 alam 58 a © U5 58 54

36 16) 38 15 + 9 57 =P @ 15 58 51

36 45 | 37 52 +19 pu SO) TG 59 3

40 10} 41 13 a 2 59 —I oOo 59 23

40 58 | 42 47 aS || 20 @ =i © 59 32

42 15) 44 20 =e) I are at nae 59 26

43, 28 | 44 48 aie O39) aa E24 59 20

40 46} 42 15 fo) fo) eats 59 18

43 52/45 30 ar & 3 seule 5 59 43

Mean 59 185 59 15

296 47 36/44 50 +20 |207 6 52| + 212 | 207 8 43

43 50| 46 28 +34 | 206 59 ain LA 8 43

297 00 30] 00 55 +16 | 207 19 — 7 16 12) 2p)

296 57 10| 59 18 +16 17 == 7850 9 32

Mean | 207 10 207 I0 5

276 49 34/50 6 — 21/187 9 44; + 118 | 187 11 36

45 12/46 o + 2 7 + 118 9 48

48 37| 48 27 By Wi 8 =p Tae 9 55

48 28/48 32 + 4 6 +1£5 8 30

48 32/51 20 +I1I nK@) +.1 5 I2 23

47 48 | 49 27 apa 3 u& II 15

55 49) 57 54 apa? 15 — bas 12 II

56 38/59 32 + 6 7 — 4 18 I2 28

57 27|58 28 — 16 — Si IO 30

59 31) 57 45 qe 2 15 = Al Shy Io 18

57 23158 26 + 2 16 35| — 4 39 I2 10

277 00 42) 4 8 +5 21 = 4 BY T3 53

Mean] 187 12 187 II 15

~~ “a

: 7%

“7

174 Rutherfurd Photographic Measures of

TABLE V.—RESULTS OF MEASURES Or DisTANCE. (Continued.)

served Dist. Corrections for r- i

Star = Kee’ : z coried cae Proper Gorsented

No. oe Mean. | tion, | Motion. | Distance.

East. | West. |Refrac.| Aberr.| Scale. A a

14 I | .gg2I | .9886| 241 | —23 | 123 | .0214| — 8|-+.0015] 79.0221

(11) 2 | .9942 | .9893 | 238 | —23 | 123 |.0225| +21 | +.0015 .0261

3 | .9912 | .9902 | 239 | —23 | 123 | .0215| + 3 | +.0015 .0233

4 | .9856 | .9872 | 237 | —29 | 123 | .0164) +91 | +.0012 .0267

5 | .9839 | .9894| 241 | —29 | 123 | .0170| +14 | +.0012 .O196

6 | .0009 | .9952) 251 | —29 | 123 | .0295 | —4o | +.0012 .0267

7 | .0067|.9917| 224 | +35 | 123 | .0343| — 5 | —.0048 .0290

8 | .9980 | .9899| 224 | +35 | 123 |.02900| + 5 | —.0048 .0247

g | .0037 | .0073| 224 | +39 | 124 |.o41r | —31 | —.0051 -0329

TO | .0043 | .003I1| 218 | +39] 123 | .0386) +11 | —.0051 .0346

II | .0OOI | .c040| 227 | +40] 122 | .0378 | —29 | —.0052 .0297

I2 | .9977 | .9912) 225 | +40 | 123 | .0302 | —33 | —.0052 .O217

Mean 79.0264

15 Bradlely 3077

16 I | 8460} .8478| 246 | —24 | 128 | .8787| — 8|-+.0010] 79.8789

(12) 2 | .8421 | .8386 | 243 | —24 | 128 | .8720| +21 | +.0010 .8751

3 | .8450 | .8397 | 240 | —24 | 128 | .8737| + 3 , +.00I0 .8750

4 | .8380 | .8354 | 240 | —29 | 126 | .8672| +92 | +.0008 .8772

5 | .8317| .8400| 241 | —29 | 128 | .8667] +15 | +.0008 .8690

6 | .8454 | .8426| 247 | —29 | 128 | .8755 | —4I | +.0008 .8722

7.\| 8450) <8497 | 227.435.) 126 1.8833) 5 eae .8796

8 | .8386 | .8396] 227 | +35 | 126 | .8753| + 5 | —.0032 .8726

9 | .8440 | 8532] 233 | +40 | 126 | .8854 | —31 | —.0034 8789 |

Io | .8516| .8420] 222 | +40 / 126 |.8825 |} +12 | —.0034 .8803

Ir | .8385 | .8405 | 231 | +40 | 126 | .8761 | —30 | —.0034 .8697

12 | .8381 | .8349]) 227 | +40] 126 | .8727 | —34 | —.0034 .8659

Mean 79.8746

17 I |.1610] .1509| 118 | —I2] tor |.1763| — 4 | —.0026} 39.1733

(34) 2 | .1661 | .1638] 119 | —12]| 102 |.1855 | +10 | —.0026 .1839

3 | .1664| .1624| 121 | —12] tor | .1850| + 1 | —.0026 -1825

4 | .1569 | .1605 | I19 | —I4 | Io2 |.1790} +45 | —.co22 .1813

5 | .1613 | .1573 | 124 | —14 | 102 |.1801| + 7 | —.0022 .1786

6 | .1685 | .1719| 134 | —I4 | Ior |.1919 | —20 | —.0022 .1877

7 | .1522|.1574| 112 | +17 | 1r |.1784| — 3 | +.0086 .1867

8 | .1550|.1482] 114 | +137] rir |.1754| + 3 | +.0086 .1843

9 | -1546| .1376| 108 | +19; I11r |.1696|} —15 | +.0121 .1802

IO | .1376| .1481 | I08 | +19] I05 |.1656|) + 6 | +.0121 .1783

II | .1445|.1444| 112 | +20] tor | .1673 | —15 | +.0122 .1780

I2 | .1461 | .1446| 113 | +20] 102 | .1684] —17 | +.0122 .1789

Mean 39. 1811

Thirty-four Stars near “Bradley 3077.” 175

Taste VI.—Resutts or Measures OF ANGLE. ( Continued.)

= eee ere Gor: :

2 tioumplas) Metae, rected lichen. | reneabenble

: East. West. | Preces:

sion, ete. 2@ T

I 271 7 32 Qh Siig 569) 5) 18r 28 11) +> 0 25 || 185 29) 10

2 5 10) 6 43) 21 45 | — 2 PAD) ap © A5 29 I2

3 8 5/ 855| 20 19} + 4 28 53} + 0 25 28 57

4 8 44]I0 50| 18 22/+ 1 28 10} + 0 20 28 59

5 G] G2 {3 |) BO) I SS 27 58; + 0 20 29 21

6 () Bin || Gi) awh wh | eas 2I 32) + 0 20 28 59

7] IO 35|II 40| 18 37 | — 2 29 43| — I 21 29 25

8 Ir 18) 12 33/ 18 54|+ 3 30 53| — I 21 29 13

9 I2 55|15 18| 18 13 | —1o 32 9] — I 27 29 46

10 IANS) | WAR 57/\ 1G) 3O)| "3 10) Sy) ee EE 29 15

II II 34|12 30| 18 38 | — 5 30 35| — I 28 29 21

12 I4 28/15 20) 18 4o|-+ 2 32) 36)|) — 128 29 30

Mean] 181 29 11 I8I 29 16

I |268 8 40/10 24] I9 56 | — 5 }178 29 23| + 0 25 | 178 30 22

2 6 23) 7 8] 21 45 |— 2 28 29} + 0 25 Zour

3 9 17/10 12; 20 19) -- I 30 4| +0 25 30 8

4 9 52/11 38/ 18 22 | — 2 29 5| + 0 20 29 54

5 756} 9 50| 20 8|;+ 4 29 5| +020 30 28

6 SORIA TApaer An eT or3 27) 5 || ae © 2 30 2

7 TR BA || 1B By | sis) aap) |) cae 80057) — = 211 30 39

8 T2PAO) EAs 3) 1S 54) | =o 32 17| — I 21 RO) Bay

9 | 13 28/15 57| 18 13 | —14 Be Ait || —3 i By 30 18

Io I5 0/15 57| 16 30|— 2 31 56| — I 27 30 14

II I2 38/13 43) 18 38 | —5 Bu AA = 27 BO Bit

12 14 28/16 47| 18 4o O Bil Ti} |) <= 1 Dy 20) 13

Mean] 178 30 13 179) 20) 17

I | 98 30 35|31 20| I9 56 | — 2 8 50 52} —0O 47 8 50 39

2 ZT BN BO He AR VAS | a 99 51; —°0 47 St It

3 31 38/31 55| 20 I19| + 9 52 15| — 0 47 52 7

4 33) S133) 0) 181228) 25 51 29| — © 39 51 19

5 29 6/30 26] 20 8] +13 50 7| — 0 39 50 31

6 29 42/30 30) 14 4 | +23 A433) == 2 39 Su

7 2003) 258 3S Sif rE AIG BE Se 2. 35) 49 29

8 2eAT | 28) 27) 18) BAN oi Ai SUN aise eS 49 21

9 28 47| 30 28) 18 13 | — 3 AT AS 2 a7 49 39

10 29 34/31 40| 16 30 | + 3 AU AO sie 2047 49 42

II 27 50| 29 25) 18 38] + 3 47 19| + 2 48 50 21

12 29 18/30 12| 18 4o | + 6 48 31} + 2 48 48 41

Mean| 8 48 39 8 50 15

176 Rutherfurd Photographic Measures of 4

TaBLE V.—REsuLTS OF MEASURES or Distance. ( Continued.)

t | Observed Dist. Corrections for Cor- Stasiike Final Ny

Star sy rected | y755;,.|_Proper | Corrected

No. = ; Mean. | jion, | Motion. | Distance. _

East. | West. | Refrac.| Aberr.| Scale. hs

18 I | .3692|.3590] 88 | — 8 | 113 | .3832/— 3]|—.0053]| 28.3776

(33) | 3 | -3860 | .3727| Iot | — 8 | 113 | .3998|-- I|—.0053 -3946

4 | .3821 | .3729| 95 | —I0 | 124 | .3982)\-- 33)|— 0044 -3971

6 | .3806 | .3646} 122 | —1o | 112 | .3948|— 14] —.0044 .3%90

II | .3330/ .3232] 90 | +14 | 113 | .3496|— 11] +.0188 -3673

12 | .3444 | .3357 ol | +14 | 113 | .3616)— 12] +.0188 -3792

Mean 28.3841

19 I | .9604 | .9622| 182 | —17 | 103 |.9871/— 5|—.c0I13] 55.9853

(14) 7) 2 | -9638:|.9538) 178 || —17 | 103 | -9837)|-|- 15) cog -9839

3 | .9560 | .g669 | 174 | —17 | I04 | .9865|-+ 2] —.co13 -9854

4 | .9503 | .9490| 176 | —20 | 104 | .9747 | + 64] —.ooI1 -9800

5 |.9515 | .9655 | 172 | —20 | 103 | .9830|-+ 10] —.oo11 -9829

6 | .9636 | .9625 | 169 | —20 | 103 | .9872 |— 28] —.oo11 -9833

7 | -9464 | .9467 | 172 | +24 | Too | .9752|— 4| 4.0042 -9790

- 8 | -9410 | .g460 | 162 | +24 | 100 |.9711|+ 4] +.0042 -9757

‘| 9 | .9478 | .9522| 188 | +28 | I00 | .9806 | — 22] +.0045 .9829

IO | .9449 | .9497 | 168 | +28 | 103 } .9763 8 .0045 -9816

II | .9503 | .9477| 176 | +28 | 106 | .9790|— 21) +.0046] } .9815

I2 | .9530 | .9375 | 165 | +28 | 103 | .9738|— 24] +.0046 .9760

Mean 55-9815

20 I | .5073|.5128] 269 | —27 | 134 | .5432|/— 9] —.0033| 89.5390

(35) |) 2) -5142 | 5126) 2731) 27. 135 |)-5470 > 241) —.0ega 5462

8 | -5201 | 5099) 284 || 27) 134) 5407) |) 3)| Gas 5467

4 | .5090 | .5036| 275 | —32 | 134 | .5396 | +103 | —.0027 9472

5 |.5176|.5086| 2901 | —32 | 134 |.5480|-+ 16 | —.0027 .5469

6 | .5228 | .5256| 322 | —32 | 134 j .5622|— 46| —.0027 ~5549

7 | -4895 | -4994| 256 | +39 | 132 | .5327|— 6) +-.0108 5429

8 | .4880 | .4998 | 264 | +39 | 133 |-.5331|/-+ 6] +.0108 -5445

9 | -4948 | .4784 | 247 | +44 | 129 | .5242|/— 35| 4.0116 5323

10 | .4964 | .4906| 249 | +44 | 134 | -5318| + 413] +.0116 5447

II | .4836| .4807]| 259 | +45 | 134 | .5216|— 33] +.0117 5300

I2 | .4925 | .4884] 266 | +45 | 134 | .5306|— 38] +-.0117 5385

Mean . 89.5428

21 I | .9995 | .0222)| 122 | —I0 | 119 ||.0337|— .3 | —.c059)|) 32-0275

(22) 3 | .0215 | .0238 | 130 | —Io | 119 | .0463|/-+ 1] —.0059 -0405

4 | .0225 | .0284| 128 | —12]| 124 | .0492|-+ 37] —.0049 .0480

6 | .0242 | .O170] 132 ,; —I2 |} II9 | .0443 |— 16| —.0049 .0378

7 | .9806 | .9690 | 132 | +1314 | 121 | .0013|— 2] +.0195 .0206

8 | .9991 | .9762| 112 | +314 | 121 |.0122|/+ 2] +-.0195 .0319

9 | .9821 | .9786| 157 | +16 | 122 | .c097 | — 12/| +.0209 .0294

II | .9916|.9710| 137 | +16 | 121 | .0085 |— 12] +.02I0 .0283

12 | .c040 | .9812| 118 | +16 | 121 | .o179 |— 14] +.02TO .0375

Mean ; 32.0335

Thirty-four Stars near “Bradley 3077.”

TABLE VI.—ReEsutLtTs oF MEASURES oF ANGLE.

177

( Continued.)

= Observed Position Gees Cor- ae

Tec- n b

S Hodmia|/Bemac|) tected |) Ftoper "| ced) Angle.

° East. West. | Preces-

sion, ete. Pp 7

fo) / “i / Md / “i fo) fe f Md {o) ‘ a

I |II6 3 5/31 42/ 19 56) + 5] 26 51 24| —0 56 AL Hit D

3 34 8|34 50) 20 19 | +19 SSS O50 53 50

4 35) 2732) |) 18) 22) =- 14 5 9 = © ay 54 51

6 BPs) || Aes aidby wl dL | gel A S| == @) A 53 48

II 29 35/29 14| 18 38 | +16 48 18| + 3 20 5I 52

12 32 24} 30 35| 18 40 | +14 50 23| + 3 20 Er

Mean| 26 51 18 26 52 45

I | 254 20 16/22 27| I9 56 | — 9/164 41 9| + 0 35 | 164 42 18

2 18 45/19 38] 21 45 | —Io 4047) On35 42 29

Q 2I 12/21 48| 20 19 | — 9 4I 40} + 0 35 AI 54

4 22 3/24 22| 18 22 | —I0 4I 24| + 0 29 42 22

5 18 50/22 6/20 8|—8 4o 28; + 0 29 42 0

6 20 30/21 18/ 14 4|—5 34 53| + 0 29 42 29

7 24, 34:| 25 40) 18 37 | —14 AZ NS ON ea an A. 42 39

8 AS dl (2G ABS US Gal = IS 45 4 I 54 42 51

9 27 S| ZEN 50) 18. 135) —— 24 AS WAS ia 2 and 42 49

af) 29 26/28 I1| 16 30 | —I5 A | == B 2 42 45

II 26 18/27 40| 18 38 | —16 45 21| —2 3 43 32

12 27 40|}29 58} 18 4o | — 8 AG Bi ——= @ 42 40

Mean | 164 42 42 164 42 34

I | 102 41 28/43 28] 19 56 © | 13, 2 24 |. — © 20 13 2 Be

2 39 38) 40 45| 28 45 | + 5 Z 2) —= © 2 2 49

R 42 35| 43 28) 20 19 | +11 3 32| — oO 20 2 51

4 43 27/45 10/ 18 22 | + 2 49| —o 16 22

5 40 45/42 10} 20 8 | +15 15 — On To 2 38

6 4I I10|4I 42) 14 4 | +27 | 12 55 57| —o 16 2 48

7 AO) (533 Ali Abes|| ake)” Bi 4 ae | oe) On BI Set 2 14

8 WAZ) 3,43 8) 918) 545-8 138) 16 2 25

9 43 27|44 25/18 33 | + 3 2 12| -+ 1 Io I 26

Io 43 50/45 32| 16 30 | + 6 I 17| + I 10 5 WA)

II 4I 32|42 47| 18 38/+ 6 053) + 111 2 18

12 43 56/45 30} 18 4o| + 8 Q air oa ir an BD a

Mean| 13 I 31 22 2 By

I | 223 10 27/13 8| 19 56 | —I0 | 133 31 34) + 0 48 | 133 32 56

3 IO 35/12 2) 20 I9 | —22 31 15| + 0 48 31 42

4 II 24/15 35| 18 22 | —19 3I 32| + 0 39 | 32 40

6 9 13|/11 20; 14 4 | —33 23 48) + 0 39 31 34

7 13 28/14 32| 18 37 | —21 32 16| — 2 36 30 43

8 5 Oils O| ws | Gy yaa 34 42) — 2 36 31 47

9 16 50/20 25| 18 13 | —28 36 23| — 2 48 32 39

It Ly Bi Up AS |) US eS) ae 35 40; — 2 49 33D

12 T/A ACSA LOMA OM ee 7 65) We) 29 48

Mean | 133 32 29 133 31 53

178 Rutherfurd Photographic Measures of

TasLe—E V.—ReEsutts or MEAsuREs or Distance. ( Continued.)

ty | Observed Dist. Corrections for Cor- | geale Final

0. o | re Mean | tion, | Motion. | Distance.

eg East. | West. | Refrac., Aberr.| Scale. a Bs

92 | 8 | .2376| .2377| 2905 | +45 | 125 | .2775| + 7 | +.0040] 102.2822

(15) | 11 | .2489| .2607 | 320 | +51 | 134 | .2987 | —38 | +.0043 2992

| 12 | .2472 | .2366| 301 | +51 | 125 | .2830| —43 | +.0043 .2830

| | Mean 102.2881

| | |

93 | 1 | .5766|.5912) 410 | —37 | 84 | .6175 |— 12| —.0016| 124.6147

(Gey) yee gee 7/4 ON 51720) AOA eee ai7 84 | .6068 + 33) —.o016 .6085

| 4 | 5400) 5519) 397 | —45 84 | .5770 | +144 | —.0013 +9901

15 1.5488) .5608-| 389 9-45) | 982 175853) 22)) oan 5863

| 6 | .5830 | .6004| 381 | —45 | 82 | .6214 | — 63 | —.0013 .6138

| 7 | 5582 | .5378) 392 | +54| 84 | .5889|/— 8|+.0054} —.5935

| 8 | -5514| -5656| 364 | +54] 85 | -5967|+ 8|+.0054| 6029

| To | .5485 | .5727 | 385 | +62 84 | .6016 | + 18) +.0058 .6092

| IE | .5523 | .5609)| 397 || -—-63 84 | .5989 — 46) +.0058 .6001

| 12 | 5545 | 5378 | 370 |.-+-63 |. 104 | -5878 | — 53 | 42.0058 .5883

| Mean 124.6007

MM | I | 5444! .5442| 238 | —20 | Io7 |.5750|— 6|—.0043| 66.5701

(21) | 2 | 5444) .5316| 241 | —20} 107 | .5690|-+ 18 | —.o043 -5665

3 | -5391 | -5332"| "240 | —20'| 106 | .5669)) - 2)| — 008 .5628

A | 5466 | .5563 | 240 | —24 | rag | 5821 | + 77 | —.0035 5863

5 | .5401 | 5340) 237 | 241) 107 || -5672 | 4-) 12) 1aess -5649

6) 5583) 5482!) 234 || 24" |) To7 9) 5832) —— 340) o0gs -5763

7.2583 i 0-5 149") 245) 5 |) 1-29 i) 000 4) 5600) | Se aoe 5741

|S SLGSH 5144s) 2074 B20) | Vi tOu | 25400) 1 isa ec eoute 5635

| 9 | 5112] .4964| 290 | +33 | ITO | .5453 |— 26] --.0150 5577

| ir 5 372\) 516n.| 253° 1) =-a37) P1067 5641 | 25 | Oust -5707

| 12 | .5177| .5113 | 223 | +33 | 106 | .5489 | — 28) +.0151 .5612

| Mean 66.5691

25 1 | 5484/5453 | 396 | —35 | 123 | .585 | 11 | ooze lenmpeqame

(a7) 2.) -5400))'.53371) 30% 9] —35 1) 123 [25746)) 1-932) eon -5756

3 | -5549 | -5545'| 383 | —35 | 123 | -5903 | 4) —eoa2 -5895

4 | 5350 | -5390| 386 | —43 | 123 | .5735 | +137 | —.co18 -5854

5 | -5296 | .5345 | 378 || =43/| 123 | -5677 || -- 22.018 5081

7 || -5290)) 52763) 383 9) 4-525) 123 | |/-5690)|/— Si jee mn 5753

8 | .5395 | 5224) 352 | +52 | 124 | .5737|+ 8|-+.0072z 5816

9 | 5226) .5122| 428 | +59 | 123 | .5683 | — 46/| --.0076 57s

II | .5294 | .5288| 393 | +60] 123 | .5766|— 44) +-.0076 5798.

12 | .5205 | .5310| 358 | +59 | 123 | .5697 |— 50| +-.0076 -5723

Mean 118.5781

Thirty-four Stars near “Bradley 3077” 179

TaBLE VI.—ReEsvuuts or MEASURES OF ANGLE. ( Continued.)

I Uhsenved Posien qe Cor- uo

= ngle. orrec- n =

= a tion plus | Refrac. neuiee uaoves rected peaeies

. East. West. | Preces- p

sion, ete. 7

Or JO UD ”] “\ “1 On eertic| fi ih 4 / “

ae o 3440) 15) 6:54) 0/165 442) —— 1 3 | 165 3 20

II MASS] AO SONS, Zor) 15 Ah Seyi eT as 3 23

12 ATAT AS 55) Lou 40 | 8 (SSG) aaa Bel

| Mean;165 5 17 nos 2 iW

| |

I | 252 Io 42|1I 42| 19 56 | —I0 | 162 30 58/ + 0 16 162 31 48

2 8 48| 9 52| 21 45 | —10 30 55| +0 16 22 18

4 Dh 50) 147 | 0 22.) 10 31 13; +0 13 21055

5 Q) 28) BT. 32°20 S| ——10 30 28) + 0 13 31 44

6 De Soren oye iy A 5 2AT st Ours 3I 51

7 13 3/14 13| 18 37 | —15 32 0); —O 52 2 sult

8 AGES Su Mee jal EOn Pye 7 33 27) — O52 32 16

10 16 26|17 50| 16 30 | —16 33 22| — 0 56 2) Teil

II 13 38/15 12) 18 38 | —17 32 46) —o 56 Bah

12 16 2/18 13) 18 4o | — 8 35 40| — 0 56 Boo

| | Mean | 162 31 32 | 162 32 2

1 |235 18 8/19 22) 19-56 | —11I | 145 38 30} + 0 26 T45 39 30

2 £5 38/16 32) 20 45 |, —16 Bil BAL ai @) 2D 3997

3 TOAD) | MOPLSi 20, LO) ——20 38 54, + 0 26 38 59

4 I9 20|19 53| 18 22 | —17 37 Ar| + 0 22 38 32

5 16 34|18 50] 20. 8 | —22 37 28; + 0 22 38 53

6 16 48\18 18| 14 4 | —27 ZO | =O 2 38 39

Fj AG) 35 || Qe AWS) || IkS) B77 || Bit 329 26} — I 27 B10)

8 21 48| 23 18| 18 54 | —14 ATT) e277 Ao) D7/

9 23 26|26 48) 18 13 | —31 42 49 — I 33 40 20

II Pit Dg || 2 P|! ws) BhS) |) =) AON Sela ela 39 17

12 23 2|26 6/18 4o | —16 42 58| — I 34 28 46

| Mean | 145 38 e 145 39 8

I | 248 57 30|58 56| 19 56 | —I0 /159 17 59} + 0 16 | I59 18 49

2 55 48/56 46) 21 45 | —12 17 50; + 016 I9 13

B 58 18|59 38| 20 19 | —13 19 4| + 0 16 18 59

4 59 18/00 35| 18 22 | —13 its) hl Se Cy ual 18 48

5 BOO Sil 20s Oa) 1S 17, 53)) step Ona: 19 10

TAQ OO) 7, To 324) 18) 37 | 17 19 9| —0 54 19 18

8 bs Gy ee J-s ( -y/ ( ) 20 26| — Oo 54 19. 13

9 218} 4 18| 18 13 | —27 21 A | —o58 19 10

II E08) 2°45) 18 38) —18 20 22} —o0 58 19.38

12 2s Aso LO AO Ms LOn 22 26) —o0 58 18 50

| | Mean | 159 19 26 | 159) LOM;

180 Ltutherfurd Photographic Measures of

TABLE V.—ReEsuLTs oF MEASURES OF DISTANCE. ( Continued.)

ty | Observed Dist. Corrections for Cor-_| Seale Final

Star-| 5 : rected | Varig-| Proper | Corrected

No. | ¢ Mean. | tion, | Motion. | Distance,

. East. | West. | Refrac.) Aberr. | Scale. a ae

26 | 1 | .9975 | .0135 | 183 | —1I5 | 114 | .0330 | —25 |—000n)|) Agiozat

(29) | 2 | .0162|.0226| 207 | —15 | 114 | .0492|) +13 | —.c091 -O414

3 .0286 | .0154| 242 | —15 |‘114 | .0553 | + 2 | —.oog1 .0464

4 | .0159 .o140) 220 | —18 | 121 |.0464) +56 | —.0075 .0445

5 | -0173 | 9999 | 259 | —18 | 120 | .0439| + 9 | —.0075 -0373

6 | .o185 | .0212| 309 | —18 | IIO | .0591 | —25 | —.0075 .O491

7.9586 | .9565 | 221 | +21 | 114 | .9923| — 3 | +.0299 .0219

8 | .9839 | .9789 | 203 | +21 | 114 | .0144) + 3 | +.0299 .0446

II | .9504 .9571 | 228 | +25 | 124 |.9951 | —18 | +.0322 .0255

| 12 |..9566 | .9410| 209 | +25 | 120 | .9834 | —21 | --.0322 .0135

| | Mean 49.0348

Ca) | 12 | .8166| .8112) 298 | +45 | 132 | .8570) —38 | +.0144] 89.8676

28 4 | .7395 | -7356| 265 | —23 | 117 |.7720| +72 | —.0056] 62.7736

(24) | 6 | .7193 | .7225| 269 | —23 | 114 |.7554| —32. | —.0056 -7466

II | .7391 | .7261 | 285 | +31 | 114 | .7741 | —23 | +.0241 +7959

I2 | .6891 | .6803 | 243 | +31 | 113 |.7219| —26 | +.0241 - 7434

: Mean 62.7649

29 I | .0709 | .0682 | 200 | —15 | Ito |.0982 | — 5 | —.0094] 51.0883

(28) 92 | fo724 |o72s 227) fis) tO) Oger oIa hoa .0958

3 | .0856 | .0750| 264 | —15 | Ito |.1154| =— 2°) —{coo4 .1062

4 | .0794| .0760| 242 | —I9 | I17 |.1109| +59 | —.0078 . 1090

5 | .0785 | .o611 | 280 | —19 | 114 | .1065| + 9 | —.0078 0996

6 | .0877 | .0677 | 329 | —I9 | 110 |.1189 | —26 | —.0078 .1085

7 | .9937 | .9865 | 246 | +22 | 115 | .0276| — 3 | +.0309 .0582

8 | .0371 | .0175 | 219 | +22 | 113 | .o619; + 3 | +.0309 .0931

II | .O104 | .0034| 254 | +26 | 110 | .0451 | —I9Q | +.0333 .0765

T2 | .0354 .0176| 228 | +26 | 113 | .0624 | —22 | +.0333 .0935

Mean 51.0929

es 4 | .5448 | .5838 | 259 | —22 | 110 | .5977 | +-69 | —.0072 || -59:5974

By | I | .4623 | .4634| 307 | —24 | 137 |.5014| — 8 | —.0053]| 82.4953

(23) a) 22 | 24626) 4558) 314) 24) | 137 ||, 4084 |) (23) |) ean -4953

3 | -4533 | -4532| 318 | —24 | 137 | .4928| + 3 | —.0053 -4878

A | .4606 | .4474| 318 | —30 | 136 | .4929| +95 | —.0044 .4980

5 | -4502 | .4638) 318 | —30 | 140 | .4963 | +15 | —.0044 -4934

6 | .4646 | .4577 | 316 | —30 | 137 | .5000 | —42 | —.0044 .4914

74279 | 4204 || 327. | 7-30) 141 124756) — Oh Ol 4923

8 | .4457 | .4360| 279 | +36 | 138 | .4826) + 6 | +.0173 25005

9 | .4184 | .4200| 386 | +41 | 136 | .4720) —32 | +.0186 4874.

IO | .4276| .4293 | 323 | +41 | I40 | .4754| +12 | +.0186 -4952

II | .432I | .4333) 336 | +41 | 137 | .4806 |} —31 | -+.0187 .4962

I2 | .4344 | .4208} 290 | +41 | 140 | .4712 | —35 | +.0187 .4864

Mean 82.4933

Thirty-four Stars near “Bradley 3077.” 181

TasLeE VI.—REsuLTS oF MEASURES OF ANGLE. (Continued.)

3 epscrved Fesiion | (cone. Cor- era

=) : | Correc- : =

= nee | tion ine | Refrac. ected: BrOper, rected Angle.

= East. West, | _PEecess | |

| | sion, ete. Pp | T

Fgh aL / “| OQ ¢ ear “

I 156 31 26 | 34 24| 19 56 | +10] 66 53 I oO 10 | 66 53 25

2 299-3:\39 55.) 20. 45. | 4-13 Se S| == Oe) 52 54

3 31 42/33 17| 20 19 | +15 58 Fl One) 52 34

4 33 38/35 55) 18 22 | +14 53223} = AO. <9 53 43

5 BE 1/32 35; 20 8 | +14 52 ALONSO. 2.9 5B a)

6 31 5/32 18| 14 Ala ett 46 I} —o 9 52 59

7. 31 20| 30 45| 18 37 | +18 49 58) + 0 34 55

8 30 52/31 58| 18 54 | + 9 50 28) + 0 34 50 43

II 32 25| 34 26| 18 38 | +19 52 23} + © 37 53 14

12 33 13/35 15| 18 4o | +73 | SF | ap © By 5 ©

| | | Mean| 66 51 33) 66 52 32

| |

TPB ORAS ESA 50h | PTSeyAOy|e—— T5047 84 | — ry |) 147 4 12

| |

APROPOS) TORTS) Eom. 22 (| 7) || 126/27 18) --o 18 126 28 5

6 OPAF Su rO) ANS A 35 2053 +018 28 18

II QP5O} 13, 3) LS 3o) |s——2it 29 43) —1 18 | 28 39

12 II 12|}14 53) 18 40 | —16 31 26| — 1 18 | 27 30

| | Mean| 126 27 29) le 20) 2808S

I |168 36 24) 38 27| 19 56 | + 8}; 78 57 29| —o 2 78 58 1

Pa GONS2 1139), 2045: |a-8 5O 2) —=@ 2 57 26

3 36 8/38 8] 20 19 | + 7 SSA = On 2 Gyn

4 | 38 28) 38 36; 18 22 | + 8 57 2|/—o0 2 57 29

5 35) 231/37 59) 20 8 | - 5 52 AS) —= ©) 2 57 BS

6 BONO ZO ZO) ean 4 er 50 26) —o 2 | 57 31

7 37 2|36 42| 18 37 | +10 55 29a OW) 56 49

8 38 30| 38 32| 18 54 | + 3 Sy 2S SO | 57 16

II 39 16] 39 55| 18 38 | +13 5 27| ae © 7 | 58 48

12 39 38|42 6|.18 4o| +5 OSA t= Ol neven| 57 6

| Mean} 78 56 41 78 57 33

4 |150 3 18] 5 32] 18 22 | +16] 60 23 3;| sO; 40 60 23 22

I | 228 14 25/15 55| 19 56 | —II |138 34 55| + 0 20 138 35 49

2 I2 0/13 53| 21 45 | —16 34 26; + 0 20 35 53

3 15 42|16 5| 20 19 | —22 35 50, + 0 20 35 49

4 16 0 17 28) 18 22 —I19 34 47| + 0 16 BS a,

5 TANTS LS 130; S205 Sly 24 34 33| + 0 16 35 52

6 1G EATS OA Adie oe 27551 Oe LON ints 35408

i Lee TaleUOT NS «LOL 0375 |e 22 S555) On| 35 50

8 18 3/19 36) 18 54 | —14 278 30)|)—) 0 36 5

9 Ig 25|2I 48] 18 13 | —30 38 I9| — 1 Io | Boma

Io 20 45/21 43| 16 30 | —23 Qe Dit i u@ | 35 56

eit 18 52/19 5] 18 38 | —24 37 13| — 111 | 36 16

12 TO) 39) 22). 51S Ho 17 39 I5| — 111 | 35 26

| | Mean} 138 35 40 138 35 50

Rutherfurd Photographic Measures of

TABLE V.—REsuLTS of Measures oF Distance. (Coneluded.)

i | Observed Dist. Corrections for Cor- | geale Final

NOS |) | ] | Mean. | tion, | Motion. | Distance.

Bre East. | West. | Refrac.| seers | Seale. chats m

32 I | 2646 .2658 | 344 | —32 | 120 | .3005 Peers /—.0062 | 109.2933

(32) 2 | .2655 | .2600| 368 —32 138 | .3014|-+ 29 | —.o062 .2981

4 | .2768 | .2702 | 384 | —4o | 128 | .3128 | +125 | —.0052 .3201

7 | .2306 | .2495| 364 | +48 | 130 | .2863|/— 7| 4.0205 .3061

8 | 2388 |).2309"| 368 | 1-48! | 30 ||.2815) | 4-9 7a ogy .3027

9 | .2557 | -2180.| 349 | +54 | 139 | .2631 | — 43) —- 02mg 3007

IO | .2360 | .2386 | 355 | +54 | 128 | .2831 | -+ 16| +.0219 .3066

II | .2292 | .2214| 368 | +55 | 138 | .2735 |— 41 | +.0221 .2915

12 |..2333 |..2124 | 370.) --55 | "118 | 22603 |—— AG |e oa .2868

| | | | Mean | | 109.3007

33 I | .0454 | .O412 | 221 | —28 | I4o0 | .o812|}— 9) —.0078| 95.0725

(31) | 2 | .0511 | .0403 |} 357 | —28 | 144 | .0876|-+4 25 | —.0078 .0823

| 3 | .0424 | .0366 | 412 | —28 | 140 | .0865|-+ 4| —.0078 -O791

4 | .0404 | .0354| 377 | —34 | 144 | .0812 | +-109 | —.0064 .0857-

5 | .0409 | .0282 | 44t | —34 144 | .0843 |-+ 17 | —.0064 .0796

6 | .0380 | .0428 | 529 —35 | 138 | .0982 | — 48 | —.0064 .0870

7 | .c000 | .9866 | 366 | +42 | 143 | .0430|— 6| -+-.0256 .0680

8 | .ooor | .9929) 356 | +42 | 142 | .0451/-+ 6] +.0256 .O713

9 | .0036 .g918 | 366 | +47 | I40 | .0476 — 37} +.0274 <O7a8,

10 | .9968 | .0042 | 360 | -+-47 | 143 | .0500/-++ 14| +.0274 .0788

| II | .9996 | .9859| 373 | +48 143 | .0388 |— 35 | +-.0276 .0629

12 | .0000 | .9922| 364 | +48 | 144 | .0463 |— 4o! +.0276 .0699

| Mean 95-0757

a4 7 | 9473 | .9391 | 472 |.+54 | 118 | .9957|— 8| +-.0158] 1240107

(19) | 8 | .9583 | -9454| 420 | +54 | 118 | .9982}-+ 8] +.0158 .O147

II | .9655 | .9507| 490 | +62 | 108 | .o122 |— 46) +.0171 .0247

12 | .9702 | .9496| 427 | +62 | 113 | .o082 |— 52| +.0171 .0201

Mean 124.0175

38 | To | 5560) .5567| 516 | +57 | I19 | .6164|-+ 17|+4-.0251 | 114.6432

(27) | 11 | .5637 | -5550| 535 | +58 | 114 | .6209/— 43| --.0253 .6419

| | Mean .6426,

Thirty-four Stars near “ Bradley 3077”

TABLE VI.—RESULTS oF MEASURES OF ANGLE.

Observed Position

Proper

Motion.

HO CON AU BW NY H

Lal

“

(oe) (ec) ©) ©) (©) f&) ©) SC) OK

JIBS

+4+4+4+4+4 1 | |

( Concluded.)

184 Rutherfurd Photographic Measures of

TABLE VII.—For Proper Motion, ETC.

Correction for Variation.

Seale X10? | Orientation.

° i 4

Leal

iS)

“I

—.00957

-+.02660 |

+.00373

= ol

-+.01820

—.05086

—.00677

+ .00677

—.03896

+.01446

— .03733

BRBRRR UHHH

nABRHHOOON

H COMM MOMMY

444444] 1 1 1 |

Thirty-four Stars near “Bradley 3077.” 185

Taste VIII.—For Propvper Morion.

In Distance. In Position Angle.

Star

No. v ae Stee I

Si Ss Ss S;,

I —1I.000 —.O104 .OOSI —.00008

2 —0.935 —.3558 .0085 —,00304

3 — .984 -+.1783 0132 -+-.00235

4 — .960 —.2803 O125 —.00352

5 — .664 —.7481 0083 —-.00621

Oe) —o.838 —.5454 O165 —.00899

Te — .622 —.7829 OII2 —.00875

Sue — .673 +.7401 OI7I +.01265

9 | — .990 +.1428 0337 +.00482

TO | — .978 —.2087 0535 —.OI122

II —9.232 —.9727 .0094 —.00919

12 — .568 —,8231 .0826 —.06795

13 — .253 —.9676 -O416 —.04022

14 55 —.9879 .0126 —.01250

16 —0.103 —.9947 O125 —.01245

17 + .280 -+-.9601 .0255 +.02450

18 + .563 +.8263 .0352 -+.02911

19 + .137 —.9906 O179 —.01769

20 + .349 +.9370 O1I2 + .01047

21 0.630 —.7768 0312 —.02424

22 + .130 —.9915 0098 —.00970

23 + .174 —.9847 0080 —,00791

24 + .453 —.8916 O150 —.01339

25 .229 —.9734 0084. —.00821

26 +0.963 +.2709 0204. +.00553

Dy 430 —.9030 OIII —.01005

28 721 —.6932 O159 —.OI104

31 —.8292 ,O121 —.O1005

22 661 +.7508 .0092 +.00687

33 .826 +.5636 .O105 +-.00593

34 .510 —.8599 .008I —.00693

—.00570

+.00634

—++.00124

186 Rutherfurd Photographic Measures of

TaBLE [X.—MeEAN RESULTS.

Durchmusterung.

nin ORE oe Sais TSS ice

No. Mag.

I 3471.54 261 57 38 — 6200.11 | — 528.57 2 56.2942 9.4

2 | 3279.96 | 241 44 1 | —5170.81 | —1583.43 8 55.2898 9.1

3 | 2125.81 | 272 51 16 | —3846.67|-++ 89.36] 12 56.2952 7.5

4 | 2233.14 | 246 18 15 | —3677.83 | — 912.64] 12 56.2953 8.6

5 | 3376.37 | 214 9 24 | —3363.40 | —2806.80 5 55-2908 9.3

6 | 1699.59 | 229 30 18 | —2321.22 | —II109.73 5 56.2956 8.5

7 | 2505.96| 211 2 20 | —2303.23 | —2153.15 8

8 | 1639.11 | 310 19 51 | —2279.93 | +1055.07| 12 56.2958 7.0

9 | 830.27 | 270 47 43 | —1503.17 9.01 | 12 56.2961 9.0

IO | 521.11} 250 31 59 | — 888.41 | — 174.55] 12 56.2962 9.0

II | 2964.74 | 185 59 15 | — 548.13 | —2948.90] 12 | +55.2915 9.3

I2 | 339.10] 207 10 5 |— 279.71 | — 301.78 4. 56.2963 8.7

13 | 673.84] 187 I1 15 | — 151.89 | — 668.58} 12 56.2964 9.1

I4 | 2213.72| I81 29 16 | — 102.40 | —2212.98] 12 55.2917 8.2

15 Bradley | 3077 56.2966 6.0

16 | 2237.48 | 178 30 17 | + 104.00 | —2236.73| 12 55-2919 7.6

17 | 1097.56 8 50 15 | + 307.73 | +1084.43] 12 56.2969 8.0

18 | 795.11 26 52 45 | + 654.24 | + 708.74 6 56.2970 9.1

Ig | 1568.18] 164 42 34 | + 740.56 | —1513.29] 12 55.2920 9.3

20 | 2508.31 IZ 2 27 | +1043.41 | +2442.43| 12 57.2712 8.0

2i_| 897.34 | 133 31 53 | +1172-55|— 619.58} 9 | 56:2072 |) 93

22 | 2865.34 | 165 3 17 | +1311.41 | —2770.35 3 55.2922 9.5

23 | 3490.36 162 32 2 | +1851.74 | —3333-34| 10 | 55.2925 | 8.5

24 | 1864.76 | 145 39 8 | +1883.65 | —1543.60| I1 55.2926 8.5

25 | 3321.66| 159 19 7 | +2076.84 | —3112.52] I0 55.2928 8.3

26 | 1373.58| 66 52 32 | +2206.06 | + 533.57] I0 56.2974 9.4

27 | 2517.41 | 147 4 12 | +2439.97 | —2119.69 I

28 | 1758.20| 126 28 8 | +2540.40 | —1052.30 4

29 | 1431.23| 78 57 33 | +-2548.30| + 266.85] 10 56.2975 9-4

30 | 1669.47 60 23 22 | +2643.71 | + 817.13 I 56.2976 9.5

31 | 2310.84 | 138 35 50 | +2732.23 | —1741.73| 12 55.2929 7.6

32 3061-77) 33 55 3 | +-3952.75 | 41-2529:88 |) 19 1 57-27 tole

33, | 2663.30) 48 18 15 | +3647.57 | +1756.88] 12 56.2978 7.0

34 | 3474.03 | I41 51 18 | +3808.68 | —2748.62 4 55-2933 8.9

35 | 3211.41 | 123 20 48 | +4794.57 | —1791.25 2 55-2935 9-4

Thirty-four Stars near “Bradley 3077.”

TABLE X.—CATALOGUE OF STARS.

187

1 |

its

No. | #297 sion, 1874. 1874.

CE J K 1, Mu

hm s s s Oo ” Ww | “ “

I 23 0 20.015 | 2.5557 | +.0276 | 56 19 33.38 | +19.378 | +.088

A avery Aly I 28.635 2.5709 .0279|56 158.52) 19.404] .086

3 | 13768 256.911 | 2.5746 .0286 | 56 29 51.31} 19.436] .084

4 | 13773 QB Syiloy/ 2.5814 .0285 |56 13 9.31 19.440 -084

5 3) Zeh2ie) 2.5939 | .0283 | 55 41 35.15 19.447 -084

6 | 1380T | 4 38.608 | +2.5952 +.0289]56 9 52.22 +19.472 | +.082

7 | 4 39.807| 2.6004] .0288]55 52 28.80| 19.473| .083

8 | 13805 | 4 41.361 2.5846 .0293 | 56 45 57.02| ~ 19.473 .082

9 | 13814 | 5 33.145 2.5973 .0294 | 56 28 30.96) 19.491 | .081

IO | 13826 | 6 14.129 2.6041 | .0296]|56 25 27.40; 19.505 .080

Il | 13829 | 6 36.814 | +2.6206 +.0292 | 55 39 13.05 | +19.513 +.080

12 | 13836 6 54.709 | 2.6105 | .0298|56 23 20.17} 19.519] .079

13 | 13837 | Te BAR| BLU .0298 | 5617 13.37) 19.522| .079

T4 | 13839 | 7 6.529| 2.6213] .0295]55 51 28.97| 19.523] .079

15 13841 23 7 13. 356 | 2.6116 = .0800 | 56 28 21.95 19.525 6078

16 | 13844 7 20.289 | | 42.6233 +.0296 ]55 51 5.22; +19.527 | +.079

17 | 13848 | 7 33.871 | 2.6093 | .0303 | 56 46 26.38] 19.532 .078

18 | 13850 | 7 56.972 2.6145 | .0303|56 40 10.69| 19.539| .077

IQ | 13852 Se 72 7) ek O259 .0299|56 3 8.66 19.541 | .078

20 | 13856 8 22.917 2.6098 | .0308]57 9 4.38 19.548} .077

21 8 31.526 | +2.6255 | +.0303 } 5618 2.37 | +19.551 | +.077

22 8 40.783 | 2.6369] .0303|55 42 11-60] 19.554) .077

23 | 13870 9g 16.805 | 2.6445 .0300 | 55 32 48.61 19.565 .076

24 | 13871 | 9 18.933 | 2.6367") .0303]56 238.35] 19.566) .076

25 | 13875 | 9 31.812 | 2.6454| .0301 155 36 29.43| 19.570} .076

26 9 46.427 | +2. 6310. +-.0308 | 56 37 15.52 | +19.575 | +.074

2a 9 56.021| 2.6445| .0304|5553 2.26] 19.578 .076

28 TOM eG 2.6407 .0304 | 56 10 49.65 19.580|} .076

29 IO 3.243 2.6347 | .0304 | 56 32 48.80] 19.580 .076

30 IO 9.603 2.6332 | .0304 156 41 59.08) 19.582 .076

31 | 13885 TO 15.505 | +2.6455 | +-.0306 | 55 59 20.22 | +19.584 | +-.075

32 |13894) 10 43.473| 2.6300) .0316|57 1031.83) 19.593| .073

33 | 13903 II 16.527| 2.6385] .0316]56 57 38.83| 19.603 .073

34 | 13907 II 27.268] 2.6600) .0308]55 42 33.33 19.606 .073

35 12 32.994| 2.6652 .0313 | 55 58 30.70) 19.626 -O71

VI.—The Prexsepe Group; Measurement and Reduction of the

Rutherfurd Photographs.

By FRANK SCHLESINGER.

Read April 4, 1898.

Description of the Plates.

The collection of astronomical photographs presented by the

late Lewis M. Rutherfurd to the Observatory of Columbia Uni-

versity contains eleven photographs of Prasepe taken with his

larger and improved instrument; only eight of these were meas-

ured and reduced, three having been judged inferior to the rest.

According to Rutherfurd’s invariable practice, each plate shows

two complete pictures of the group separated by about a milli-

metre in right ascension, the driving clock of the instrument

having been stopped for a few seconds after the completion of the

first or eastern impression. Near the west edge of the plate still

a third image of each of the brighter stars in the group is found,

separated by about forty miilimetres from the two other impres-

sions, the driving clock having been stopped for an interval of:

about three minutes after the completion of the second impres-

sion, and then started again and allowed to run long enough to

permit the brighter stars to leave well-defined images. The ob-

ject in securing these third impressions or truils was to afford

means for orienting the group, but in the present work they were

not used for this purpose, the orientation having been effected in

another way. It is important, however, to know how accurately

the use of trails will give the orientation, and they were therefore

completely measured and reduced, and the results compared with

those obtained by the method actually employed, which is of un-

questioned accuracy but may not be always available.

A perpendicular to the plate passing through the optical centre

of the object glass pierces the plate at a point whose approximate

position must be known in order to reduce the measures of the

stars to right ascensions and declinations. Rutherfurd so ad-

justed his plate holder that this point coincides approximately

with the image of the central star of the group, numbered 15 in

the following pages.

189

ANNALS N. Y. ACAD. ScI., X, May, 1898—13.

190 Presepe Group; Measurement and Reduction

Table I gives the data of exposure for the plates. Plates VI, X

and XI do not appear, these being the ones that were not meas-

ured, on account of their inferiority. This is due to the fact that

the photographic images of the stars on these plates, when viewed

under the microscope of the measuring machine were neither

so round nor so well defined as on the other plates and therefore

did not admit of so accurate measurement. - The irregularity of

the images is not due to a deterioration of the plates since they

were taken, but to the bad behavior of RUTHERFURD’s clock dur-

ing the exposures. For this reason these three plates were never

measured, it being deemed probable that more reliable results are

to be obtained from the eight plates actually reduced, than if all

the plates had been measured, in spite of the greater number of

observations in the latter case. In this connection I should also

say that not all the stars which appear on the plates were meas-

ured. A few whose images come near the edges of the plates

were rejected, for not only are these images much distorted, but

as we shall see later, the corrections become uncertain as we re-

cede from the centre of the plate.

TABLE I.—PHOTOGRAPHS OF PR#SEPE.

Observatory of L. M. Rutherfurd, New York.

Lat. = 40°43/48/7.5 Long. = 4"55™56°.62 W.

Thermometers.

Sidereal Time.

1870 Apr. 24 IO 45 05

1870 Apr, 24 II 25 35

1870 Apr. 25 II 10 35

1870 Apr. 25 II 59 35

WSyigf Lore, awl = 3G) 3X9) YS)

1877 Apr. 25. | II 26 02

1877 Apr. 25 ie ye) ie)

1877 May 2 IO 57 08

The column marked “ sidereal time ” gives the mean of four in-

stants for each plate: beginning of east exposure, end of east ex-

posure, beginning of west exposure and end of west exposure;

each exposure lasted six minutes. Three thermometers were

read : attached, external and telescope, the last being in contact

of the Ruther furd Photographs. 191

with the telescope-tube. The last column, marked “ focus,” gives

the reading of a micrometer head attached to the eye end of the

telescope and shows the position of the plate holder; this infor-

mation is not used in the reductions and is given only to provide

for the possibility of determining a relation between this reading

and the scale-value after a sufficient number of the photographs

made with this instrument has been reduced.

If.

Measurement of the Plates.

The plates were measured with the older Repsold Measuring Ma-

chine of this Observatory, which is a counterpart of the one by the

same maker belonging to the University of Leyden except that an

alteration has been made which obviates “ projection errors.”

(See III.) A full description of the Leyden machine is given

in the “ Bulletin du Comité Permanent,” Vol. 1, page 169, and

also in the recent work by Dr. Scheiner, ‘‘ Photographie der Ge-

stirne,”’ page 148. The machine is so constructed that. the posi-

tion of a star may be determined either by position angle and

distance or by rectangular coordinates; the latter method was

adopted in the present case. A star which is to be measured

may be brought into the field of the reading microscope by

moving the plate along a straight guiding cylinder and then

moving the microscope at right angles to the cylinder on another

straight guiding way. The wire of the micrometer is made te bi-

sect the image of the star and the micrometer head is read. Then

the whole microscope is revolved through a small vertical angle

and the wire set upon a scale of millimetres placed parallel to the —

motion of the microscope. The difference of the two readings

on star and scale, together with the number of the line on the

scale gives us the position of the star. Having gone through

the same operation for all the stars we obtain their relative

positions, at least in one direction; the plate is now revolved

through 90° by means of the graduated circle and the stars are

again measured; these two sets of measures are sufficient to fix

the relative positions of the stars, but in order to secure greater

accuracy and especially to eliminate personality the plate is turned

180° and 270° respectively from its original position, and the

stars are read a third and a fourth time. By means of the trails

192

The Rutherfurd Photographs. — 193

or otherwise the plate may be so placed in the machine that a cir-

cle of declination through the central star shall be approximately

parallel to the guiding cylinder; in this way we obtain rectangu-

lar codrdinates which are nearly in the directions of right ascen-

sions and declinations, thus rendering their conversion into the

latter a comparatively easy matter.

Two observers alternated in the measurements, one recording

while the other observed; the details of each morning’s work,

which usually lasted a little over two hours, are as follows: the

first observer reads the circle, runs and temperature, the second

reads on the central star thus: Hast image, scale, scale, east

image; west image, scale, scale, west image. Continuing, the

second observer goes through the same operations for usually

three other stars, experience having shown that four stars could

be read conveniently without fatiguing the eye; thus the ob-

servers alternate till twenty or twenty-five stars have been read

and then the temperature is recorded a second time. The morn-

ing’s work is now half finished ; the same stars are then observed

in the reverse order, care being taken that each observer shall now

read those stars that he had not read in the first half; having

finally gotten back to the central star, temperature, runs and the

circle are read as at the beginning. This process of repeating all

the measurements in the reverse order, eliminates the effects of

any change in the machine or in the observers that is pro-

portionate to the time, for the mean of the two times of ob-

servation is nearly the same for all the stars. In the first half of

the morning’s work the micrometer head is set at about 9.*0

when pointed at a star; but in the second half the reading is made

9.°5; in this way periodic errors of the screw are nearly elimi-

nated, for both star and scale are read with two different parts of

the screw separated by half a turn.

The measurements made in the first position of the plate, 7. e.,

with the stars having the greatest right ascensions farthest from

the cylinder are recorded as “ x direct ;” on the next day the plate

is turned 90° ina counter-clockwise direction so that now the stars

having the greatest north polar distancesare farthest from the cylin-

der. The measurements taken in this position are called ‘ty direct,”

while those taken in the two opposite positions, 180° and 270°

from the original position are called respectively “ « reversed ”

and ‘“‘ y reversed.” As only twenty or twenty-five stars could be

194 Presepe Group ; Measurement and Reduction

measured on each day, and as the photographs of Przsepe show

about forty-five stars that admit of measurement, it was neces-

sary to spend two days on each position of the plate. To

eliminate the effect of a possible motion of the plate or of the

scale the central star 15 was read each day by both observers.

After three of the plates had been measured, viz.: III, VII and

IX, it was decided to read the central star more often, so that on

the succeeding plates four such readings were made every day, in-

stead of two.

Three observers were engaged in the measurement of the first

five plates, but only two were concerned in the work for any single

day. Care was always taken to have the same pair of observers

make both the direct and the reversed measurements of a particu-

lar set of stars, in order to eliminate personality. Suppose one

of the observers has contracted the habit of always setting the

micrometer wire too far to the right of the centre of a star’s im-

age by an amount depending upon the size of the image; the

distance between two stars as obtained by such an observer will

be subject to an error which depends upon the difference of magni-

tudes of the stars. But when the plate is reversed 180°, the same

observer will get a distance which is too small by as much as the

first distance was too large or vice versa; consequently the mean

of the two measurements will be free from such personality as we

have supposed. However,this method of measurement does not

eliminate all personality, for the star images are seldom round

and are usually more sharply defined on one edge than upon the

other ; two observers will thus sometimes differ considerably in

their estimations of the true centre of the image.

Table II gives the runs, circle reading, etc., foreach day. Runs

were observed twice daily, once before and once after the measure-

ment of the stars ; the number in the column headed “runs ’’is the

mean of the two determinations expressed in millimetres. The

circle was also read twice, employing two microscopes 180° apart

for each reading; in the column marked “ circle ” the degrees and

minutes are always taken from the right-hand microscope, while

the number of seconds is the mean of both microscopes. The

thermometer occupied a fixed position near the plate and was

graduated in Fahrenheit degrees. The last column gives the in-

itials of the three observers, Kretz, Hays and Schlesinger.

of the Rutherfurd Photographs. 195

TasBLe I].—Datny ReEcorps.

Runs in

| Position of Plate, and Stars ,

a Ther. Obs’rs.

| Circle. | Measured.

Plate JII.

58 00 | 63.3 | x direct; 2-4, 6, 8, 10, 11, 14—|

| 18, 20, 22-24, 26, 28, 29, 45.

275 5757 | 67.0 | “y direct; 2-4, 6, 8, Io, II, 14-|

| 18, 20, 22-26, 28, 29, 33. |

5 58 00) 63.2 x reversed; see Jan. 12.

| —0.002I | 185 57 57| 60.8 | # direct; 1, 2, 5, 7, 15, 234, 25,

| | | 27, 31-373 39, 40, 43-45. |

—0O.0016 | 95 58 02 | 63-6 | y reversed; see Jan. 13.

| —0.0025 | 275 58 OT | | 85. 2y a ivechs iy 5a 15s 235A, 2700

| | | 31-37; 39, 40, 43-45. |

—0.0035| 5 58 00 60.5 a reversed; see Jan. 19.

| 1275 58 00) Trails; 15, 23, 27, 31.

—0.0020 | 95 58 oa) 61.6 y reversed; see Jan. 21.

ees we

mn im bite

TAnm HH pA A

Plate IX.

+0.0028 | 177 37 02)| 63.2 | x direct; 2-4, 6, 8, Io, I1, 14—|

| | | 18, 20, 22-20, 45. |

| 267 37 OL | | ‘Trails; 15, 23, 31, 37.

0.0016 | 267 37 00) 62.2 | y direct; 2-4, 6, 8, Io, II, 14-|

| | | 18, 20, 22-29, 33. |

63.6 | y direct; I, 5, 7, 15, 23A, 3I-|

| | 40, 43-45.

+o0.0021 | 87 37 02) 60.9 y reversed; see Feb. Io.

| +0.0006 | 87 37 OL | 63.5 iy rev ersed; see Feb. 9.

+0.0031 | 357 37 02| 64.2 |x reversed : see Feb. Ig.

/—0.0016 357 37 00 65.9 x reversed: see Feb. 5.

| +0.0036 | 177 37 02| 66.4 | x direct; I, 25 Cpe 3 AG

| pO Bree, 43-45. |

| 0.0010 | 267 36 58

Plate VII.

| +0.0026 86 54 00 | 63.8 | # direct; 2-4, 6, 8, 10, 11, 14-|

18, 20, 22-29, 31-33, 45.

0.0030 | 356 54 00| 62.1 | y reversed; see Mar. I.

_+0.0039 176 54 02, 59.4 | y direct; 2-4, 6, 8, 10, 11, 14- |

18, 20, 22-290, 31-33.

+o.001f | 176 54 02) 65.1 y direct; is Be We Tne Moy aed

| 21, 23A, 33-45. |

+0.0039 | 86 53 58 65.9 | x direct; I, 2, 5, 7, 7A, 15, 19,

21, 23A, 34-45

+0.0044 | 266 53 56) 66.8 | x reversed; see Feb. 26.

| 176 54 00 IUEMISE ss, 2A Bek cae

+0.0045 | 356 54 03 | 65.8 | y reversed; see Mar. 2.

| 0.0026 | 266 54 00) 60.8 2 reversed; see Mar. 3.

qe?)

nD oA

DMN

A £

todd om AA oO

196 Presepe Group; Measurement and Reduction

TABLE I].—Daity Recorps. ( Continued.)

uate: shuns Circle. | Ther. Position Ge Pla ae Stars Obsr’s.

Plate VIII.

Mar. 15 | +0.0036 | 177 02 28 56.8 | w direct; 2-4, 6, 8, 10, 11, 14-| S, K

18, 20, 22-29, 31, 45.

‘© 16-| +0.0036 | 267 02 30| 62.6 | y direct; 2-4, 6, 8, 10, 11, 14-| K, H

Ms} AO}, 2, AG), Bil, 2),

“ 17 | +0.0039 | 357 02 31 | 60.4 | w reversed; see Mar. 15. Ss, K

« 18 | +0.0036 | 357 02 27 | 62.3 | a reversed; see Mar. 25. 8, H

““ 20) +0.0050 87 02 32) 62.0 | y reversed; see Mar. 16. K, H

«22 | 10.0045 | 87 02 28 | 64.6 | y reversed; see Mar. 24. 8, K

Hua | 267 02 29 Trails; 15, 22, 23, 3I. K,H

“24 | +-0.0042 | 267 02 34] 63.9 | y direct; I, 5, 7, 7A, 15, 19,| S, K

23A, 32-45.

‘* 25 | 40.0045 | 177 ©2 29) 62.8!) @ direct; I, 2,5, 7, 7A, 15, 19)|/ 5, ie

23A, 32-45.

Plate II.

Apr. 3 | +0.0015 | 276 00 00| 65.9 | y direct; 2, 4, 6, 8, 10, 11, 14—-| K, H

18, 20, 22-26, 28, 29, 33.

5 | t0.0015 | 185 59 59) 65.9 | x direct; 2, 4, 6, 8, 10, 11, 14—| 8, K

18, 20, 22-29, 45.

“* 6 | ++0.0001 | 96 09 02) 67.8 | y reversed; see Apr. 3. K, H

«7: | +0.0018 6 00 OO| 67.8 | # reversed; see Apr. 5. S, K

“8 | +0.0035 6 OO 00} 67.6 | w reversed; see Apr. IO. 8, H

‘€ 9 | +0.0046 | 276 00 00| 64.7 | y direct; I, 5, 7, 7A, 15, 19,| K, H

| 23A, 27, 31-40, 43-45.

“* “10 | +0.0055 | 185 59 58| 65.6 | a direct; I, 2, 5, 7, 7A, 15, 19, | S,

23A, 31-40, 43-45.

““ 14 | 0.0062 | 95 59 59) 65.9 | y reversed; see Apr. 9. K,

Plate IV.

Apr. 24 | +-o.o101 | 186 16 58) 69.7 | x direct; 2-4, 6, 8, 10, 11, 14—-| S, K

18, 20, 22-20, 45.

“* 28 | +0.0109| 6 17 O1| 65.9 | a reversed; see Apr. 24. S, K

«* 29 | +0.015I | 276 17 00| 66.9 | y direct; 2-4, 6, 8, Io, 11, 14—| S, K

18, 20, 22-26, 28, 29, 33.

May 1 /|-+0.0165 | 96 17 02/| 67.5 | y reversed; see Apr. 29. 8, K

““ 3} +0.0155 | 96 16 58| 65.0 | y reversed; see May 5. S, K

‘* 4 | +0.0136 | 186 16 58| 66.0 | a direct; I, 2, 5, 7, 7A, 15, 19,| S, K

23A, 31-40, 43-45. f

«5 | +0.0156 | 276 16 57| 66.9 | y direct; 1, 5, 7, 7A, 15, 19,| S, K

23A, 27, 31-40, 43-45.

«6 | +0.0160 6 17 00/| 68.8 | reversed; see May 4. S, K

Ca iS 276 17 OL Trails; 15, 23, 31, 37- S, K

of the Rutherfurd Photographs.

TABLE [].—Datty ReEcorps.

'( Concluded.)

197

Date; Buns ue Circles Ther. Position create one Stars

Plate I.

fo) r] “a

Noy. 3 | —0.0080 | 187 10 05 | 65.3 | x direct ; 2-4, 6, 8, 10, 11, 14-| S, K

18, 20, 22-29.

“4 | —0.0062 | 187 Io 04] 63.8 | x direct; I, 2, 5, 7, 15, 23A,|S, K

31-40, 43, 44.

«* 6 | —0.0076 | 277 10 06| 65.4 | y direct ; 2-4, 6, 8, 10, 11, 14-| S, K

18, 20, 22-29, 33.

«10 | —0.0056 | 277 10 03| 65.0 | y direct ; 1, 5, 7, 15, 23A, 31-| 8S, K

40, 43, 44.

** II | —o0.0064 7 10 O07 | 67.0 | # reversed ; see Nov. 3. S, K

«* 13 | —0.0066| 7 IO 05 | 64.1 | w reversed ; see Nov. 4 Ss, K

“* 16 | —0,0069 | 97 10 05 | 65.2 | y reversed ; see Nov. 6. Ss, K

ON ekg) 277 10 08 Trails ; 15, 23, 31, 37. Sh, LEC

“* 18 |—0 0065 97 10 05) 64.6 | y reversed ; see Noy. Io. Ss, K

Plate VY.

o) i 44)

Nov. 20 | —0.0041 | 176 09 07 | 64.5 | w direct ; 2-4, 6, 8, 10, 11, 14-| S, K

TOW 2On 22-204 AS en

«« 23 | —0.0060 | 176 09 07 | 64.2 | a direct ; 1, 2,5, 7, 15, 19, 23A,/|S, K

31, 32, 34, 35,37,39,40,43-45.

“* 24 | —0.0061 | 266 09 07 | 68.7 | y direct ; 2-4, 6, 8, 10, 11, 14-| 8S, K

: | c 18, 20, 22-29.

“* 26 | —0.0059 | 266 09 06) 71.0 | y direct ; I, 5, 7, 15, 19, 23A,/|8, K

31, 32, 34, 35)37539,49,43-45.

“27 | —0.0068 | 356 09 07 | 68.5 | # reversed ; see Nov. 20. Syke

“30 | —0.0072 | 356 09 04 | 63.4 | & reversed ; see Novy. 23. S, K

Dec. I | —0.0065 | 86 09 07) 66.1 | y reversed : see Noy. 24. Ss, K

a 86 09 08 | 65.4 | y reversed ; see Nov. 26. S, K

it. <a

198 Presepe Group; Measurement and Reduction

On the next page is given a specimen of the recording sheets ;

all the measurements relating to the same star for any one plate

are recorded on one sheet. The forms are not designed for the sepa-

rate reduction of the two impressions of a group which appear on

each plate, but the mean of the measurements on the two images

of a star is taken at once; that is, each star is treated as though

it occupied the middle point between its two images. The place

of this point is known when we have given the lines of the scale

used in the measurement and the quantity 4 m, which is obtained

thus: from the reading on the scale we subtract the reading on

the star, and the mean of these differences for both images is

taken, giving “‘ Mean of Diff’s;” as the scale is one of millimetres

and as two complete turns of the screw correspond to a space on

the scale we divide by 2and get} m. In reading on the scale

it was made a rule to select the line having the next lower num-

ber; consequently the place of a star is obtained by adding 4 m

to the mean of the numbers of the lines used; in rare cases, how-

ever, the next higher line was employed when it came nearly op-

posite to a star, as on March 24; this has been indicated by affix-

ing a minus sign to 4m. In the y measurements the same line

was always used for both images, since the latter differ only in

apparent right ascension.

Table III gives the uncorrected observations ; it is only neces-

sary to set down the numbers of the lines used and $m, for these

not only fix the place of the star but, as we shall see later, they

are sufficient for the application of all instrumental corrections.

The numbers of the stars are in the order of increasing right as-

censions and are those given by Professor Schur,* excepting 7TAand

23A, which do not appear in his triangulation of the group. The

table gives the observations of 4m by both observers, followed by

the difference reduced to seconds of arc in order to facilitate a

comparison.

* ** Astronomische Mittheilungen der K. Sternwarte zu Gottingen,’’ part IV.

of the Rutherfurd Photographs.

199

oL9S'0 = w %

‘Tyo Aq peprosaxy

“Zjoly Aq poinsvoyy

OVel‘*I —s, FIC Jo uve

“Tq9g Aq papsooayy

‘skvpy Aq pornsvayy

96350 —_w %

z6Z1°I —S8,HIq Jo uvayy

‘TU9S &q peIp1o0ds9y

‘Zyo1y AQ poinsvayy

‘skey Aq popr0sayy

‘TyoR Aq poinsvayy

uvoW

489M

Uva

qsug

Cov1'1) o€$9'o1 Czvs'6

£89" os:

€g9°01| €g | SVS'6"

CZzI 1| Szgg'o1 oSSS'6

Uva Il

Jo vg9° occ:

s.giq| 18901) £g | SSs-6

"MOOI | '9UTT | ‘mMOTOTPY

‘alBog "1849

*zyary AQ paps0de ry

*Tyog Aq poinsvayy

0g9S°o = Ww %

OOLI‘*I = Ss Hiq jo uvayy

O¢VI'1| Si1z‘o1 ¢690°6

Ilz° 690°

| €1Z‘O1l| €g | ofo6 |

OO£T*I| Of 1Z*o1 ofgo'6

Uva

Jo (Atay Sicto

Sqyyiq | VIc'OI| €g | 1906

“ULOLOL | eUry | ‘worry

"O[BOS "IBIS

Crgg o| S61v-o1 oS¢S‘6

61t" ces

ozyor| €y | SES-6

obZy 1| Sozo'11 SobS'6

| Uvayy |= ~

jo OcO* Cys:

s.giq| 12011) bb oSS-6

“MOTO | OULT | “ULOTOTIX

*a[BOS *IR49

“skvpy Aq papi0oaxy

‘TyoS Aq painsvayy

gt6S'o— wm %

C/g1°I —S,gIq Jo uvayy

026g 0| 0016°6 Ogro'6

O16" £zo-°

0166 | €% | 106

o£gv'1| SzrS‘or ¢6z0°6

uvay |———— oa

jo z1S°* Cfo-

S.UId €1S01| br | tzo'6

“WOLOT | OULT | “OTT

‘o[Bog "14S

uvayl

489M

uvayl

4seyy

glio‘°o— = w % 6£9b'0 = wu %

¢Sto‘o— — §.HIq Jo uvaly 3/760 = 8 FIG Jo uvayy

ofvo o—| of1S 6 o19$'6 |S£zz-0| 000g°6 C9ZS°6

L1S° 09S" 008° plc:

Z1G°6 | 9€ | zoS'6 00g'6 | 9£ | 6256

ofzo0 o—}| Sg1S'6 StvS'6 loztg 1) S6zz'11 G/6S°6

UvIT Uva fT

jo gS" ovS: jo ofz" 965°

SWIG c1S°6 (oh Sy LVS 6 S.BId 62711 bZ L6S°6

“WOLOTY |OULY | MOTT, “MOLI | OUTT | “MOTI

ce "1B49 ‘TBogg "IBS

*Zyo1y AQ pop10daxy fe "Tqog Aq papi10dex7

“Tyo Aq poinsvayy ‘skeyy Aq poinsvoay

vS10°0— = ul % grgh'o = wu %&

goto‘o— = s JIq jo uvay z6z6°0 = S,JJIq Jo UvayT

o1vo°0—| 0600°6 00S0°6 |$6zz-0| 00gz"6 SoSo 6

600° oSo° Ogz° 1So°

600°6 | 9€ | oSo6 cgz‘6 | gf | oSo'6

Gozo0'‘0—| $600°6 00¢0'°6 j06z9:1| Sogg‘oT S1S0°6

uUvaTL uvoTN

jo O10" ofo" jo Ig9° oSo°

sgiq | 6006 | 9€ | ofo6 syiq) 08901) vZ | fS06

WOOT |“OUly | “MOTT WOLI]T |*OUly | “WOTOLW

“8[B90S “IBIS “8[BIS “IBIS

“Ppesradel f : 1687 ‘eo WOE

"POsI9AOL & 16ST “Sl Torey

Lavig “TITA @ivig

“Q090IIp & * L68T “Fo WOleyL

‘Tdasw ug

“{O0IIp & {LEST ‘GZ YorIeW

200 Prexsepe Group; Measurement and Reduction

TABLE III.—PuatEe I: 2 MEASUREMENTS.

x direct. x reversed.

Star. % M, Or %M, OY

Tales: Seale minus Star. Bajrae|laiteee Scale minus Star. S-K

Schl. Kretz. Schl. Kretz.

I5 | 60,61; ©0.9016| 0.8984) +0.19]57,58| 0.6695| 06681) -+0.07

I5 | 60,61} O.go10} 0.8994| + .07]57,58| 0.6685] 0.6696) — .06

2 |94,95| O.AII4| 0.4114 .00 | 24,25 | 0.1652} 0.1635| + .08

3 | 93,94| 0.2961} 0.2954) + .04] 25,26] 0.2798] 0.2782] + .08

4 | 91,92} 0.5395) 0.5419) — .13 | 27,28] 0.0356] 0.0348) + .04

6 | 78,79) 0.3274] 0.3290} — .08] 40,41 | 0.2472] 0.2455) + .08

8 | 71,72| 0.4849| 0.4878) — .15|47,48| 0.0884] 0.0849] + .19

Io | 70,71} 0.5885} 0.5859) + .14] 48,49 |— .0174 |— .0169| — .03

II | 69,70| 0.7241| 0.7252) — .06] 48,49} 0.8429] 0.8451) — .12

14 | 61.62] 0.1022} 0.1020} + .o1 | 57,58| 0.4649] 0.4684) — .19

16 60 0.4836} 0.4858) — .12]58,59| 0.5859) 0.5871} — .06

17 | 58,59) 0.5726| 0.5739) — .07 | 60,61 |— .0020 |— .0006| — .07

18 | 57,58| 0.0299) 0.0321) — .12]61,62| 0.5404| 0.5391) + .07

20 | 56.57 | 0.6860} 0.6865 | — .03 | 6:,62| 0.8866) 0.8865 .0O

22.) 54,55 | Os7450)| 0.7494) 9.23 1635641) ©) 3206) 0; 62210 mor

23 | 53,54| 0.3750) 0.3759] — .05 | 65,66| 0.1946] 0.1944| -- .o1

24 | 51,52) 0.2446| 0.2451} — .03]67,68| 0.3272) 0.3256| + .08

25 | 50,51) 0.6644) 0.6640) + .02 | 67,68| 0.9106} 0.9080} + .13

26 |50,51| 0.5456) 0.5480) — .13] 68,69] 0.0282) 0.0231) + .27

27 |50,51| 0.2915) 0.2942} — .14]| 68,69] 0.2752) 0.2784) — .17

28 | 50,51) 0.0596| 0.0622} — .14] 68,69) 0.5080] 0.5075] + .03

29 | 49,50) 0.4759) 0.4772} — .07 | 69,70) 0.0936] 0.0944) — .04

15 | 60,61 | 0.9005 | 0.8999 | +0.02 | 57,58) 0.6698| 0.6682} +0.08

I5 | 60,61} 0.9009; 0.8990) + .12]57,58 0.6688) 0.6669) + .10

I | 95,96) 0.4069} 0.4066) + .02] 23,24| 0.1675) 0.1684| — .05

2 |94,95| 0.4126| 0.4120) + .03 | 24,25 0.1625! 0.1616) + .05

5 | 82,83) 0.5152) 0.5181| — .15 1 36,37} 0.0534| 0.0540) — .03

7 | 75,76) 0.5840} 0.5830] + .05 | 43,44 |— .o130 |— .0164| + .18

23A | 52,53 0.3599} 0.3531| + .36|66,67| 0.2135) 0.2155) — .II

31 | 48,49] 0.8738] 0.8725] + .08] 69,70} 0.6971| 0.6972| — .Or

32 | 47,48 — .0078 |— .0088|} + .05] 71,72} 0.5745| 0.5799, — .29

33 | 45,46] 0.3332] 0.3376| — .23| 73,74 | 0.2350| ©.2410| — .32

34 | 44,45 | 0.6959] 0.7006| — .25}]73,74| 0.8731| 0.8708] +- .13

35. | 42,43) 0.7008| 0.7029} — .12]75,76| 0.8659) 0.8645} + .08

36 | 41,42) 0.2239] 0.2221| + .09]|77,78| 0.3489] 0.3515| — .14

37 | 41,42 | 0.0792| 0.0799| — .04] 77,78 | 0.4944) 9.4919] + .13

38 | 37,38| 0.4668) 0.4691; — .12} 81,82} o.1081| 0.1061; + .10

39 | 36,37 | 0.7224) 0.7174] + .26] 81,82) 0.8555} 0.8554 -0O

40 | 34,35 | 0.8836) 0.8819] + .08| 83,84.| 0.6880} 0.6890] — .05 | -

A3 | 27,28 |= .@094-|— .0124| +— 116 91,92| 0.5789| 0.5781} + .04

44 | 26,27) 0.4574| 0.4624| — .26] 92,93 0.1164] 0.1168} — .02

of the Rutherfurd Photographs. 201

TasLe I[].—Puate I: y MEASUREMENTS.

y direct. | y reversed.

Star. oc yum, oe 2 ym, or |

L= . . . ec L .

ike cale minus Star Gam || tire, | ale minus Star | a

Schl. Kretz. Schl. Kretz. |

15 52 0.3166 | 0.3169 | —0.02}] 67 0.2538 | 0.2550

15 52 0.3140 | 0.3176

.I9| 67 0.2551 | 0.2545 | + .03

2 48 0.8969 | 0.8979 .06| 70 0.6722 | 0.6735 | — .07

B 34 0.3140 | 0.3131 | .05| 85 0.2620 | 0.2640 | — .11

4 17 0.2278 | 0.2255 .12 | 102 0.3502 | 0.3512 ees 05

6 66 0.5180 | 0.5181 OL] 53 0.0520 | 0.0530 | — .05

8 67 0: 265n)|/10:2686 .08 | 52 | 0.3064 | 0.3069 | .03

Loe

Bae

IO 45 0.2985 | 0.2952 0.2756 | 0.2744 | 06

II 39 0.5589 | 0.5594 .03 | 80 | 0.0149 | 0.0134

14 73, 0.2576 | 0.2595 -1I0}| 46 0.3138 | 0.3102 | 19

16 18 | 0.0766 | 0.0752 .07| ror | 0.4996 | 0.5044 | 225

17 36 | 0.1639 | 0.1634 .03 | 83 | 0.4050 | 0.4050 | .00

18 ai 0.0128 | 0.0138

20 36 0.2369 | 0.2336

22 68 |—.0124 |—.OIOI |

23 65 | 0.5135 | 0.5144

.05| 82 0.5598 | 0.5579 | + .I0

17] 83 0.3358 | 0.3385 | —

sT@ || Hit 0.581I | 0.5822 |) —

.05| 54 | 0.0558 | 0.0571 | — .07

Lol bariharae | bare israel

24 35 0.6510 | 0.6511 | OL} 83 0.9205 | 0.9208 | — .03

25 46 0.1918 | 0.1918 | .00| 73 0.3802 | 0.3779 | + .12

26 23, 0.2064 | 0.2035 | + .15]| 96 0.3684 | 0.3689 | — .03

27 Ae OsO5808 | OsO585in—— 03) (ha 74. OMS2US ml Oly Le |e fan 22

28 56 0.2920 | 0.2919 | + .o1| 63 0.2778 | 0.2786 | — .o4

29 79 0.9150 | 0.9150 00} 39 0.6569 | 0.6605 .. — .19

33 15 0.0512 | 0.0539 | — .14] 104 | 0.5241 | 0.5222 | + .10

15 52 OHANOie | CygiyZa | ——eHle) |) Ley/ 0.2540 | 0.2525 +0.08

15 52 0.3174 | 0.3172 | .O1| 67 0.2535 | 0.2536 | — -Or

I 68 0.0005 | 0.0006 Or || BL 0.571£ | 0.5720 | 05

5 8I 0.2686 | 0.2674 |

F. 33 0.2762 | 0.2805

23A | 67 0.1061 | 0.1066

31 36 0.5514 | 0.5510

32 12 0.7218 | 0.7219

2B 15 0.0512 | 0.0515

34 48 | 0.4732 | 0.4788

35 85 0.7528 | 0.7519 |

36 63 0.1924 | 0.1936 |

37 39 0.0658 | 0.0655 |

38 56 0.0759 | 0.0802 |

39 | 62 | 0.3799 | 0.3780

4o 1077 0.4095 | 0.4081

43 59 0.2589 | 0.2636

4A 78 0.6826 | 0.6850

.06| 38 0.3002 | 0.2992 |

22 86 0.2989 | 0.2975

03 | 52 | 0.4675 | 0.4684

.02| 83 0.0161 | 0.0155

.OI | 106 0.8538 | 0.8489

.02| 104 | 0.5244 | 0.5242

oO || Fe 0.0906 | 0.0889

0.8198 | 0.8231 |

061 56 0.3759 | 0.3762 |

.02] 80 0.5042 | 0.5071 |

.23| 63 0.4912 | 0.4900

10] 57 0.1916 | 0.1932 |

.07 | 102 0.1689 | 0.1674 |

.25| 60 0.3096 | 0.3105

-13| 40 0.8895 | 0.8870 |

P+ IFI4+I | | 44441441

aeons na

| pb EPS) (2VSie

202 Presepe Group; Measurement and Reduction

Taste III.—(Continued.) Puate IL: » MEASUREMENTS.

x direct. x reversed.

j Star. ym, or %™M, Or :

Tues: | Seale minus Star. Soeae ines Scale minus Star. S_K

Schl. | Kretz. Sehl. Kretz.

| “ | “

I5 | 63,64 | 0.7105 | 0.7096 | +0.05 | 54,55 | 0.8424 | 0.8400 | +0.12

15 | 63,64 0.7085 | 0.7099 .07 | 54,55 | 0.8422 | 0.8426 | — .o2

-O4 | 21,22 | 0.3390 | 0.3380

: 0.2039 | 0.1984

-20 | 37,38 | 0.4219 | 0.4200

.08 | 44,45 | 0.2625 | 0.2612

-14| 45,46 | 0.1579 | 0.1584

-I2} 46 0.5189 | 0.5141

.OL | 54,55 | 0.6420 | 0.6401

-05 | 55,56 | 0.7551 | 0.7531

2 | 97,98 | 0.2185 | 0.2192 | —

4. | 94,95 | 0.3538 | 0.3585 | —

6 | 81,82} 0.1314 | 0.1352 | —

8 | 74,75 | 0.2991 | 0.2916 | —

TO | 7374 | 9.3949 | 9.3975 | —

IX | 72,73 | 9.5386 | 0.5364 | 4-

14 64 0.4098 | 0.4100 | —

16 | 62,63 | 0.7976 | 0.7986 | —

17 | 61,62 | 0.3892 | 0.3901 | — .05] 57,58) 0.1654 | 0.1615

18 | 59,60} 0.8448 | 0.8468 | — .12] 58,59) 0.7078 | 0.7072

20 | 59,60/ 0.5010 | 0.4991 | + .10] 59,60] 0.0539 | 0.0565

— 6

22 | 57,58 | 0.5558 | 0.5589 I 0.4941 | 0.4908

23 | 56,57 | 0.1874 | 0.1871 .02 | 62,63 | 0.3664 | 0.3642

24 | 54,55 | 0.C6IO | 0.0612 -OI | 64,65 | 0.4884 | 0.4902

25 | 53,54 0.4784 | 0.4780 .02 | 65,66 | 0.0745 | 0.0722

26 | 53,54 | 0.3661 | 0.3669 | .04 | 65,66 | 0.1869 | 0.1885

27 | 53,54 O.I11II | 0.1118 .04 | 65,66 | 0.4440 | 0.4401

28 | 52,53 | 0.8736 | 0.8748 .06 | 65,66 | 0.6789 | 0.6774

29 | 52,53 | 0.2845 | 0.2878 - .17 | 66,67 | 0.2669 | 0.2612

45 25 | 0.4730 | 0.4744 -07 | 93,94 | 0.5818 | 0.5840

Sehl. Hays S—H Schl. Hays S—H

Jt Ett tt | 44+

I5 | 63,64) 0.7105 | 0.7124 | —o.10| 54,55 | 0.8412 | 0.8419 | —0.03

I5 | 63,64 0.7130 | 0.7108 | + .12] 54,55 | 0.8408 | 0.8409

I | 98,99] 0.2198 | 0.2182 .08 | 20,21 | 0.3396 | 0.3376

2 | 97,98 | 0.2161 | 0.2202 .22 | 21,22} 0.3398 | 0.3376

5 | 85,86) 0.3189 | 0.3158 -16 | 33,34 | 0.2370 | 0.2384

7 | 78,79 | 0.4000 | 0.3978 .12} 40,41 | 0.1598 | 0.1588

7A | 74,75 | 0.3018 | 0.3010 .04 | 44,45 | 0.2538 | 0.2531

Ig | 59,60) 0.8144 | 0.8172 -15 | 58,59 | 0.7409 | 0.7334

23A | 55,56| 0.1681 | 0.1626 .29 | 63,64 | 0.3889 | 0.3884

31 | 51,52| 0.6894 | 0.6871 .12 | 66,67 | 0.8675 | 0.8676

32 | 49,50 | 0.8098 | 0.8086 0.7445 | 0.7426

33, | 48,49 | 0.1569 | 0.1561 .04 | 70,71 | 0.3988 | 0.4004

24 | 47,48 | O.51II | 0.5140 ois || it 0.5398 | 0.5425

35 | 45,46] 0.5094 | 0.5122 “IS | 73 | 0.5412 | 0.5445

36 44 | 0.5342 | 0.5275 -36.] 74575 | 0.5245 | 0.5174

37 | 43,44 | 0.8969 | 0.8980 05 | 74,75 | 0.6581 | 0.6594

328 | 40,41 | 0.2764 | 0.2762 .O1 | 78,79 | 0.2790 | 0.2751

39 | 39,49 | 9.5344 | 90-5344 00] 79 | 0.5228 | 0.5226

40 | 37,38 | 0.6996 | 0.6971 .13 | 80,81 | 0.8536 | 0.8578

43 | 29,30 | 0.8098 | 0.8078 -II | 88,89 | 0.7468 | 0.7445

44 | 29,30] 0.26906 | 0.2618 -4I1 | 89,90} 0.2901 | 0.2881

45 25 | 9.4734 | 0.4758 -12 | 93,94 | 0.5821 | 0.5852

[+++ +/+] | +444] +++] 4+

[ttl ++141 1 1+1+4+4++1 ++!

Perera

of the Rutherfurd Photographs.

TasBLeE III.—(Continued.) Puate II: y MEASUREMENTS.

y direct. y reversed.

Star. | 4 yam, or 44m, or

Tare Seale minus Star. eee || Strauss | Scale minus Star. K-H

Kretz. Hays. | Kretz. | Hays.

I5 51 0.4148 | 0.4171 | —o.12| 68 0.1352 | 0.1344 | +0.04

15 68 0.1355 | 0.1368 | — .07

2 48 0.0102 | 0.0088 | + .07| 71 0.5406 | 0.5432 | — .14

4 16) |COs34Tr |) 0.3412 | 0n |! 103) <| ©.2192''| 0.2192 .0O

6 65 0.6206 | 0.6175 | + .16| 53 0.9339 | 0.9344 | — .08

8 66 | 0.3665 | 0.3671 |-— .03| 53 | 0.1856 | 0.1838 | + .10

10 A4 | 0.3996 | 0.3972 | + -13] 75 | 0.1539 | 0.1514 | + .13

II 38 | 0.6644 | 0.6645 | — .or| 80 | 0.8918 | 0.8906 | + .07

14 72, | 0.3570 | 0.3578 | — .04] 47 | 0.1970 | 0.1950 | + .11

16 17, 0.1786 | 0.1791 | — .03 | 102 0.3780 | 0.3768 | + .06

17 35 0.2662 | 0.2641 | + .11} 84 | 0.2851 | 0.2858 | — .04

18 36 | 0.1135 | 0.1128 | + .o4] 83 0.4404 | 0.4381 | + .12

20 35 0.3360 | 0.3325 | + .19| 84 0.2159 | 0.2160 | — .OTI

22 67 0.0880 | 0.0889 | — .05] 52 0.4618 | 0.4609 | + .05

Ba 64 | 0.6105 | 0.6099 | + .03| 54 | 0.9411 | 0.9408 | + .03

24 34 0.7494 | 0.7484 | + .06] 84 | 0.8025 | 0.8048 | — .13

25 45 | 0.2892 | 0.2860 | + .17] 74 | 0.2620 | 0.2612 | + .04

26 22 | 0.3085 | 0.3072 | +-:.07| 97 CONGO) || OPO || <= oitit

28 55 | 0.3882 | 0.3879 | + .02| 64 | 0.1601 | 0.1598 | + .02

29 79 | 0.0066 | 0.0085 | — .10] 40 | 0.5452 | 0.5449 | + .02

33 I4 | 0.1540 | 0.1538 | + .O1} 105 0.4014 | 0.3988 | + .14

15 51 0.4176 | 0.4178 | —o.or| 68 0.1374 | 0.1369 | +0.03

15 51 | 0.4146 | 0.4166 | — .1ry 68 | 0.1348 | 0.1381 | — .17

I 67 0.1062 | 0.1050 | + .06] 52 0.4448 | 0.4442 | + .03

5 80 | 0.3721 | 0.3734 | — .07] 39 | O.1791 | 0.1778 | + .07

Fi 32 | 0.3801 | 0.3786 | + .08| 87 | 0.1742 | 0.1741 | + .oI

7A | 47 | 0.6575 | 0.6584 | — .o4] 71 0.8970 | 0.8958 | + .07

19 77 0.3065 | 0.3075 | — .05| 42 0.2455 | 0.2440 | + .08

23A| 66 | 0.1972 | 0.1936 | + .19] 53 | 0.3584 | 0.3549 | + .19

27 44 | 0.1530 | 0.1530 00} 75 0.4005 | 0.3972 | + .17

31 35 0.6549 | 0.6524 | + .137 83 0.9032 | 0.9024 | + .05

32 II | 0.8212 | 0.8249 | — .21| 107 | 0.7351 | 0.7302 | + .26

23 14 | 0.1548 | 0.1532 | + .08] 105 0.4031 | 0.4030 | + .or

34 Amin NO 57406) O25 7250) aio 1G) 7/2011 0:97 54 G.9760, | .-|-".10

35 84 | 0.8458 | 0.8426 | + .16] 34 | 0.7100 | 0.7115 | — .08

36 62 0.2885 | 0.2879 | + .03| 57 | 0.2629 | 0.2646 | — .o9

Ba 38 0.1672 | 0.1659 | + .07| 81 0.3884 | 0.3875 | + .05

| 38 55 0.1725 | 0.1746 | — .I1| 64 | 0.3778 | 0.3762 | + .08

39 61 0.4712 | 0.4724 | — .06] 58 | 0.0776 | 0.0781 | — .03

40 16 0.5089 | 0.5050 | + .21] 103 0.0502 | 0.0514 | — .06

| 43 58 | 0.3500 | 0.3474 | + .14] 61 0.2022 | 0.2029 | — .04

44 Tae P7AOn 0. 7744.81 202). AT | 0:7800) |) 0.7749 | F387,

45 26 | 0.9096 | 0.9109 | — .06] 92 0.6474 | 0.6468 | + .03

204 Presepe Group; Measurement and Reduction

TABLE III.—( Continued.) Puatse III: « MEASUREMENTS.

x direct. x reversed.

Star. Ym, or ‘%m,or |.

Taran. Seale minus Star. S_K Ties. Scale minus Star. S-K

Sehl. Kretz. Schl. Kretz.

15 56 0.3911 | 0.3919. | —0.04 | 62,63 | 0.6618 | 0.6571 | +0.25

2 | 89,90] 0.4009 | 0.3988 | + .06 29 0.6560 | 0.6566 | — .0o4

3 | 88,89] 0.2970 | 0.2958 | + .06] 30,31 | 0.2614} 0.2550) + .34 |

4 | 86,87} 0.5528 | 0.5500 | + .16 32 0.5092 | 0.5078 | + .06

6 | 73,74 | 0.3035 | 0.3024 | + .06] 45,46 | 0.2494 | 0.2486 | + .04

8 | 66,67} 0.4601 | 0.4549 | + .28 52 0.5961 | 0.5900 | + .31

Io | 65,66) 0.5760 | 0.5751 | + .06 53 0.4779 | 0.4745 | + .17

II | 64,65 | 0.7194 | 0.7164 | + .15]| 53,54 | 0.8316] 0.8298 | + .I0

14 56 0.5784 | 0.5782 | + .o1] 62,63 | 0.4718 | 0.4712 | + .04

16 55 0.4950 | 0.4929 | + .I11] 63.64 | 0.5551 | 0.5549 | + .02

7535545 O25 7/30 Ons 7 LSet eos Gls 0.4799 | 0.4765 | + .19 |

18 52 0.5315 | 0.5326 | — .05] 66,67 | 0.5189) 0.5174 | + .07

20 | 51,52] 0.6865 | 0.6869 | — .o2 67 0.3662 | 0.3678 | — .08 }

22 | 49,50] 0.7265 | 0.7282 | — .0o8]| 68,69 | 0.8251 | 0.8240 | + .05 |

23 | 48,49] 0.3615 | 0.3651 | — .19]| 70,71 0.1871 | 0.1900 | — .16

24 | 46,47 | 0.2424 | 0.2431 | — .04| 72,73 | 0.3086] 0.3092 | — .03

26 | 45,46] 0.5581 | 0.5551 | + .15 73 0.4976 | 0.4960 | + .10

28 45 | ©5479 | 0.5492 | — -07'| 73,74 | (0.5059) | 10. 50445) Sauce

29 | 44,45 | 0.4485 | 0.4481 | + .02 74 0.6046 | 0.6075 | — .15 |

45 | 17,18| 0.1620 | 0.1652 | — .18] IOI,102 | 0.3970 | 0.3919 | 4+ .28

Kretz. Hays. Ak—H Kretz. Hays. Kk—-H

15 56 0.3914 | 0.3921 | —o.04]| 62,63 | 0.6609 | 0.6606 | +0.01 |

I- | 90,91'| 0.3850 | 0.3879 ‘| — .15| 28,29 | 0.1676 | 0.1706 | — 215 |

2 | 89,90 |. 0.4021 | 0.3982 | + .19] 29,30 | 0.1490] 0.1516 | — .15 |

5 | 77,78.| 0.4799 | 0.4805 | — .03 AI 0.5679 | 0.5720 | — .21

70,71 | 0.5824 | 0.5838 | — .07 48 0.4679 | 0.4664 | + .08

23A | 47,48 | 0.3338 | 0.3400 | — .33] 71,72 | 0.2149) 0.2169 | — .12}

25 | 45,46| 0.6594 | 0.6636 | — .23 WB ©,3872)|) 0.304 lalla

27, | 45,46 | 0.2888 | 0.2896 | — .04] 73,74 | 0.2650] 0.2638 | + .07 |

31 44 0.3776 | 0.3795 | — .I0| 74,75 | 0.6784 | 0.6780 | + .03 |

22 42 0.5044 | 0.5028 | + .09] 76,77 | 0.5489} 0.5510 | — .II |

33 | 40,41 | 0.3505 | 0.3565 | — .31] 78,79 | 0.2052] 0 2025 | + .15 |}

324 | 39,40 | 0.6875 | 0.6896 | — .12 79 0.3648 | 0.3654 | — .04 |

35 | 37,30 | 0.6701 | 0.6732 | — .16 SI 0.3848 | 0.3850 | — .Or |

26 | 36,37 | 0.2011 | 0.2008 | + .or}| 82,83 | 0.3482] 0.3489 | — .o4 |

By, 36 0.5816 | 0.5810 | + .03} 82,83 | 0.4754| 0.4729 | 4+ .13 }

39 | 31,32 | 0.7004 | 0.7045 | — .22 87 0.3522 | 0.3499 | + .12 |

4o 30 0.3930 | 0.3948 | — .11] 88,89 | 0.6641 | 0.6649 | — .05 |

43 22 | 0.4799 | 0.4785 | + .07]| 96,97 | 0.5762 | 0.5755'| +=) -03 |

“Ad. -| 21,22 | 0.4258 | 0.4301 | — .24 97 0.63CI | 0.6301 00 |

A5. | 17,18) 0.1648 | 0.1620 | + .14 | I0I,102| 0.3924 | 0.3916 | + .04

TasLe ILI.—( Continued.) Puate IIL: y MeasureMENTSs.

of the Rutherfurd Photographs.

y direct. y reversed.

Star. 4m, or | ym, OY |

Tae! Seale minus Star. S_H tae | Scale minus Star. | S_H

Schl. Hays. Sehl. Hays.

15 53 0.7856 | 0.7866 | —o.06] 65 | 0.7708 | 0.7681 | +0.14

2 BOM IG3925.) |) OL QuGm | esO5s (asin || JOG26) 0.16321) —— 04

3 B50 Polse20) losers eosin os 1) On7564) | 0.7555 9) — ean

4 18 0.7200 | 0.7194 | + .03] 100 0.8375 | 0.8408 | — .17

6 67 0.9966 | 0.9959 | + .05] 51 0.5574 | 0.5572 | + .o1

8 68 0.7408 | 0.7428 | — .10]| 50 0.8144 | 0.8135 | + .05

ae) 46 0.7719 | 0.7692 | + .14] 72 0.7849 | 0.7830 | + .10

it AI 0.0348 | 0.0328 | + .11} 78 0.5232 | 0.5200 | + .16

14 74 0.7250 | 0.7204 | + .24] 44 0.8316 | 0.8282 | + .17

16 HQ Ong458 0.5422) 18 || too | G-o146) || O,orr9, |) 214

17 Bien OL0Se9in|) C163 2Ae Ie OS: Sie) TO:9212 )0:9208) |). 03

18 38 | 0.4796 | 0.4758 | + .21] 81 | 0.0778 | o.o741 | + .20

20 37 OPOOKeOLjOuTn p= "O05! | vot. 0.8534 0.8512. hare

22 69 0.4481 | 0.4520 | — .20] 50 O.100I | 0.0995 | + .04

Be 66 0.9716 | 0.9748 | — .18]| 52 0.5775 | 0.5795 | — .II

24 Ra 0.1121 | 0.1108 | + .07.4 82 OAT I OvAGO2telees wa

25 47 0.6516 | 0.6499 | + .10] 71 0.9010 0.8996 | + .08

26 24 0.6665 | 0.6665 | .00] 94 | 0.8871 | 0 8880 | — .o4

28 57 | 0.7496 | 0.7475 | -- .11| 61 | 0.8059 | 0.8040 | + .10

29 SI 0.3720 | 0.3685 | + .18] 38 0.1829 | 0.1800 | + .15

ae 16 0.5105 | 0.5121 | — .10] 103 0.0479 | 0.0425 | + .28

15 53 0.7829 | 0.7849 | —o.10] 65 | 0.7679 | 0.7654 | +0.14

I 69 0 4875 | 0.4878 | — .03] 50 0.0631 | 0.0631 .0O

5 82 0.7499 | 0.7450 | + .25] 36 0.8035 | 0.8031 | + .02

7 34 0.7538 | 0.7535 | + .02] 84 0.8054 | 0.8001 | + .29

23A| 68 | 0.5646 | 0.5611 |, + .I9] 50 | 0.9911 | 0.9874 | + .21

27 46 0.5160 | 0.5145 | + .0o8] 73 0.0391 | 0.0369 | + .12

Bit 38 0.0155 | 0.0181 | — .14] 81 0.5379 | 0.5371 | + .04

32 14 | 0.1861 | 0.1812 | + .25] 105 0.3760 | 0.3750 | + .05

33 16 0.5112 | 0.5112 .00 | 103 0.0484 | 0.0438 | + .24

34 49 0.9341 | 0.9330 | + .05] 69 0.6175 | 0.6154 | + .II

35 87 | 0.2068 | 0.2039 | + .15] 32 0.3486 | 0.3469 | + .08

36 64 | 0.6476 | 0.6454 | + ..12] 54 | 0.9068 | 0.9066 | + .02

By) 4O | 0.5184 | 0.5215 | — .16] 79 0.0340 | 0.0320 | + .I1

39 63 0.8299 | 0,8256 | + .22] 55 0.7232 | 0.7225 | + .03

4o 18 0.8654 | 0.8618 | + .20] Io0 0.6912 | 0.6911 | + .o1

43 60 0.7026 | 0.7032 | — .03} 58 0.8524 | 0.8500 | + .13

44 80 | 0.1296 | 0.1265 | + .17] 39 0.4255 | 0.4234 | + .12

45 29 | 0.2606 | 0.2582 | + .13] 90 | 0.2991 | 0.2939 | + .28

ANNALS N. Y. ACAD. Scr., X., June, 1898—14.

206

TasBLe III].—(Continued.) Puate IV: » MEASUREMENTS.

Presepe Group; Measurement and Reduction

x direct. x reversed.

Star. % m, or 4% m, OF

Tavis Seale minus Star. SK nee Scale minus Star. S-K

Schl. Kretz. Sehl. Kretz.

15 | 58,59} 0.1086 | 0.1090 | —o.02] 60,61 | 0.4401 | 0.4376 +0.13

15. | 58,59| 0.1098 | 0.1102 | — .02]| 60,61 | 0.4404 | 0.4382 | 4+ .12

2 | 91,92] 0.6132 | 0.6136 | — .02] 27 0.4422 | 0.4411 | + .06

By 1,90, Olu) O:s4950: | 0.4922 9). a0 0.5600 | 0.5594 | + .04

4 | 88,89} 0.7311 | 0.7309 | + .o1 | 29,30 | 0.8258 | 0.8249 | -- .05

6 E7510) 005379) 80253550 ae Les 05160 | 05156 | + .02

8 | 68,69] 0.7006 | 0.6994 | + 06] 50 0.3525 | 0.3500 | + .13

Io | 67,68 | 0.7929 | 0.7919 | + .06] 50,51 0.7615 | 0.7609 | + .03

II 67 | 0.4274 | 0.4251 | + .12|51,52 | 0.6255 | 0.6258 | — <2

TA | 58,59 | 0.3225 | 0.3204 | + .II-] 60,61 0.2276 | 0.2272 | + .02

16 | 57,58 | 0.1772 | 0.1769 | + .02| 61,62 | 0.3724 | 0 3735 | — .06

£7 55,50) On7785 | 0.7760 | 4- .13,| 62,62 || 0.7741 | 0.77600 og

18 | 54.55 | 0.2394 | 0.2390 | + .02 | 64,65 0.3106 | 0.3105 | + .or

20 54 | 0.3919 | 0.3916 | + .02] 64,65 | 0.6571 | 0.6581 | — .05

22 52 0.4664 | 0.4679 | — .08 | 66,67 0.5841 | 0.5841 .0O

23 | 50,51 |. 0.5970 | 0.5962 | + .o4] 68 0.4560 | 0.4542 | + .10

24 | 48,49) 0.4505 | 0.4506 | — .o1] 70 0.6004 | 0.6036 | — .17

25 48 | 0.3772 | 0.3728 | + .23| 70,71 | 0.6758 | 0.6746 | + .06

26 | 47,48 | 0.7520 | 0.7505 + .07 | 70,71 0.8045 | 0.8032 | + .08

27, | Ag Asn G: 5050) On50040g lcm ORal an gl 0.5465 | 0.5438 | + .15

28 || 47,48.| 0:2779 | 0.2762) -- {08 | 71,72 | 0:2745) | 0.2 7Aon eas

2946, 47) 0.7020)11) 0/7 O90, Wis Ti5a|) 72 0.3510 | 0.3495 | + .08

45 | 19,20] 0.3636 | 0.3658 | — .121| 99,100] 0.1926 | 0.1918 | + .04

15 58 0.6106 | 0.6114 | —0.03 | 60,61 0.4404 | 0.4411 | —0.03

15 58 0.6108 | 0.6094 | + .06]| 60,61 | 0.4415 | 0.4379 | + .19

I | 92,93 | 0.6165 | 0.6235 | — .37]| 26 0.4415 | 0.4395 | + .10

2 | 91,92] 0.6136 | 0.6129 | + .04; 27 0.4419 | 0.4405 | + .07

5 | 79,80} 0.7375 | 0.7375 .00 | 38,39 | 0.8199 | 0.8202 | — .o1

7 |72,73 | 0.7816 || 0.7840 | — .12| 45,46 || 0.7742) oO. 7724s aoe

7A | 68,69 | 0.6918 | 0.6942 | — .13] 50 0.3619 | 0.3602 | + .09

Ig | 54,55 | 0.2284 | 0.2284 .00 | 64,65 0.3215 | 0.3205 | + .05

23A | 49,50 | 0.5751 | 0.5765 | — .o7] 69 0.4772 | 0.4790 | — .10

aI 46 | 0.5839 | 0.5828 | + .05| 72,73 | 0.4711 | 0.4691 | == <1E

32 | 44,45 | 0.1821 | 0.1831 | — .05| 74,75 | 0.3680 | 0.3692 | — .06

33 | 42,43) 0.5291 | 0.5280 | + .05| 76 0.5155 | 0.5175 | — .II

34 42 0.4086 | 0.4081 | + .03 | 76,77 0.6442 | 0.6416 | + .14

35 4o 0.4341 | 0.4365 | — .13| 78,79 | 0.6210 | 0.6191 | + .10

36 | 38,39 | 0.4386 | 0.4406 | — .11} 80 0.6144 | 0.6154 | — .06

37 | 38,39 | 0.2875 | 0.2868 | + .04]} 80,81 | 0.2640 | 0.2649 | — .05

38 | 34,35 | 0.6826 | 0.6850 | — .12] 84 0.3724 | 0.3726 | — .02

39 24 0.4401 | 0.4415 | — .07 | 84,85 0.6141 | 0.6149 | — .04

40 32 0.5829 | 0.5836 | — .03] 86,87 | 0.4729 | 0.4742 | — .07

43 | 24,25 0.2176 | 0.2154 | + .12] 94,95 0.3385 | 9.3400 | — .08

44 | 23,24 | 0.6931 | 0.6961 | — .15] 95 0.3649 | 0.3628 | + .12

45 || 19,20] 0.3628 | 0.3605 | + .12]| 99,100] 0.1922 | 0.1905 | + .09

of the Rutherfurd Photographs. 207

TaBLE III.—( Continued.) Piate IV: y MEASUREMENTS.

y direct. y reversed.

Star. % mM, or 4m, or

Tine. Seale BU Star. Bie | Tine. Seale minus Star. S_K.

Schl. Kretz. Schl. | Kretz.

No)

fey

15 54 | 0.3544 | 0.3561

15 54 | 9.3545 | 0.3578

2 50 | 0.9360 | 0.9344 |

3 36 | 0.3470 | 0.3464 |

4 19 0.2672 | 0.2691

6 68 0.5526 | 0.5525

8 69 | 02996 | 0.3001

10 47 | 0.3356 | 0.3349

II AI 0.5992 | 0.5962

14 75 0.2926 | 0.2945

16 20 | 0.1172 | 0.1185

7 38 | 0.2076 | 0.2078

18 39 | 0.0536 | 0.0534

20 38 0.2798 | 0.2785

22 70 0.0256 | 0.0255

23 67 0.5522 | 0.5525

24 37 | 0.6928 | 0.6925

25 48 0.2345 | 0.2330

26 25 0.2515 | 0.2508

28 58 | 0.3315 | 0.3305

29 | 8I | 0.9495 | 0.9505

33 I7 | 0.1019 | 0.0998

0.1952 | 0.1934 | -++0.10

.17| 65 0.1926 | 0.1939 | — .0O7

.07}| 68 0.6195 | 0.6199 | —

.03| 83 0.2059 | 0.2051 | +

.10 | 100 | 0.2875 | 0.2898 | —

-OI1| 50 0.9996 | I.001I5 | —

.03 | 50 0.2510 | 0.2481 | +

.03 | 72 0.2148 | 0.2164 | —

16] 77 0.9564 | 0.9561 | +

.I0| 44 0.2558 | 0.2565 | — .

.07 | 99 0.4378 | 0.4361 | + .

+) t+++] +++] ) 1 +4141 441

or | 81 0.3446 | 0.3442

.or! 80 | 0.4979 | 0.4991

0.2716 | 0.2736

OL] 49 0.5252 | 0.5246

.02| 52 |—.0032 | 0.0002

.02} 81 0.8572 | 0.8588

.08 | 71 0.3155 | 0.3162

04} 94 | 0.3014 | 0.3042

.05| 61 0.2180 | 0.2182

06] 37 0.6024 | 0.6021

-II| I02 | 0.4535 | 0.4555

15 54 | 0.3538 | 0.3568 | —o.15| 65 O.195I | 0.1922 | +0.15

15 54 | 0.3562 | 0.3579 | — .0o8] 65 0.1929 | 0.1904 | + .

ir 70 | 0.0282 | 0.0304 | — .12| 49 | 0.5239 | 0.5224 | + .

5 83 | 0.2979 | 0.2979 00} 36 | 0.2529 | 0.2540 | —.

a] 35 0.3186 | 0.3182 | + .02] 84 0.2356 , 0.2362 | — .

7A) 50 0.5930 | 0.5936 | — .03}] 68 0.9646 | 0.9656 | — .

19 80 | 0.2471 | 0.2455 | + .08| 39 | 0.3060 | 0.3088 | — .

23A| 69 | 0.1386 | 0.1401 | — .08] 50 | 0.4115 | 0.4120 | —.

27 47 0.0961 | 0.0966 | — .03| 72 0.4552 | 0.4564 | — .

31 38 | 0.5966 | 0.5961 | + .02] 80 | 0.9584 | 0.9589 | — .

32 14 0.7720 | 0.7728 | — .o4]| Io4 0.7861 | 0.7886 | — .

33 17 0.1015 | 0.1024 .05 | 102 0.4555 | 0.4562 | — .

34 50 0.5242 | 0.5254 .06| 69 0.0256 | 0.0276 | — .

35 87 0.7922 | 0.7922 00} 31 0.7645 | 0.7664 | — .

36 65 0.2356 | 0.2331

37 4l | O.1IIT | O.11I5

+ .13] 54 | 0.3152 | 0.3154 | — .

— .02| 78 0.4406 | 0.4410 | — .

38 58 0.1198 | 0.1186 | + .06| 61 0.4311 | 0.4320 | — .

39 64 0.4198 | 0.4202 | — .02| 55 0.1292 | 0.1296 | — .

40 19 0.4612 | 0.4622 | — .05] I00 0.0895 | 0.0895 :

43 61 0.2991 | 0.3002 | — .06| 58 0.2488 | 0.2490 | — .

44 80 | 0.7300 | 0.7276 | + .13| 38 0.8281 | 0.8304 | — .

45 29 0.8686 | 0.8679 | + .03| 89 0.6874 | 0.6874

208

Table III.—( Continued.) Puate V: «x MEASUREMENTS.

Presepe Group; Measurement and Reduction

x direct. a reversed.

Star. % Mm. or 4% mM, Or

Times: Scale minus Star. S_-K Tinee ot Seale minus Star. S-K

Sehl. Kretz. | | Schl. Kretz.

I5 | 55,50 | 0.2626 | 0.2598 | +0.15] 63,64 | 0.3082] 0.3041 | +0.22

I5 | 55,50 | 0.2629 | 0.2598 | + .16] 63,64 | 0.3078| 0.3055 | + .12

2 | 88,89] 0.7681 |. 0.7676 | + .03]° 29,30 | 0.8032 | 0.8034 | + .or

3 | 87,88 | 0.6692 | 0.6708 | — .o8} 30,31 | 0.9018 | 0.9005 | + .06

4 | 85,86} 0.9279 | 0.9281 | — .02] 32,33 | 0.6450) 0.6451 | — .Or

6 | 72,73 | 0.6664 | 0.6684 | — .II] 45,46 | 0.8999] 0.9011 | — .07

8 | 65,66] 0.8274 | 0.8279 | — .03] 52,53 | 0.7400 | 0.7415 | — .08

IO | 64,66) 0.4472 | 0.4454 | + .10] 53,54 | 0.6195 | 0.6194 | + .Or

II | 64,65 | 0.0944 | 0.092r | + .12] 54,55 | 0.4770} 0.4764 | + .03

74 | 55,560) 0.4405 | 0.4400 | + .03| 63,64 | 0.1269] 0.1251 | + .10

16 | 54,55 | 0.3751 | 0.3738 | + .07] 64,65 | 0.1938] 0.1938 .0O

17 | 52,54 0.4486 | 0.4476 | + .05]| 65,66 | 0.6221 | 0.6204 | + .09

18 | 51,52) 0.4046 | 0.4030 | + .08| 67,68 | 0.1645) 0.1631 | + .07

20 | 51,52/| 0.0611 | 0.0592 | + .10}] 67,68 | 0.5110] 0.5089 | + .II

22. | 49,50 | 0.0939 | 0.0929 | + .05} 69,70 | 0.4755 | 0.4735 | + -II

23 | 47,48 | 0.7248 | 0.7234 | + .07] 70,71 | 0.8448] 0.8422 | + .14

24 | 45,46) 0.6199 | 0.6192 | + .04! 72,74 | 0.4516) 0.4486 | + .17

25 | 45,46] 0.0336 | 0.0326 | + .05] 73,74 | 0.5389 | 0.5368 | + .11

26 | 44,46| 0.4384 | 0.4380 | + .02]| 73,74 | 0.6342) 0.6314 | + .15

27 | 44,45 | 0.6610 | 0.6584 | + .14] 73,74 | 0.9105 | 0.9106 -00

28 | 44,45] 0.4170 | 0.4146 | + .13] 74,75 | 0.1540] 0.1514 | ++ .14

29 | 43,44| 0.8122 | 0.8128 | — .03] 74,75 | 0.7590] 9.7554 | + -19

45 | 16,17! 0.5412 | 0.5450 | — .20] 102,103 | 0.0298 | 0.0298 .0O

“i Md

I5 | 55,50) 0.2614 | 0.2596 | +0.10] 63,64 | 0.3075 | 0.3050 | +0.13

15 | 55,50 | 0.2590 | 0.2598 | — .0o4] 63,64 | 0.3069 | 0.3049 | + .II

I | 89,90} 0.7531 | 0.7504 | + .14] 28,29 | 0.8219] 0.8161 | + .31

2 | 88,89 | 0.7692 | 0.7650 | + .22] 29,30 | 0.8012| 0.8020 | — .05

5 | 76,77 | 0.8410 | 0.8396 | + .08; 41,42 | 0.7296) 0.7272 | + .13

7 | 69,71 | 0.4560 | 0.4555 | + .02] 48,49 | 0.6126} 0.6108 | + .10

I9 | 51,52] 0.3436 | 0.3415 | + .11] 67,68 | 0.2275 0.2262 | + .07

23A | 46,47 | 0.7032 | 0.7029 | + .02] 71,72 | 0.8665 | 0.8656 | + .04

31 | 43,44 | 0.2522 | 0.2494 | + -15]| 75,76 | 0.3184 | 0.3155 | 4 -15

32 | 41,42] 0.3892 | 0.3901 | — .05] 77,78 | 0.1858 | 0.1832 | + .14

34 | 39,40 | 0.0630 | 0.0658 | — .15]| 79,80 | 0.5071 | 0,5039 | + .17

35 | 37,38 | 0.0308. | 0.0279 | + .15] 81,82 | 0.5371 | 0.5326 | + .24

37 | 35,36] 0.4526 | 0.4510 | + .o8| 83,84 | 0.1158] 0.1126 | 4- .17

39 | 31,32 | 0.0745 | 0.0725 | + .11 | . 87,88 | 0.4980 | 0.4962 | =- .10

4o | 29,30, 0.2818 | 0.2772 | + .24] 89,90 | 0.2950] 0.2902 | = .25

43, | 21,22 | 0.3564 | 0.3550 | + .07] 97,98 | 0.2196| 0.2159 | + .20

44 | 20,21 | 0.7966 | 0.7962 | + .02] 97,98 | 0.7794 | 0.7735 | + -31

45 | 16,17] 0.5421 | 0.5444 | — .12 | 102,103 | 0.0304 |. 0.0251 | + .28

TasBLe III].—( Continued.) Puate V: y MEASUREMENTS.

of the Rutherfurd Photographs.

209

y direct. y reversed.

Star. tm, or ym, OY

Tine Seale mixus Star. SK Tine. Seale minus Star. S-K

Sehl. Kretz. Sehl. Kretz.

15 54 0.7016 | 0.7006 | +0.05] 64 | 0.8646 | 0.8650 | —o.02

15 54 0.6999 | 0.70c8 | — .05]| 64 0.8626 | 0.8652 | — .14

2 51 0.3171 | 0.3152 | + .10] 68 0.2526 | 0.2556 | — .16

2 36 0.7258 | 0.7270 | — .06| 82 0.8448 | 0.8426 | + .II

4 19 0.6431 | 0.6422 | + .05] s9 0.9318 | 0.9300 | + .08

6 68 0.9181 | 0.9175 | + .02] 50 | 0.6506 | 0.6496 | + .05

8 69 0.6558 | 0.6568 | — .05| 49 | 0.9089 | 0.9072 | + .I0

ago) 47 | 0.6930 | 0.6931 | — .or] 7I | 0.8759 | 0.8748 | + .06

II AI 0.9518 | 0.9546 | — .13| 77 0.6155 | 0.6144 | + .06

14 75 0.6389 | 0.6386 | + .02] 43 0.9291 | 0.9300 | — .04

16 20 | 0.4612 | 0.4616 | — .02| 99 | 0.1106 | 0.1068 | + .20

17 38 0.5500 | 0.5489 | + .06} 81 0.0182 | 00166 | + .08

18 39 OLS) |) CheOWS || == OB || CO | Owls 3 | @aigy |) == soo)

20 38 0.6178 | 0.6168 | + .05] 80 | 0.9494 | 0.9476 | + .08

22 70 0.3664 | 0.3648 | + .08] 49 | 0.2002 | 0.2016 | — .07

23 67 0.8894 | 0.8892 | + .02] 51 0.6755 | 0.6768 | — .07

24 38 0.0304 | 0.0291 | + .07| 81 | 0.5392 | 0.5402 | — .05

25 48 0.5638 | 0.5661 | — .12| 71 |—.0008 |—.0005 | — .0o2

26 25 0.5840 | 0.5829 | +:.06] 94 |—.0120 |—.o119 | — .OI

27 47 | 0.4309 | 0.4318 | — .o1| 72 0.1349 | 0.1350 | — .OI

28 58 | 0.6628 | 0.6626 | + .o1} 60 | 0.9031 | 0.9042 | — .05

29 82 0.2832 | 0.2811 | + .11| 37 0.2871 | 0.2846 | + .13

15 54 0.7029 | 0.7028 | +0.01| 64 0.8622 | 0.8644 | —o.13

15 54 0.7035 | 0.70IT | + .13]| 64 0.8644 | 0.8636 | + .03

I 70 0.4172 | 0.4164 | + .04] 49 0.1516 | 0.1570 | — .29

5 83 | 0.6724 | 0.6675 | + .26] 35 0.8962 | 0.8986 | — .12

7 25 0.6772 | 0:6771 | + .or| 83 0.8942 | 0.8971 | — .14

19 80 0.5896 | 0.5870 | + .14] 39 |—.0152 |—.o150 | — .OL

23A | 69 0.4802 | 0.4760 | + .22]}] 50 0.0929 | 0.0920 | + .05

31 38 0.9318 | 0.9305 | + .08} 80 | 0.6404 | 0.6350 | + .29

32 15 0.1042 | 0.1020 | + .12] 104 | 0.4722 | 0.4699 | + .12

34 50 | 0.8502 | 0.8475 | + .15| 68 ./| 0.7165 | 0.7156 | + .05

35 88 Oeneyl || Owes | Se eB |) Bie 0.4542 | 0.4576 | — .18

37 AI 0.4381 | 0.4368 | + .07| 78 0.1349 | 0.1339 | + .c5

39 64 | 0.7380 | 0.7364 | + .08] 54 0.8279 | 0.8278 | + .oI

4o 19 | 0.7798 | 0.7792 | + .03] 99 | 0.7938 | 0.7948 | — .06

43 6I | 0.6096 | 0.6090 | + .03}] 57 | 0.9594 | 0.9584 | + .04

44 81 0.0361 | 0.0339 | + .12] 38 0.5328 | 0.5342 | — .07

45 30 0.1700 | 0.1699 | + .o1} 89 0.3978 | 0.4001 | — .13

210

Presepe Group; Measurement and Reduction

TaBie III.—(Continued.) Puiate VII: « MEAsuREMENTS.

x direct. x reversed.

Star. ___, 2M, OF 4% M, or

Tings: Seale minus Star. Ro \aanee| Seale minus Star. S—H

Schl. Hays. Schl. Hays.

I5 | 61,62 | 0.6390 | 0.6438 | —0.25 | 56,58 | 0.4129 | 0.4134 | —0.03

2 | 95,96] 0.1465 | 0.1489 | — .13 | 23,24 | 0.4122 | 0.4078 | + .23

3 | 93,95 | 9.5530 | 0.5496 | + -17| 24,25 | 0.5062 | 0.5049 | + .07

4 | 92,93 | 0.3122 | 0.3115 | + .04 | 26,27 | 0.2438 | 0.2468 | — .16

6 | 78,50} 0.5484 | 0.5484 .00 | 39,40 | 0.5079 | 0.5094 | — .08

8 | 7273] 0.2074 | 0.2076 | — .oI | 46,47 | 0.3484 | 0.3449 | + .18

IO | 71,72 | 0.32906 | 0.3339 | — .23] 47,48 | 0.2242 | 0.2252 | — .05

II | 70,71 | 0.4775 | 0.4796 | — .I1} 47,49 | 0.5779 | 0.5730 | += -25

I4 | 61,62) 0.8200 | 0.8219 | — .10| 56,57 | 0.7348 | 0.7306 | + .22

16 | 60,61 | 0.7609 | 0.7619 | — .05 | 57,58} 0.7938 | 0.7931 | + .03

17 | 59,60} 0.3314 | 0.3268 | + .24]| 59,60} 0.2208 | 0.2222 | — .07

18 | 57,58 | 0.7879 | 0.7915 | — .20| 60,61 | 0.7640 | 0.7655 | — .O7

20 | 57,58| 0.4450 | 0.4424 | + .14| 60,62 | 0.6079 | 0.6100 | — .10

22 |/55,50)| 0.4754 | 0.4781 | — -14 | 62,04 | 05755 | O:5 7420 toned

23 | 54,55 | 0.1081 | 0.1092 | — .06 | 64,65 | 0.4446 | 0.4468 | — .II

24 | 51,53 | 0.5110 | 0.5112 | — .O1 | 66,67 | 0.5442 | 0.5444 | — .OL

25 | 51,52 | 0.4162 | 0.4139 | + .12| 67,68 | 01366 | 0.1356 | + .05

26 | 51,52] 0.3231 | 0.3251 | — .10] 67,68 | 0.2321 | 0.2316 | + .03

27 | 50,52 | 0.5444 | 0.5456 | — .06| 67,68 | 0.5095 | 0.5095 .0O

28 | 50,51 | 0.8028 | 0.8031 | — .or | 67,68 | 0.7540 | 0.7515 | + .13

29 | 50,5: | 0.1946 | 0.1925 | + .I1I | 68,69 | 0.3584 | 0.3595 | — .06

31 | 49,50 | 0.6379 | 0.6386 | — .04 | 68,70 | 0.4170 | 0.4178 | — .04

32 | 47,48 | 0.7781 | 0.7770 | + .06] 70,71 | 0.7778 | 0.7756 | + .11

23 | 46,47 | 0.1226 | 0.1226 .00 | 72,73 | 0.4316 | 0.4350 | — .18

45 | 22,24) 0.4344 | 0.4370 -13 | 95,96 | 0.6214 | 0.6179 | + .19

Schl. Kretz S—ir Schl. Kretz. S—k

15 | 61,62 | 0.6420 | 0.6444 | —o.12 56,58 | 0.4105 | 0.4090 | +0.08

I | 96,97 | 0.1244 | 0.1286 | — .22| 22,23 | 0.4282 | 0.4268 | 4- .07

2 | 95,96| 0.1474 | 0.1480 | — .03 | 23,24 | 0.4101 | 0.4068 | + .17

5 | 83,84) 0.2168 | 0.2158 | + .05 | 35,36] 0.3389 | 0.3389 .00

7 | 76,77 | 0.3461 | 0.3411 | + .26 |"42,43 | 0.2086 | 0.2081 | + .03

7A | 72.73 | 0.2332 | 0.2351 | — .10 | 46,47 | 0.3231 | 0.3216 | + .08

19 | 57.58 | 0.7251 | 0.7224 | + .14| 60,61 | 9.8312 | 0.8338 | — .14 |

21 | 56,58) 0.4262 | 0.4250 | + .06| 61,62} 0.6336 | 0.6280 | + .30

23A | 52,54| 05909 | 0.5854 | + .28] 65,66 0.4660 | 0.4674 | — .07

34 | 45,46 | 0.4486 | 0.4469 | + .09| 73,74 | 0.1078 | 0.1046 | + .17

35 | 43,44| 0.4162 | 0.4164 | — .o1 | 75,76| 0.1359 | 0.1390 | — .16

36 | 41,43 | 0.4652 | 0.4626 | + .14| 76,77 | 0.5950 | 0.5931 | + .10

37 | 41,42 | 0.8426 | 0.8446 | — .12| 76,77| 0.7156 | 0.7064 | + .49

38 | 38,39 | 0.2091 | 0.2134 | — .23 | 80,81 | 0.3486 | 0.3459 | + .14

39 | 37,38 | 0.4620 | 0.4608 | + .06] 80,82 | 0.5946 | 0.5924 | + .12

40 | 35,36| 0.6735 | 0.6731 | + .02] 82,84 | 0.3860 | 0.3824 | + .19

AI | 31,32] 0.6124 | 0.6054 | + .37 | 86,88 | 0.4504 | 0.4526 | — .12

42 | 29,30| 0.6276 | 0.6230 | + .24| 88,90 | 0.4315 | 0.4300 | + .07

43 | 27,28 | 0.7438 | 0.7431 | + .04] 90,91 | 0.8136 | 0.8128 | + .03

44 | 27,28 | 0.1826 | 0:1789 | == .20)| 91,92)| 0.374) | O37A ial me eee

45 | 22,24| 0.4362 | 0.4340 | + .I1 | 95,96| 0.6239 | 0.6222 | + .09

of the Rutherfurd Photographs. 20

TasLe III.—(Continued.) Puate VII: y MEASUREMENTS.

y direct. y reversed.

Star. ye, Os +4 M, OF

Ties Seale minus Star. lo pare Timets| Scale minus Star. SK

Sehl. Kretz. Sehl. | Kretz.

15 62 0.0196 | 0.0186 +0.05 57 0.5301 | 0.5302 —o,01

2 58 | 0.6448 | 0.6446 | + .o1| 60 | 0.9095 | 0.9045 28

B AA 0.0536 | 0.0534 OL] 75 0.4972 | 0.4942 | + .16

4 26 | 0.9754 | 0.9744 SOTO One| O-50741 |, tn Le

6 76 0.2415 | 0.2414 Or | 43 | o.31r4 | 0.3072 | => .22

8 76 | 0.9804 | 0.9799 (2 || Ae) Gis7ew I Cugete aS os

—+-

“10 55 0.0164 | 0.0149 | + .08} 64 0.5348 | 0.5346 |

II 49 0.2788 | 0.2782 | + .03] 7o 0.2735 | 0.2714 |

14 $2 0.9624 | 0.9610 | + .06| 36 0.5922 | 0.5928

aia

(oS)

16 27 0.7882 | 0.7840 .23| Q1 | 0.7689 | 0.7664

17 45 |-0.8736 | 0.8712 IAN 73a a ORO 7SS) O10 794.

18 46 | 0.7182 | 0.7169 O74) 9 72") Of8305.) 0.8336

20 45 0.9394 | 0.9379 MO} 7B |) OL | Lig)

22 Ta 0.6870 | 0.6864 0% || Ali 0.8685 | 0.8691

23 75 0.2095 | 0.2090 .03 | 44 0.3416 | 0.3448

24 45 0.3472 | 0.3462 | .05}| 74 | 0.2028 | 0.2011 |

25 55 0.8854 | 0.8852 OF |) 68 0.6631 | 0.6628 |

26 32 0.9052 | 0.9058 .02}| 86 | 0.6512 | 0.6496

0.7488 | 0.7494 .03 | 64 0.8004 | 0.7996

28 65 0.9808 | 0.9806 OI1| 53 0.5726 | 0.5720 |

29 89 0.6049 | 0.6022 -14] 29 | 0.9515 | 0.9535 |

pues eas

LS)

iS)

44+] | Ett+] | | $44] 4+

ee res

Ne)

31 46 O,2505 | O.25u5, | —= OF} 7/2 0.3002 | 0.3026 | 53

22 22 0.4230 | 0.4215 | + .08] 97 0.1355 | 0.1334 II

Be 24 0.7514 | 0.7492 | + .I11] 94 0.8048 | 0.8038 .05

Kretz. Hays. A—H Kretz. | Hays. Kk— AH

a a/

15 62 OOUCA || CKO | OLB) yy || Obiygits) 0.5329 | —0.06]

I 77 0.7418 | 0.7462 | — .231 4tr | 0.8111 | 0.8120 | — .o4

5 go | 0.9979 | 0.9966 | + .c8} 28 | 0.5592 | 0.5605 | — .06

7 43 |—.0005 |—.0001 | — .0o2! 76 | 0.5508 | OL5 G21 |= 06 |

7A | 58 | 0.2669 | 0.2690 | — .11] 61 | 0.2860 | 0.2868 | — .o4}

19 87 0.9085 | 0.9064 | + .10] 31 0.6464 | 0.6486 | — .12}

21 86 0.3856 | 0.3829 | + .14]| 33 0.1770 | 0.1775 | — .O2 |

23A | 76 0.7939 | 0.7956 | — .o8| 42 | 0.7582 | 0.7600 | — .10f

BR 24 0.7534 | 0.7530 | + .02) 94 | 0.8038 | 0.8059 | — .12

34 58 0.1652 | 0.1675 | — .12] 61 0.3841 | 0.3861 | — .I1

35 95 | 0.4320 | 0.4320 00 | 24 | 0.1251 | 0.1244 | + .04

36 72 0.8776 | 0.8750 | + .I4] 46 0.6749 | 0.6749 .00

37 48 0.7515 | 0.7538 | — .12] 7o 0.8013 | 0.8045 7,

38 65 0.7550 | 0.7541 | + .05] 53 0.8013 | 0.8026 | .O7

39 72 0.0530 | 0.0519 | + .06|] 47 0.5000 | 0.5019 10

40 Dy 0.0934 | 0.0952 | — .IO| 92 0.4606 | 0.4615 .05 |

Al 54 0.4615 | 0.4634 10] 65 0.0992 | 00882 | + .II

42 54 0.3646 | 0.3646 .00| 65 0.1885 | 0.1909 ate

43 68 | 0.9215 | 0.9211 | + .or} 50 | 0.6322 | 0.6345 2

44 88 0.3458 | 0.3438 | + .10] 31 0.2065 | 0.2076 | — .06

45 Qa 0.4842 | 0.4869 .14} 82 0.0679 | 0.0672 | + .04

212 Presepe Group; Measurement and Reduction

TABLE ILI.—( Continued.) Puatse VIII: « MEASUREMENTS.

x direct. : x reversed.

Star. fo A 0, Ox | Ym, or

Wartnnsct Scale minus Star. | Soe tines | Scale minus Star. S_K

Schl. Kretz. | | Schl. Kretz.

15 | 60,64] 0.2674 | 0.2648 | +0.12] 58.59 | 0.2850 | 0.2819 +0.16

15 | | 58,59 | 0.2851 | 0.2828 | + .12

2 | 93.94] 0.7701 | 0.7728 | — .14| 24,25 | 0.7856 | 0.7825 | + .17

3 | 92.93 | 0.6742 | 0.6731 | + .06] 25,27 | 0.3849 | 0.3842 | + .04

4 | 90,92] 0.4280 | 0.4276 | + .02] 27,28| 0.6299 | 0.6285 | + .07

6 | 77,78| 0.6768 | 0.6800 | — .17| 40,42 | 0.3745 | 03741 | -— .02

8 | 70,72.| 0.3415 | 0.3375 | + .21| 47,48 | 0.7154. | 0.7150 | + .02

Io 66971 0.4545 0.4509 | + .19] 48,49 0.6002 | 0.5968 | + .18

II | 68,70 | 0.6009 | 0.6011 | — .OL| 4950} 0.4522 | 0.4505 | + .09

14 | 6061} 0.4509 | 0.4502 | + .04 57.59 | 0.5990 | 0.5988 | + .o2

18 | 56,57| 0.4119 | o.409f | + .15 | 62,63 | 0.1374 | 0.1385 | — .o6

20 | 55,57 | 0.5689 | 0.5650 | + .21 | 62,63 | 0.4841 | 0.4874 | — .18

22 | 53.55 | 0.6064 | 0.6061 | + .o1 | 64,65 | 0.4450 | 0.4465 | — .08

23 | 52 53 | 0.7400 | 0.7380 | + .I1 | 65,66| 0.8161 | 0.8162 .00

24 | 50.51 | 0.6309 | 0.6234 | + .40] 67,69} 0.4269 | 0.4252 | —= Jc9

25 | 49.51 | 0.5430 | 0.5401 | + .15 | 68,69} 0.5071 | 0.5089 | — .I0

26 | 49 51 | 0.4416 | 0.4394 | + .12] 68,69) 0.6129 | 06110 | + .10

27 | 4950] 0.6729 | 0.6702 | + .14| 68,70| 03799 | 0.3794 | + .03

28 | 4950| 0.4262 | 04281 | — .10} 68,70| 0.6234 | 0.6234 .0O

29 | 48.49 | 0.8270 | 0.8258 | + .07| 69,70] 0.7252 | 0.7242 | + .05

3I | 48,49 | 0.2589 | 0.2556 | + .17 | 70.71 | 0.2974 | 0.2940 | + .18 |

A5e 21522), O55658) 1015545) || -- -07190 98 | 0.5000 | 0.4980 | + .I0

| Schl. Hays. \—H | Schl. Hays. S—H

15 | 60,61 0.2681 | 0.2700 | —o.10] 58.59 | 0.2839 | 0.2840 —o.01

15 60,61 | 0.2664 | 0.2661 | + .02] 58,59 | 0.2852 | 0.2856 | — .o2

[ | 94.95 | 0.7576 | 9.7529 | + .24 | 23,24 | 0.8044 | 0.7984 | + .32

2 | 93,9}| 0.7709 | 0.7736 | — .14] 24.25 0.7872 | 0.7855 | + .08

5 | 81,828 0.8511) "0.8485. | —--.13)| 36,37 | 0/7059) | 10: 7065 ear

7 | 74,76 | 0.4639 | 0.4646 | — .03 | 43.44 | 0.5938 | 0.5896 | + .22

7A | 70.72 | 0.3661 | 0.3594 | + .35| 47,48 | 0.6921 | 0.6902 | + .10

IQ | 56.57 | 0.3584 | 9.3575 | + .05 | 62 63 0.1961 | 0.1901 | -+ .31

23A 51,52| 0.7200 | 0.7181 | + .10] 66,67) 0.8364 | 0.8356 | + .05

32 | 46,47 | 0.3970. | 0.3920 | + .26] 72,73 | 0.1592 | 0.1631 | — .2r

33. | 44,45 | 0.7401 | 0.7400 | + .or| 73,74 0.8152 | 0.8174 | — .II

34 | 43,45 | 0:5712 | 0.5742 | — .17| 74,75 | 0.4800 |: 0.4814 | — 07

35 | 41,43 | 9.5529 | 0.5520 + .0417677| 9.5016 | 0.5000 | + .08

36 | 40,41 | 0.5946 | 0.5938 | + .04] 77,79 | 0.4630 | 0.4615 | + .08

37 | 40:41 | 0.4676 | 0.4679 | — .02 | 77,79 | 0.5885 | 0.5921 | — .19

38 | 36,37 | 0.8402 | 0.8384 | + .08! 81,82 0.7172 | 0.7172 .0O

39 | 35.37 | 0.5885 | 0.5916 | — .17]| 82.83 | 0.4624 | 0.4592 | + .17

40 | 34,35) 0.2886 | 0.2882 | + .02] 84,85 | 0.2649 | 0.2655 | — .03

41 | 30,31 | 0.2381 | 0.2302 | + .42| 88,89 | 0.3200 | 0.3199 | + .or

42 | 28,29 | 0.2592 | 0.2594 | — .o1 | 90,91 | 0.3016 | 0.2991 | + .13

43 | 26,27| 0.3708 | 0.3731 | — .12| 82,93 0.1818 | 0.1814 | + .02

44 | 25,26! 0.8192 | 0.8188 | + .03 | 92,93 | 0.7378 | 0.7345 | + .17

45 | 21,22| 0.5601 | 0.5591 | + .05 | 96,98 | 0.5009 | 0.4981 | + .14

of the Rutherfurd Photographs.

213

TasLe III.—( Continued.) Puare VIII: y MeasuREMENTS.

y direct. y reversed.

Star. 4% Mm, OF 4m, or

Tate. Seale minus Star. FE || ane Scale minus Star. K-H

Kretz. Hays. Kretz. Hays.

15 55 0.0068 | 0.0070 | —o.o1] 64 0.5411 | 0.5416 | —0.03

I5 64 | 0542t | 0.5425 | — .o2

2 51 0.6239 | 0.6241 | — .o1] 67 | 0.9258 | 0.9290 | — .I9

3 37 | 0.0348 .| 0.0326 | + .12]| 82 0.5169 | 0.5194 | — .13

4 Ig | 0.9572 | 0.9590 | — .08| 99 | 0.5984 | 0.6002 | — .10

6 69 012228) 40122008 ete iSy eno 0.3288 | 0.3249 | + .2I1

8 69 0.9606 | 0.9614 | — .03} 49 0.5875 | 0.5898 | — .12

ae) 48 |—.0029 | 0.0000 | — .I5] 71 | 0.5505 | 0.5512 | — .o4

init 42 0.2579 | 0.2596 | — .0g} 77 0.2900 | 0.2915 | — .08

14 75 0.9466 | 0.9432 | + .16] 43 0.6034 | 0.6072 | — .20

16 20 | 0.7739 | 0.7724 | + .07] 98 0.7801 | 0.7820 | — .II

17 38 | 0.85909 | 08614 | — .07| 80 | 0.6928 | 0.6949 | — .II

18 39 0.7045 | 0.7068 | — .12] 79 0.8506 | 0.8478 | + .15

20 38 0.9272 | 0.9284 | — .05]| 80 0.6249 | 0.6264 | — .08

22 70 | 0.6700 | 0.6721 | — .11| 48 0.8775 | 0.8769 | -4- .04

23 68 | 0.1906 | 0.1938 | — .17] 51 0.3525 | 0.3596 | — .37

24 38 | 0.3356 | 0.3372 | — .o8| 81 0.2140 | 0.2150 | — .05

25 48 | 08722 | 0.8729 | — .03| 70 | 0.6748 | 0.6775 | — .14

26 25 | 08939 | 0.8966 | — .13] 93 | 0.6598 | 0.6611 | — .07

27 47 | 0.7358 | 0.7394 | — .I9| 71 | 0.8111 | 0.8096 | + .08

28 58 0.9688 | 0.9678 | + .04] 60 0.5792 | 0.5779 | + -07

29 82 0.5856 | 05869 | — .07| 36 | 0.9645 | 0.9650 | — .o4

31 39 0.2340 | 0.2400 | — .32] 80 0.3161 | 0.3192 | — .16

33 17 0.7346 | 0.7341 | + .03] IoI | 0.8170 | 0.8195 | — .14

Schl. Kretz. S—k Schl. Kretz. S—It

15 55 00095 | 0.0072 | +0.12] 64 O0.541I | 0.5409 | +0.01

15 55 0.0105 | 0.0076 | + .15| 64 | 0.5458 | 0.5418 | + .21

I 70 | 07176 | 0.7158 | + .o9| 48 0.8352 | 0.8331 | + .10

5 83 | 9.9740 | 0.9754 | — .09] 35 | 0.5774 | 0.5751 | + .12

ay 36 |—.0154 |—.0178 | + .13] 83 0.5680 | 0.5670 | + .05

4A| 51 0.2508 | 0.2484 | + .13] 68 0.3062 | 0.3025 | + .20

19 80 | 0.8938 | 0.8884 | + .28] 38 | 0.6646 | 0.6609 | + .20

23A| 69 0.7815 | 0.7792 | + .12] 49 0.7719 | 0.7688 | + .16

32 15 0.4090 | 0.4109 | — .IO] I04 01476 | 0.1456 | + .I1

33 17 0.7384 | 0.7378 | + .03 | IOI 0.8194 | 0.8171 | + .13

34 51 0.1562 | 0.1560 | + .o1| 68 0.3972 | 0.3955 | + .09

35 88 0.4174 | 0.4150 | + .13] 31 0.1369 | 0.1330 | + .21

36 65 0.8636 | 0.8619 | + .10] 53 0.6901 | 0.6880 | + .11

37 4I 0.7460 | 0.7445 | + .08} 77 0.8105 | 0.8101 | + .02

38 58 0.7471 | 0.7446 | + .13] 60 0.8075 | 0.8049 | + .14

39 65 0.0412 | 00418 | — .03] 54 0.5091 | 0.5089 | + .OI

40 20 | 0.0869 | 0.0869 00} 99 | 0.4692 | 0.4708 | — .08

4I 47 0.4586 | 0.4596 | — .05| 72 | 0.0951 | 00960 | — .05

42 47 0.3562 | 0.3532 | + .16| 72 0.2010 | o.198t | + .15

43 6I | 0.9196 | 0.9135 | + .33] 57 | 0.6349 | 0.6349 -00

44 8I 0.3348 | 0.3334 | + .07] 38 | 0.2199 | 0.2176 | + .12

45 30 0.4771 | 0.4782 | — .06} 89 0.0745 | 0.0785 | — .21

214 Presepe Group; Measurement and Reduction

TABLE III.—( Continued.) Puate 1X: x MEASUREMENTS.

Oe RN TT ee :

x direct. a reversed.

Star. 4M, or | % M, OF

Teal Seale minus Star. | s-x Lincs: Scale minus Star S-K

Sehl. | Kretz. Schl. | Kretz.

15 | 54,55 | 0.8900 | 0,890I | —o.o1 63,64 | 0.6599 | 0.6628 —o.15

2 | 88,89] 0.3924 | 0.3978 | .29] 30,31 | 0.1621 | 0.1625 | — .02

3 | 87,88 | 0.3025 | 0.3008 | 09| 31,32 | 0.2570} 0.2544 | + .14

4 | 85,86| 0.5701 | 0.5648 | 28| 32,34 | 0.4876] 0.4918 | — .22

6 | 72,73 | 0.2920 | 0.2899 II | 46,47 | 0.2621 | 0.2621 .00

26} 53,54 | 0.1020! 0.1029 05

8 | 65,66 | 0.4511 | 0.4461

| 6 | 0.5751 | 0.5730

iit || OR (ov || O7Ao || Oh7/BIUs

14 | 55,56 | 0.0608 | 0.0609

16 | 53.55 | 0.5259 | 0.5236

17 | 52,53 | 0.5848 | 0.5914

I8 | 50,52 | 0.5451 | 0.5448 |

20 | 50,51 0.6969 | 0.6962 |

22 | 48,49 | 0.7159 | 0.7158 |

53:55 | 0.4780 | 0.4776 | +

54,55 | 0.8220) 0.8205 | +

63,64 | 0.4905 | 0.4886 | +

64,65 | 0.5291 | 0.5299 | —

65,67 | 0.4656| 0.4661 | —

67,68 | 0.5085 | 0.5105 | -——

67,68 | 0.8598 | 0.8592 | + .04

fee

|-F+H | | AHL + ++ +444 |

OOH:

Irnl Lot leon!

69,70 | 0.8362 | 0.8382

HOO Oo

le on Le Oa

23 | 47,48 | 0.3495 | 0.3515 71,72 ‘| 0.2038 | 0.2044 03

24 | 45,46} 0.2512 | 0.2520 04} 73,74 | 0.2981 | 0.2989 .04

25 | 44,45 | 0.6609 | 0.6601 04} 73.74 | 0.8926 | 0.8914 .O7

26 | 44,45 | 0.5798 | 0.5791 04} 73,75 | 0.4729 | 0.4739 05

27 | 44,45 | 0.2938 | 0.2900 20| 74,75 | 0.2616 | 0.2608 O04

28 | 43,45 | 0.5416 | 0.5436 -II | 74,75 | 0.5095 | 0.5086 .05

29 | 43,44) 0.4295 | 0.4300 .03'| 75,76 | 0.1226 | 0.1228 .O1

16,17 | 0.1870 | 0.1888 |

.I0 | 102,103 | 0.3682 | 0.3689

Kretz. Hays. | eee Kretz. Hays.

T5 | 54,55 | 0.8899 | 0.8898 40.01 63,64 | 0.6629) 0.6628 | +0.01

I | 89,90} 0.3738 | 0.3658 | + .42] 29,30 | 0.1809 | 0.1800 | + .05

2 | 83,89 | 0.3938 | 0.3946 | .04 ] 30,31 | 0.1600] 0.1602

5 | 76,77 | 0.4536 | 0.4546 | 05 | 42,43 | 0.0996 | 0.0986

7 | 69,70} 0.5980 | 0.5940 .21| 48,50 | 0.4599 | 0.4625

23A | 46,47 | 0.3264 | 0.3236 -14 |. 72,73 | 0.2242 | 0.2258

31 | 42,43 | 0.8836 | 0.8880 | .22] 75,76 | 0.6685 | 0.6692

32 | 40,42] 0.5325 | 0.5338 | .07] 77,78 | 0.5216 | 0.5194

39,40 | 0.3811 | 0.3829 | -I0| 79,80 | 0.1719, 0.1732

34 | 38,39 | 0.6959 | 0.6980 | .I2} 79,80 | 0.8624 | 0.8601

35 | 36,37 | 0.6520 | 0.6511 | .05 | 81,82 | 0.9028 | 0.9005

36 | 35,36 | 0.2006 | 0.1999 | .04 | 83,84 | 0.3488 | 0.3510

37. | 35,36 | 0.0874 | 0.0931 .30] 83,84 | 0.4661 | 0.4621

38 | 31,32 | 0.4465 | 0.4495 .16] 87,88 | 0.1064 | 0.1052

39 | 30,31 | 0.7034 |. 0.6981 .28) 87,88 | 0.8530} 0.8550

4o | 28,29 | 0.9286 | 0.9256 .17 | 89,90 | 0.6300 | 0.6298

43, | 20,22 | 0.4879 | 0.4882 -O1| 97,98 | 0.5671 | 0.5681

44 | 20,21 | 0.4152 | 0.4138 -07 | 98,99 | 0.1415 | 0.1409

45 | 16,17 | 0.1885 | 0.1902 -09 | 102,103 | 0.3685 | 0.3682

ete lectetee te Petesteeledleeleal teste’

SS ees

of the Rutherfurd Photographs. 215

TaBLE II].—(Concluded.) Puate IX: y MEASUREMENTS.

y direct. y reversed.

Line. % Mm, Or Ym, Or

Star! Scale minus Star. Pe |) tine. Seale minus Star. K-H

Kretz. Hays. Kretz. | Hays.

“ | | | “

15 56 | 0.6574 | 0.6586 | —o.06] 62 0.8968 | 0.8969 | 0.00

2 53 0.2924 | 0.2885 || G6 | OG.Aoon | 0.2619 .10

2 38 0.7025 | 0.7022 .02} 80 | 0.8546 | 0.8548 .02

4 21 | 0.6201 | 0.6211 .05| 97 | 0.9386 | 0.9390 | 03

G |) Fo 0.8824 | 0.8836 .05| 48 | 0.6685 | 0.6701 | 08

Sian 0.6176 | 0.6160 08 | 47 | 0.9336 | 0.9311 | 12

10 49 | 0.6535 | 0.6530 | 02] 69 0.8961 | 0.8986 12

ii 43 0.9194 | 0.9174 | IO] 75 0.6335 | 0.6356 git

14 77 | 0.5956 | O5951 03 | 41 | 0.9594 | 0.9579 10

Ow ly 22 0.4234 | 0.4211 | 12 |) yf |) @hwSived || Wpusersy | Io

| 0.0450 | 20

18 4 0.3556 | 0.3512 | P2BV eu O:20TO)|O:2028 aK)

04] 78 | 0.9788 | 0.9775

03] 47 | 0.2341 | 0.2351

.06} 49 | 0.7089 | 0.7I0L |

-I7| 79 | 9.5705 | 9.5735 |

.04 | 69 | 0.0304 | 0.0294 |

AO || CD || @xOiiz{o) || Keeney |

| 0.1659 | 0.1660

| 0.9371 | 0.9361

HO, 25 | OB || O.BuSeb |

.10| 100 | 0.1718 | 0.1716 |

20 40 0.5775 | 0.5768

22 "2 0.3186 | 0.3181 |

23 69 0.8454 | 0.8441

239 0.9861 | 0.9831 |

A || IO 0.5185 | 0.5192 |

26 27 0.5389 | 0.5426

2, 49 0.3845 | 0.3856

28 60 0.6129 | 0.6126

29 | 84 0.2345 | 0.2326

BR 19 0.3819 | 0.3838

Schl. Hays. HT | Schl. | Hays.

@ cera di aell hts Paes bt

role)

“J

fe)

is)

ee)

17 4O 0.5092 | 0.5088 | + .02] 79 | 0.0488

—+-

—

15 56 0.6586 | 0.6598 | —o.06} 62 0.8946 | 0.8964 | —O.II

I 72 0.3909 | 0.3881 at || Aly 0.1674 | 0.1626

5 85 0.6366 | 0.6354 | 2061/9 33) |) G:9176)||0.0172

7 37 0.6385 | 0.6375 SOF) OL) |) O:OLO9) | O:9132

BIN | aie 0.4271 | 0.4246 13] 48 0.1265 | 0.1219

Ait 4o 0.8852 | 0.8874 512 || 5s) 0.6710 | 0.6731

32 17 0.0584 | 0.0532 .28| 102 | 0.5040 | 0.5041

33 19 0.3802 | 0.3842 .21 | 100 0.1728 | 0.1711

34 52 | 0.7965 | 0.7979 -07| 66 | 0.7548 | 0.7551

35 90 0.0624 | 0.0638 O07 || 26) 0.4945 | 0 4920

36 67 0.5094 | 0.5024 | 0.0486 | 0,0412

Bui 43 0.3850 | 0.3868 10] 76 | 0.1650 | 0.1701

38 60 0.3900 | 0.3834 35) 59 0.1671 | 0.1660

39 66 0.6850 | 0.6826 -13] 52 | 0.8684-| 0.8680 |

4o 21 0.7210 | 0.7220 | IO! 97 0.8329 | 0.8329 .00

Ww on

++) ++] 4+] |4++++

ee eee ee

iS)

me Ww

fae | | | epee

43 63 0.5462 | 0.5432 15] 56 0.0040 | 0.0062 | — .12

44 82 0.9712 | 0.9688 -II| 36 0.5834 | 0.5864 | — .16

45 32 0.1102 | 0.1076 SAL || | 7 0.4465 | 0.4474 | — .05

IIT.

Instrumental Corrections.

The first step towards turning the foregoing measures into

right ascensions and declinations will be to apply the following

instrumental corrections, which are here considered in the order

of their application.

1° Division Errors of the Scale.

Just before beginning the measurement of the Presepe plates

a thorough examination of the division errors of the scale was

completed. The details of this investigation together with the

determinations of other constants of the measuring machine are

reserved for another ‘publication from this observatory. It will

suffice for present purposes to set down merely the final results.

Previous to the above investigation the scale had also been ex-

amined by the Kaiserliche Normal Aichungs Kommission at Ber-

lin; the results of this determination were published in the “An-

nals of the New York Academy of Sciences,” Vol. IX, page 206.

The two determinations agree quite well, the largest difference

for any line being o.’’11, and usually the agreement is much closer.

As the investigation at Columbia was made with the same micro-

scope and under the same conditions in which the plates were

measured, it was thought best to use only our own results, as

givenin Table IV. The coordinates of a star depend upon several

divisions for one plate, and the same star usually comes opposite

different divisons for different plates. It follows therefore that

our final positions will be nearly independent of inaccuracies in

the determination of the division errors; for example, the right

ascension of Star 1 depends upon eighteen different lines of the

scale and its declination depends upon thirteen. In Table IV

the corrections are given in millimetres, and are always to be

added to observed readings.

2° Corrections for Runs and Screw Errors.

The screw used in the measurements is of such a pitch that two

complete turns of the micrometer head correspond to one space

on the scale; the micrometer head is divided into one hundred

equal parts and may therefore be read directly to half-microns

216

The Rutherfurd Photographs.

Taste 1V.—Division Errors oF THE SCALE.

Correction

in mm.

Correction

in mm.

Correction

in mm.

O OI ADnNBW NH O

0.0000

+0.0011

—0.0007

—0.0001

-+ 0.0002

—0.CO004

+o ooo!

—0.0013

—0.0008

—0.0009

—0.000I

+0.0014

+0.0006

+-0.co14

0.0016

+0.0015

-+0.0009

--o0.0008

0.0012

-+0.0012

-++0.0007

+0.0015

-+0.0016

+o0.0014

+0.0012

-++0.0007

+0.0026

0.0033

+0.0026

-+-0.0020

0.0035

0.0030

+0.0022

-++0.0024

0.0013

0.0032

+0.0024

+0.0025

+0.0016

+0.0025

+0.0033

-+-0.0020

0.0025

+0.0024

0.0029

+0.0020

+0.0021

+0.0006

+0.0013

0.0015

-++0.0007

+0.0018

+0.0025

+0.0026

+0.0018

+0.0027

+0.0025

+0.0026

-+-0,0026

-+0.0019

+ 0.0008

++ 0.0014

—++0.0004

-+0.0019

+0.0004

—0.0005

+0.0002

+0.0014

-- 0.0009

+0.0012

-+ 0.0002

+ 0.0012

0.0000

—0O ©002

+ 0.0002

—0.0006

—0.0013

0.0005

—0.0003

0.0000

+0.0020

+0.0022

+0.0026

+ 0.0021

-++0.0014

+0.0024

+0.0015

+0.0c624

0.0012

+o.0orL&

+o.0014

_ +0.0005

0.0015

0.0000

218 Presepe Group; Measurement and Reduction

and by estimation to twentieths of a micron. The details of the

operation of observing runs were to set the micrometer head at

about 5."0 and to read on the scale as follows: :

Line 70, Line 65, Line 65, Line 7o.

These two lines were selected because they have practically the

same division errors, thus avoiding an extra correction, and also

because they happen to have more accurately determined division

errors than most other lines. The correction for runs need not

be applied to the separate readings on the stars and on the scale

but may be applied to the quantity 5 m directly ; for let us put

2h — reading on Line 65, minus reading on Line 70, minus

10.*0000.

Dividing by 2 we obtain #, the quantity given in Table II; we

must then add to $m the correction

sth G m) = millimetres,

This correction may conveniently be combined with the cor-

rection for non-periodic errors of the screw or variations in its

pitch; investigation showed that the following quantities must

be added to observed readings of the micrometer head in order

to reduce them to what they would have been had the screw been

of uniform pitch, but of the same total length:

Reading of one Micrometer Head. Correction in Millimetres.

5. 6 ef akenaysegsisesiavcne eve le neeaeeets jatolelere tia ieueeets O.

Goes ited tase tear Awacieve stant Sra eucalleyen’ + 0.0005

FROG OR OOOO COI SEHD oe co mIG bale bid ces + 0.0002

Siosirah aie rsters pete ert ates alge eevereeetale — 0.0003

OOscpecods. Sosocogcossgnsageodooode — 0.0012

UGLOR Sagoo ooSogedondoooDobOdCOdOOHOOS — 0.0017

ISO) cvolelensiadslietaltelsiokeialalaiviele/cieksleleieheisteneererehers — 0.0022

WHOA Go OGaS oo oMCooO6OCoO ood Oe Oba OM — 0.0021

A 3's Ole: dsauaralens el uerat si tenatece re evoialevane ovale aereiersieress — 0.0022

WAS Ole -aevate Secs este et aierae een te ats eee eee rare ren — 0.0014

FS Ola wicheveretote ietenercheveislerehotctarrenisie rtenstetonsmenete oO.

The screw is actually longer than ten turns, but as only this

length was used in the determination of the error of runs the rest

of the screw was not investigated. It will be observed that the

corrections progress uniformly in the interval from 9.'o to 11.70;

advantage was taken of this fact to make the application of the

corrections a simple matter. For if the micrometer head be set

at 9."o when the microscope is pointed at a star, then the reading

of the Rutherfurd Photographs. 219

on the scale will lie between 9.*o and 11."o because a whole space

of the scale corresponds to two turns of the micrometer head ;

consequently the correction to the difference of the readings on

scale and star will be proportionate to that difference, that is to

4m; the correction to the latter is easily seen to be

— (}m) X 0.0010 millimetres.

Adding this to the correction for runs we obtain

— (4m) ( 0.00010 ++ * ) millimetres.

As an example let us correct the first observation given on the

specimen sheet on page 199. The date being March 25, we get

from Table IT,

E = -+ 0.0045.

Consequently the correction for runs and screw errors is

— ($m) X 0.0019 millimetres.

A table may now be constructed with the argument 4 m which

applies to all observations taken on March 25.

um. Correction.

ORO eerste rater oveleyisorererecaver svecoeat aral a racatavorsreuecollerecs 0.0000 millimetres.

OTE ae ere tot ees aerial Sialieaitaleseitiehenal aver tuewenwy Wistels — 0.0002

OD eee Ah eure intiacuarerergnchubnieasmuutanats esetets — 0.0004

Ona yenaresstare:sicncoveiensssyereoverelelcanertrsrer sais osnaies — 0.0006

RAN Mie ar arassheratate tataeae sia isiehere eliserarre.c eich asco — 0.0008

OEE erostta rajetonta tesevel antic nals levee eit ual bral WeaveZalre — 0.0010

ONG ee ie aldara Neca Siehetne Sle este aie oe wate — 0.O0II

ONFiineve ss slbisusliersjatlavereraie Chsleusscia seueuee sai ses — 0.0013

ORG eeaveratarerencishevecrteraivcveneiersccvate ioausiovere rs. cue — 0.0015

ONO py aretoranetebey hensvoyieron okel sieve ererersvetsueccuene raters)» — 0.0017

Ope tare caterers role etaiares Shay sla stealer sakes cererarelaus iets — 0.0019

For the star given on the specimen sheet the correction is

—o.0009. During the second half of each morning’s observations

when the micrometer head is set at 9.°5 instead of at 9."o it some-

times happens that the reading on the scale exceeds 11.*o, in

which case the correction will not be exactly proportionate to

+m; but the error committed by using the same table throughout

will never reach o.’’o2, and in most cases is entirely negligible.

3°. Having applied the corrections given above we have now to

change the measures into rectangular coordinates x and y, referred

to the central star 15 as origin, one axis being parallel to

the cylinder and the other at right angles to it. For this purpose

we subtract the mean of all the readings on the central star for

220 Prexsepe Group; Measurement and Reduction

any one day from the readings of all the other stars that were

measured on that day. As we wish to have positive values of x

for those stars which have greater right ascensions than the central

star, we must subtract the reading “ x direct” from the reading on

Star 15; but we must subtract the reading on Star 15 from the

reading ““x reversed.” Similiarly to get positive values of y

for those stars having greater declinations than the central star,

we subtract the reading on Star 15 from each “ y direct ” and the

contrary for “y reversed.”

4° Rotation Corrections.

It was found very difficult to set the circle at exactly 90° plus

the reading for the previous day. Even when this had been ac-

complished the circle-reading was sometimés found to have

changed a little during the measurement of the stars. A correc-

tion is therefore necessary to reduce the rectangular codrdinates

to what they would have been had the readings of the circle for

different days differed only by multiples of 90°. Let

@ =the number of seconds which occurs most often in the cir-

cle readings of a particular plate.

() —71= the number of seconds in the reading for any day.

Then we have,*

Correction for « —=—y. 7 sin 1.’/

: Ups en ISTUL: Tler

For the present measurements these corrections are very small,

never exceeding o.’’05; they have however been applied through-

out.

The values of @ adopted for the various plates are as follows:

Plate LARS ae crepe ionic GBS ccna ice athe ca asters Pay O==5u

TD Ties ea R av ae eee a a ON A eae Se ed CRS co ecu fo)

UO eis ee arte eons heer Ae a ee meh CI fo)

beget Mra reclaim tas Cen tie mien BuEn ee lal 58

ri aig dea MPa E OR ane A Mee La 1 7

VAT Reece ete ee ea ee ie ae, Soe ea a O

AVOWED Saba tekaroedee Grane nhee sameeren ag ae tae eee pe cue 29

1 DCT RO iesere aise wincwils Weep | Ae ln a 2

5° Sceale-value corrections.

The scale being made of German silver has a greater coefficient

of expansion than the glass plate, and hence it would appear that

if the temperature changed during the measurement of a plate,

* “* Permanence of the Rutherfurd Photographic Plates’’ by Harold Jacoby,

Annals of the N. Y. Acad. of Sciences, Vol. IX, p. 267.

of the Rutherfurd Photographs. 221

the coordinates would require a correction to reduce them to

what they would have been had the temperature remained con-

stant. Investigation shows, however, that such a correction is

unnecessary by reason of its minuteness, at least within the limits

of the range of temperature at which the present plates were

measured. To ascertain the amount of the correction, two well

defined specks, such as may be found in the film of any plate,

were selected, one near either edge of the plate, and the distance

between them was measured at various temperatures. On the

morning of April 30, 1897, this distance was measured six times

each by Mr. Kretz and myself with the following results :

Schlesinger : Kretz:

104.1548 mm. 104.1505 mm.

67 514

36 505

39 497

59 540

25 317

Mean, 104.1543 104.1513

Probable Error, 0.00042 =£0,00041

The temperature of the measuring room had been kept at 69.°3

during the measurement by means of artificial heat, the heating

apparatus being at the other end of the room from that occupied

by the measuring machine. The heat was now turned off and the

plate allowed to assume the natural temperature of the at-

mosphere; on the afternoon of the same day, three hours having

elapsed since the first series was completed, the distance between

the specks was again measured by the same observers as follows:

Schlesinger: Kretz:

104.1550 mm. 104.1557 mm.

ge 44

63 48

87 60

go 53

79 79

Mean, 104.1572 ; 104.1556

Probable Error, 0, 00041 ==.00031

The temperature for this series was 52.°2. Denoting by v the

increase in the measured distance due to an increase of 1° in the

temperature we have

ANNALS N. Y. ACAD. ScI., X, May, 1898—15.

222 Presepe Group; Measurement and Reduction

Schlesinger : Kretz:

Vv = — 0.00017 mm. : v = — 0.00025 mm.

=— 0.000034 =—E 0.000030

These two values are not very accordant, but they agree sufii- —

ciently well for present purposes. As, however, some doubts

were entertained as to whether the plates had been thoroughly

cooled in the intervening three hours, and as to whether it

would not be better to measure the distance between the

specks at a season when artificial heat could be entirely dis-

pensed with, the following third series of observations was under-

taken by myself, several days elapsing between the various

measurements. No artificial heat was allowed in the measuring

room during the whole period.

May 20, 1897. Temperature — 73.°6.

104.1530 mm.

Mean, 104.1536 + 0.00047

May 22,1897. Temperature = 69.°6.

: 104.1534 mm.

Mean, 104.1543 + 0.00036

May 29, 1897. Temperature = 71.°o.

104.1548 mm.

Mean, 104.1537 - 0.00031

of the Rutherfurd Photographs. 223

July 27, 1897. Temperature = 82.°1.

104.1532 mm.

525

595

539

520

495

510

542

510

522

548

525

Mean, 104.1522 + 0.00031

Denoting by v as before the increase in the distance due to an in-

crease of 1° in the temperature, and by Z the distance between

the specks at the temperature 69.°6 we have the following four

observation equations :

L — 104.1543 =o weight 3

L+ 1.4 v— 104.1537 =o Testes

L+ 4.0 v — 104.1536 =o Sage ie)

LI, + 12.5 v — 104.1522 = 0 Soe es

The weights are calculated from the probable errors given above,

the probable error of an equation of weight unity being

=- 0.00067

Solving by least squares we get

Y = — 0.00015 + 0.000032

Taking into account the two previous series, the mean by weight is

Vv = — 9.00019 mm.

which very probably does not differ from its true value by as

much as 0.00005.

Now the largest coordinate in the Preesepe measures is less

than forty millimetres, and the greatest deviation for any single

day from the mean of the temperatures for the corresponding

plate is less than 5°; consequently the largest correction which

it will ever be necessary to apply is

0.00037 mm.

which corresponds to 0.’‘o2. As this is so small, even in the ex-

treme case, no appreciable error will be committed by neglecting

the correction altogether. We may indeed conclude that for the

: : |

224 Prexsepe Group; Measurement and Reduction

scale under consideration and for the Rutherfurd plates, a cor-

rection for change in the scale-value will be unnecessary so long as.

the temperature does not vary more than 10° during the measure-

ment of a single plate.

6° Projection Errors and Deviation of the Cylinder from

Straightness.

In the present work corrections have been applied for neither

of these; the first were discussed by Donner * and are very small

in most cases; it is indeed very difficult to determine them with

sufficient accuracy. Repsold has recently devised a new guiding

way which is free from this source of error; the measuring ma-

chine used for the Preesepe plates had been furnished with such

a guiding way in 1896. As regards the straightness of the evlinder,

investigation showed that it had been admirably made7+; the

greatest error which we shall commit in assuming it to be straight

is 0.’’04; the reversal of each plate and the insertion of different

plates in different positions in the measuring machine will tend

to eliminate even this small error.

Having now completed the consideration of all the instrumental

corrections which it is necessary to apply, I shall conclude this

subject by correcting the measurements of Star 7, Plate VIII, as

given on page 199, or in Table IIT.

March 25, March 24, March 18, March 22,

xz direct: y direct: «reversed: ey reversed :

TEINS yes: Sauerelaerese Gea 74,76 26 43,44 83

zm; First obs’v’r.,.. 0.4646 — 0.0154 0.5938 0.5680

Second “ .. 0.4639 — 0.0178 0.5896 —-0.5670

Mean, Sep. siovaeve eoetere 0.4643 — 0.0166 0.5917 0.5675

Cor. for Runs, ete., — 9 o — Il — II

Div. Correction, .... + 5Ou lh 24 + 26 + 50

Corrected 3m, ...... 0.4684 — 0.0142 0.5932 05714

Measurement, ...... 75.4684 35.9858 44.0932 83.5714

Where two lines have been used the division correction is the

mean of the division corrections for the separate lines; the final

“measurement ” is then obtained by adding the mean of the num

bers of the lines to the corrected $ m. The corresponding meas-

urements for the central star 15 when similiarly corrected are:

* ““Tyétermination des Constantes nécessaires pour Ja Reduction des

Clichés.’’ Acta Societatis Scientiarum Fennicae, Vol. X XI.

{ ‘‘ Permanence of the Rutherfurd Plates’’ by Harold Jacoby ; Annals of

the N. Y. Acad. of Sciences, Vol. LX, page 210.

of the Rutherfurd Photographs. 225

March 25, March 24, March 18, March 22,

x direct: y direct: x reversed : y reversed :

60.7692 = 55.0133 58.7883 64.5497

7695 O104 7887 5457

TB OI00 7870 5448

7712 0123 7871 5450

Mean, 60.7708 55-0115 58.7878 64.5463

Taking the differences between these and the corresponding

measurements for Star 7, having regard to signs, we get:

Codrdinates,........ —1I4.6976 —I9.0257 —1I4.6946 —I9.0251

Rotation Cor.,...... o + Se Abentet 2 fo)

Final Coord.,...... —14.6976 —19.0253 —I14.6944 —19.0251

These are the quantities given in Table V, which needs no further

explanation. In comparing the direct with the reversed codrdin-

ates, it should be remembered that unity in the fourth decimal

place corresponds to about o.’’005 of arc of a great circle.

oe wie

226 Presepe Group; Measurement and Reduction

TABLE V.—CoRRECTED COORDINATES. PLATE I.

Star, ¥ y

Direct. Rev’d. Mean. Direct. Rey’d. Mean

if —34.5052 | .5028| —34.5040 +15.6854 | .6850) +15.6852

2 —33.5104 | .5082 | —33.5093 — 3.4200 | .4188 | — 3.4194

3 —32.3942 | .3922| —32.3932 —18.0042 | .0055 | —18.0049

4 —30.6393 | .6348 | —30.6370 —35.0918 | .0906 | —35.0912

5 —21.6168 6161 | —21.6165 +28.9521 | .9571| +28.9546

6 —17.4281 .4236 | —17.4258 +14.2048 | .2048} -+14.2048

7 —14.6839 | .6843 | —14.6841 —19.0394 | .0412 | —TIg.0403

8 —10.5876 | .5849| —10.5862 +14.9500 | .9500} +14.9500

Io | — 9.6888 | .6886| — 9.6887 | — 7.0204 | .o201 | — 7.0203

II | — 8.8264 8270 | — 8.8267 —12.7576 | .7577 | —12.7576

14. | — 0.2020 2022; — 0.2021 +20.9438 | .9455 | +20.9446

15 0.0000 0000 0.0000 0.0000 | .0000 0.0000

16 + 0.9159 9173| + 0.9166 —34.2424 | .2429 | —34.2426

18 + 3.8697 | .8712| + 3.8705 —15.3037 3022 | —I5.3030

20 + 4.2144 2182 | + 4.2163 —16.0818 | .0826| —16.0822

22 + 6.1437 | .1546| + 6.1541 +15.6744 | .6760) +15.6752

23 + 7.5258 | .5276| + 7.5267 -+-13.2000 2000 | -+13.2000

23A| + 8.5446 | .5478| + 8.5462 | +14.7914 | .7874| +14.7804

24 + 9.6569 | .6587) + 9.6578 —16.6650 | .6664 | —16.6657

25 + 10.2385 2420) +10.2402 — 6.1255 | .1240} — 6.1248

26 +10.3560 | .3580|} +10.3570 —29.113I | .1110} —29.1120

25] -+10.6100 | .6095 | -+10.6098 — 7.2644 | .2646| — 7.2645

28 +10.8422 | .8406| -+10.8414 + 3.9756 | .9756| + 3.9756

29 +11.4264 | .4272| +11.4268 +27.6000 | .5983) +27.5992

31 +12.0292 .0308 | +12.0300 —15.7662 | .7623 | —15.7642

32 +13.9115 | .9104| +13.9110 | —39 5974 | .5944| —39.5959

33 +15.5667 | .5705| +15.5686 —37.2662 2662 | —37.2662

34 +16.2032 | .2048| +16.2040 | — 3.8424 8368 | — 3.8396

35 | +18.1994 | .1978) +18.1986 | +33.4348 | .4344| +33.4346

26 +19.6786 | .6824| +19.6805 -+- 10.8790 8794 | -+10.8792

37 +19.8224 | .8254| +19.8239 —13.2516 2506 | —I3.2512

38 +23.4340 | .4385| -+23.4362 + 3.7612 7620| + 3.7616

39 +24.1815 | .1872|} +24.1844 +10.0636 | .0626| +10.0631

4o +26.0190 | .0207) +26.0198 | —34.9100 | .g092 | —34.9096

43 | +33-9119 | .9091| +33.9105 | + 6.9450 | .9450| + 6.9450

44 | +34.4409 | .4470| +34.4440 | +26.3683 | .3666| +-26.3674

of the Rutherfurd Photographs. 2

TasLeE V.—( Continued.) CorrectED CodrDINATES. Puate II.

x y

Star.

Direct. Rev’d. * Mean. Direct. | Rey’d. | Mean.

IT | —34.5040 | .5037| —34.5038 | +15.6928 | 6954. +-15.6941

2 —33.5044 | .5036 | —33.5040 — 3.4064 | .4061 | — 3.4062

4 —30.6440 | .6420 | —30.6430 Se O50 O79) 35.0772

5 —21.6032 | .6037) —21.6035 +28.9578 | .g610) +28.9594

6 —17.4227 4214 | —17.4221 +14.2064 | 2055 —+14.2059

7 —14.6867 | .6812 |) —14.6840 —19.0368 | .0348 | —19.0358

PSD eae O15 O94" |) 5074s 105004 a —— 357003)" | 7585,| —— 37594

8 | —10.5806 | .5799) —TI0.5803 | +14.9550 | .9538) +14.9544

Io | — 9.6862 | .6838 — 9.6850 — 7.0164 | .0154)| — 7.0159

II — 8.8272 | .8259 — 8.8266 —12.7520 | .7530| —I2.7525

14 — 0.2004 | .2006 — 0.2005 +20.9444 | -9442| +20.9443

15 0.0000 | .0000 0.0000 0,0000 | .0O6OO | 0.0000

16 + 0.9121 | .9122| + 0.9122 —34.2378 | .2359| —34.2368

17 -+- 2.3210 | .3230| + 2.3220 —16.1492 | .1480 —16.1486

18 + 3.8660 | .8664| + 3.8662 —15.3018 | 3032. —15.3025

19 | + 3.8978 | .8967; -+ 3.8972 | +25.8933 | .8950] +25.8942

20 + 4.2114 | .2147| + 4.2130 —16.0802 | .0786| —16.0794

22 + 6.1538 | .1518| + 6.1528 +13.1972 | .1972| +13.1972

23A| + 8.5476 | .5505| + 8.5490 | +14.7833 | -7834) +14.7834

24 + 9.6502 | .6500| + 9.6501 || —16.6680 | .6658) —16 6669

25 +10.2337 | .2350| +10.2344 — 6.1280 | .1255| — 6.1268

26 +10.3454 | .3492| -+10.3473 —29.1082 | .1090| —29.1086

27 +10.6000 | .6032; -+10.6016 — 7.2620 | .2598) — 7.2609

28 +10.8382 | .8390| +10.8386 + 3.9732 | .9757| + 3.9744

29 11.4256 | .4253| -+11.4254 | +27-5944 | -5926) --27.5935

31 + 12.0266 | .0287| - 12.0276 —15.7620 | .7641 | —15.7630

32 +13.9074 | .9049| +13.9061 | —39.5946 | .5894 —39.5920

23 +15.5584 | .5616) +15.5600 —37.2621 | .2607| —37.2614

34 +16.2032 | .2031| +16.203I — 3.8444 | .8394| — 3.8419

35 | +18.2036 | .2038) +18.2037 | +33.4284 | .4314) +-33-4299

36 +19.6828 | .6814| +19.6821 +10.8745 | .8752| -+10.8749

Bi +19.8174 | .8190) +19.8182 —13.2498 | .2495 | —13.2496

38 | +23.4373 | .4378| +-23.4375 | + 3.7584 | -7606| + 3.7595

39 24.1793 | .1830 | -+24.1812 +10.0571 | .o604 +10.0587

40 | +26.0170 | .0153 | +26,0162 | —34.9106 | .gogt —34.9098

43 | +33.9056 | .9042| +33.9049 | + 6.9342 | .9360 ~+ 6.9351

44 | +34.4474 | .4480} +34.4477 | +26.3596 | .3632| +26.3614

45 +38.7409 | .7417| +38.7413 | —24.5064 | .5066) —24.5065

228

Taste V.—( Continued.) CoRrRrECTED COORDINATES.

Presepe Group; Measurement and Reduction

Puate III.

Direct.

Rev’d.

Mean.

Direct.

Mean.

CON DURW DN H

—34 4942

—33-5°73

—32.4044

—30.6587

—21.5902

—17.4130

—14.6935

—10.5682

+38.7302

-4942 |

-5094

-4030

.6538

+9939

-4134

6974

.5685

.6859

.8312

.1878

~0000

.8959

.3190

.8590

.2076 |

.1653

+5297

»99904

.6490

.2295

-3369

.6032 |

.8452

.4462

.O165

.8889

.5422°

-2034

.2234

.6868

.8124

.1879

.OO12

-QII4

-4650 |

.7281

—34.4942

—33.5084

—32.4037

—30.6562

—21.5920

—17.4132

—14.6954

—10.5684

— 9.6862

— 8.82098

— 0.1872

0.0000

0.8969

2.3192

3.8593

4.2066

6.1658

7.5298

8.5560

9.6497

+ 10.2305

+ 10.3365

-+10.6034

+10.8447

-+-11.4451

-+-12.0150

+13.8891

+15.5406

+16.2034

+18.2221

+-19.6889

+19.8118

+-24.1888

+25.9995

+33.9126

+34.4649

+38.7292

+4444 +++

+15.7075

= PSY)

—17.9840

—35-0679

+ 28.9642

+14.2124

—I9.0312

+14.9584

— 7-9159

—12.7523

+20.9390

0.0000

— 34.2431

—16.1527

—15.3089

—16.0852

+15.6676

+13.1907

+14.7819

—16.6740

— 6.1371

—29.1205

— 7.2689

+ 3.9637

-++27.5865

15-7975

—39.6008

37-2759

— 3.8514

+33-4219

+10.8652

—13.2630

+10.0472

—34.9216

+ 6.9199

+26.3452

—24.5248

+15.7076

— 3.3948

—17.9842

—35.0670

+28.9652

+14.2141

—19.0327

+14.9593

— 7.0148

—12.7517

+20.9405

0.0000

—34.2420

—16.1516

—15-3074

—16.0835

+15.6706

+13.1919

+14.7820

—16.6714

— 6.1340

—29.1180

— 7.2700

+ 3.9648

+27.5888

—15.7688

—39.6028

—37.2740

— 3.8508

+33.4218

+ 10.8636

—13.2643

+ 10.0467

—34.9214

+ 6.9184

+26.3450

— 24.5257

of the Rutherfurd Photographs. 220

TaBLeE V.—(Continued.) CorrEcTED CodrpinaAtges. Prats IV.

Direct. Mean. D rect. Mean.

34.5081 | . OMG | UG oyORS Ile +15.6756

—33-5014 | - —33-5000 | — 3.4249 | .- — 3.4241

—32.3816 | . —I8.0095 | . —18,0I01

—30.6188 | . b —35.0890 | . —35.0897

—21.6262 | . : +28.9437 | . +28.9430

—17.4268 | . , +14.1982 | . +14.1999

—19.0377 | - —I9.0394

— 3.7664 | . — 3.7678

+14.9470 | . +14.9482

— 7.0229 | . — 7.0219

—12.7601 5 —I12.7592

+20.9386 | . 20.9394

0.0000 | . 0.0000

—34.2394 | - — 34.2383

—16.1490 | . —16.1490

—I5.3017 |. —15.3016

+25.8905 | . 25.8896

—16.0778 | . —16.0777

Sere Wec +15.6737

13-1976 || . -+-13.1971

+14.7866 ; +14.7865

—16.6652 | . —16.6629

— 6.1234 | . — 6.1227

—29.1068 | . —29. 1064.

— 7.2612 | . — 7.2613

+ 3-9759 | - + 3.9765

+ 27.5930 | . +27.5945

+12.0288 | . : —15.7623 | . —I5.7616

+13.9279 | . —39.5870 | . —39.5876

F15.5832 | - —37-2559 | - —37-2555

+16.2028 | . : — 3.8344 |. — 3.8347

+18.1752 | . +33.4338 | . +33.4328

+19.6722 | . : -+10,8808 | . -+ 10.8804

+19.8242 | . 5 —13.2450 | . —13.2454

+23.4288 | . + 3.7647 | . + 3.7642

24.1717 | . e +100655 |. _ +10.0655

+26.0288 | . —34.8968 | . — 34.8953

+33-8955 | . : + 69446 |. + 6.9450

+34.4188 | . P +26.3714 | . +26.3706

> +38.7495 | . E —24.4909 | . —24.4904

NOU BROW NH

230 Presepe Group ; Measures and Reduction

TaBLE V.—(Continued.) CorrEcTED CodrpinaTEs. PLATE V.

Direct. Mean. Direct. ‘ Mean.

—34.4912 |. — 34.4906 +15.7164 | . +15.7147

—33.5004 | — 3.3860 | . — 3.3878

—32.4077 —I7.9751 | .- —17.9762

—30.6650 —35.0600 | . —35.0610

—21.5817 +28.9692 | . +28.9686

—17.4084 +14.2193 | . -+14.2190

—14.6982 —I19.0254 | . —19.0288

—10.5686 +14.9581 | . +14.9589

— 9.6884 | — 7.0102 | . — 7.0109

— 8.8331 —12.7484 |. —I12.7492

— 0.1797 +20.9386 | . -+20.9380

0.0000 . 0.0000 | . 0.0000

+ 0.8870 —34.2418 | . —34.2406

+ 2.3141 —16.1528 | . —16.1524

+ 3.8576 | .—15.3042 |. —15.3043

+ 3.9190 +25.8858 |. +25.8836

+ 4.2025 —16.0850 | . —16.0838

-+ 6.1690 +15.6671 | . +15.6672

+ 7.5383 -+13.1906 | . +13.1911

825592) | 247780): +14.7768

+ 9.6429 —16.6726 | . —16.6736

+ 10.2299 — 6.1376 | . — 6.1364

+ 10.3246 —29.1198 | . —29. 1204.

-+ 10.6030 YOR Nc — 7.2711

-+10,8456 + 3.9626 |. + 3.9624

+11.4495 +27.5812 |. +27.5812

-+12.0098 —15.7728 | . —15.7726

+13.8744 —39.6013 | . —39.6025

-+16.1967 — 3.8561 | . — 3.8543

18.2292 +33.4117 | . +33.4108

-+-19.8077 —13.2664 |. —13.2680

+24.1876 +10,0364 | . +10.0370

25.9822 —34.9250 | . —34.9255

+33.9064 | + 6.9073 | - _ + 6.9068

+34.4657 | +-26.3334 | - +26.3335

+38.7183 —24.5324 | . —24.5326

of the Rutherfurd Photographs. 231

TABLE V.—( Continued.) CORRECTED COORDINATES. Puate VII.

Direct. Mean. Direct. Mean.

—34.4817 | . —34.4830 = iT Te | 15.7226

—33-5043 | - =aO3-5048, f= 38-3759. |: = 3-3/0E

—32.4086 | . —32.4093 —I17.9669 | . —17.9664

—30.6694 | . —30.6684 | —35.0474 | . —35.0473

—21.5742 | . —21.5728 +28.9724 | . + 28.9730

—1I17.4069 | . —17.4062 +14.2230 | . +14.2223

—I4.7014 | . —14.7018 —19.0236 | . —I19.0221

—10.5922 | . —10.5908 — 3.7542 | - — 3.7545

—10.5673 | . —10.5680 -+-14.9603 | . +14.9595

— 9.6920 | . ; — 7.0050 | . — 7.0055

— 8.8388 lies : —12.7439 f —12.7443

+20.9396 | . + 20.9392

0.0000 | . | 0.0000

—34.2354 | - — 34-2359

—16.1506 | . | —16.1500

—15.3052 | . —-15.3054

+25.8832 | . +25.8843

—16.0844 |. —16.0849

+24.3594 | - +24.3574

+15.6664 . +15.6648

-+-13.1890 | . +13.1881

FILA | +14.7738

—16.6755 |. —16.6745

— 6.1370 | . | — 6.1359

—29.1174 | . —29.1177

== BF2S || 72S

+ 3.9608 | . | ++ 3-9599

+27.5814 |. | +27.5806

—I5.7710 | . | —15.7718

—39.6006 | . —39.6014

— 37.2730 | . —37.2726

— 3.8560 | . — 3.8548

aipsG-400K. In: +33.4084

+10.8540 | . +10.8564

—— 1382720) |e —13.2726

+23.4334 | - | “3.7330 - + 3.7323

+24.1835 |. : +10.0310 | . +10.0325

+25.9716 | . +25. —34.9286 | . —34.9284

+30.0359 ; ‘ — 7.5610 : — 7.5605

+32.0193 | . : — 7.6587 | . — 7.6595

~ +33.9009 | . : + 6.8994 | . + 6.9004

+34.4624 | . | : +26.3208 | . +26.3227

+38.7094 | . +38.7090 | —24.5388 | . —24.5374

TAN RW DH

232

TABLE V.—( Continued.)

Presepe Group; Measurement and Reduction.

CORRECTED COORDINATES.

Puate VIII.

Direct.

Mean.

Direct.

Mean.

0 ONIN DU KW YH

—34.4857

7 03-9932

—32.4060

+30.0339

+32.0097

+33-8966

+34.4516

+38.7120

—34.4862

—33.5028

—32.4036

—30.6580

—21.5809

—I17.4114

—14.6960

—10.5966

—10.5733

— 9.6882

== Sh S57/

— 0.1848

0.0000

+ 0.8871

+ 2.3130

+ 3.8561

+ 3.9100

+ 4.2016

+ 6.1623

AP 15k

+ 8.5513

+ 9.6428

+10.2262

+ 10.3285

+ 10.5974

+10.8412

11.4425

+12.0124

-+-13.8768

+15.5309

+ 16.1966

+18.2168

+ 19.6764

+19.8035

+23.4312

+24.1776

+ 25.9804

= 30.0340

-+ 32.0120

+ 33-8963

+ 34.4505

4+-38.7124

+15.7100

— 3.3848

—17.9734

—35-0517

-+28.9670

+14.2171

—19.0253

—= 3.7003

+14.9556

— 7.0098

—12.7488

-P 20.9374

0.0000

—34.2371

—16.1488

—15.3028

+25.8812

—16.0818

+15.6656

+13.1874

+ 14.7729

—16.6723

— 6.1372

—29.1152

— 7.2728

+. 3.9608

+ 27.5784

—15§-7797

—39.6012

—37-2751

— 3.8543

+33.4060

+ 10.8545

—13.2662

+ 3.7362

+10.0346

—34-9247

— 7-5534

==) O57

+ 6.9064

+26.3255

—24.5322

+15.7112

— 3.3847

—17.9736

—35.0520

-++ 28.9675

+14.2182

—19.0252

— 3570us

+14.9563

— 7.0097

—12.7488

+20.9383

0.0000

—34.2362

—16.1494

—I15§-3044

+25.8822

—16 0819

+15.6672

+13 1880

+14.7744

—16.6724

— 6.1360

—29.1158

— 7.2708

+ 3.9628

+ 27.5792

—I5.7727

—39.6013

—37-2732

— 3.8544

+33-4073

+10.8554

—13.2666

+ 37372

+ 10.0348

—34.9240

= 55°

== 710578

+ 6.9079

+26.3259

—24.5324

of the Rutherfurd Photographs.

TABLE V.—( Concluded.) CoRRECTED COORDINATES.

Prate IX.

Direct. Rev'd. Mean. | Direct. | Rev'd. | Mean

A534 4900) | A842) — 3424820 | 15.7306) | 37334 | 4-15.7325

ZI 85-5 0508-5025) oan8 35-5087 Mla: G0SO ||, -3004 | — 3.3672

3 —32.4120 | .4079 | —32.4100 —17.9574 | -9579 | —I17.9572

4 —30.6766 | .6746| —30 6756 —35.0392 .0384 | —35.0388

5 —21.5667 | .5659| —21.5663 +28.9755 | .9802| +28.9778

6 —17.4034 | .4030| —1I7.4032 +14 2269 | .2301) +14.2286

7 —14.7092 -7056 | —14.7074 —19.0220 | .0194 | —I!9.0208

8 —I10.5617 | .5612| —10.5614 +14.9613 | .9682 | +14.9648

10 — 9.6866 | .6860| — 9.6863 — 7.0064 | .o018 | — 7.0041

II — 8.8444 | .8424| — 8.8434 —12.7406 | .7372| —12.7389

14 — 0.1718 C7 ON —— ONL Le +20.9388 _| .9407 | +20 9397

15 0.0000 0000 0.0000 0.0000 | .0cOoO 0.0000

16 + 0.8652 8684 + 0.8668 —3 4.2368 | .2330) —34.2349

17 + 2.3019 | .3048) + 2.3033 —16.1486 | .1504| —16.1495

18 =e 3.0459 |),.0403 | 4-93-8470) | —15-3053 || -3054 | —15.3054

20 + 4.1952 | .I981| + 4.1966 —16.0804 | .o809 | —16.0807

22 aie O75 Oi | eel? 59) -|-6 020758 +135.6626 | .6655) -+15.6640

23 + 7.5408 | .5429) + 7.5418 +13.1893 | .1902|} +13.18098

23A | + 8.5656 | .5620) + 8.5638 +14.7698 | .7735| +14.7716

24 + 9.6386 6369) + 9.6378 —16.6742 | .6750| —16 6746

25 + 10.2299 2300 | -+10.2300 | — 6.1412 | .1352| — 6.1382

26 +10.3108 | .3114| +10.3111 —29.1168 | .1175 | —29.1171

27 | +10.5979 | .5991 | +10.5985 | — 7.2740 | .2707| — 7.2724

28 +10.8479 | .8466| +10.8473 + 3.9552 | .9610) + 3.9581

29 +11.4602 | .4605| +11.4603 +27.5766 | .5815| -+27.5790

31 +12.0046 | .0050) +12.0048 —15.7726 | .7764| —15.7745

32 +13 8562 8568 | +13.8565 —39.6046 | .6040| —39.6043

Soe ini 85-507 Ep 50001) 15-5079 |e ——37-2778, )-2789)| 31-2750

24 +16.1936 1964 | -+16.1950 — 3.8618 | .8610| — 3.8614

35 +18.2386 2367 | +18.2376 +33.4038 | .4042| +33.4040

36 +19.6886 6863 | +19.6875 +10.8493 | .8510| +10.8502

37 | +19.7985 | -8004| +-19.7994 | —13.2732 | .2738| —13.2735

B98) a-23-4416 | 4410), --23:4473 *| 37287 || -7290'| 4- 3.7289

39 24.1886 1881 | +24.1884 +10.0280 | .0287| -+10.0284

49 | +25 9634 | .9639) +25.9637 | —34.9383 | -9338 | —34.9360

43 +33.9029 | .g006| +33.9018 + 6.8892 | .8907| + 6.8899

44 | +34.4765 | .4747| +34.4756 | 26.3112 | .3123| +-26.3117

ASS liso 7025) || - 7012) {38.7018 | —24.5497 | .5502) —24.5499

inves

Method of Reduction.

The measured codrdinates having been cleared of instrumental

errors, it remains to convert them into right ascensions and dec-

linations. For this purpose the following constants must be

known for each plate:

1°, The right ascension of the centre of the plate, in this case

the central star 15.

2°. The declination of the same star.

3°. The scale-value, or the number of seconds corresponding to

one space on the scale.

4°, The orientation correction, or the angie through which we

must rotate the coordinate axes in order that they may point

respectively in the directions of a parallel of declination and a

circle of declination through the central star. .

The first plan that suggested itself for determining these con-

stants was to employ the two existing heliometer researches upon

the group. In 1856 to 1858 Professor Winnecke of Bonn meas-

ured the position angles and distances of forty-four stars from

the central star 15; and in 1889 to 1892 Professor Schur of Got-

tingen triangulated thirty-eight stars and derived the places of

seven more by measuring the position angles and distances from

stars in the triangulation. The results of both researches were

published in one volume by Professor Schur, part IV of the

““ Astronomische Mittheilungen von der K. Sternwarte zu Gottin-

gen.”’ The stars whose positions are there given include almost

all those appearing on the photographs, and consequently very

accurate values of the four constants could be obtained by com-

paring the measured codrdinates of a large number of stars with

their heliometer places. Another plan is to determine the con-

stants by comparison with meridian observations. While this is

not as accurate as the preceding, it has the advantage of being

independent of the heliometer results, thus rendering a compari-

son with the latter more instructive.

The course that I have actually pursued is this: the constants

were first determined for each plate separately by comparing the

234

The Rutherfurd Photographs. 235

coordinates of some of the stars with meridian observations. For

a star which appears on all the plates we have thus eight determi-

nations of its right ascension, and eight of its declination, and a

catalogue of the group may now be formed by taking the means.

Finally a least square solution was made to determine how much

the constants would have to be changed on the average, so as to

secure the best possible agreement with the heliometer places.

It is evident that if we now apply to our catalogue positions the

corrections which result from these average changes in the con-

stants we shall obtain the same results as though we had used the

heliometer places to determine the constants for the separate

plates, and had then taken the means.

The meridian observations used are those quoted by Professor

Schur in the work mentioned above; they were used by him to

help fix the place of his triangulation in the sky. Five stars were

observed, the central star and four others distributed symmetric-

ally over the plate; they are admirably fitted for our purpose,

being at sufficiently large distances from the central star to insure

accurate determinations of the scale-value and orientation, and

yet not so distant as to have their photographic images much

distorted. Their magnitudes are such that they appear on all of

the plates with good images. The stars were observed both at

Berlin and Gottingen ;* the positions obtained at the former ob-

servatory and reduced to the A. G. catalogue system are as fol-

lows :

Star. Epoch. Equinox of 1890.0.

4 1890. 26 8531™28.5444, +19°39/007.65

5 51 22 OD) BS) AD) By BS) le

15 26 23 23.463 20 0955 .38

40 “51 35 90.573 19 39 04 .35

44 .26 35 33-417 20 33 03 .28

Each star was observed four times, and the probable error of a

single observation is given as

-£0.‘o12 in right ascension,

-o,//25 in declination.

At Gottingen each star was observed six times with these re-

sults:

* “ Astronomische Mittheilungen von der K. Sternwarte zu Gottingen,’’

Part IV, pages 139 et seq.

236 Presepe Group; Measurement and Reduction

Star. Epoch. Equinox of 18yo.0.

4 1891.52 8531™ 28.425, +19°38/50/.83

5 5a 22\ 02338805. 20) 358 27aeis

15 55 33 23-462 20 0955 .52

40 .89 35 00.607 19 39 04 .03

44 .89 35 33-447 20 33 03 -40

Giving these observations the weight 3,and those at Berlin the

weight unity, as was done by Professor Schur, we get finally :

Star. Epoch. Equinox of 1890 o.

4 1890.58 8531™ 28.440, +19 39/00”.45

5 72 32 02.366 20 35 28 .26

15 .58 33 23-463 200955 .42

40 .86 35 00.582 I9 39 04 .27

44 .67 35 33-425 20 33:03 31

As the epochs of these observations are from thirteen to twenty

years later than the dates of our plates, it is necessary to apply

proper motions, for which the following values have been

adopted :

4 —0.50054 +0/’.007

5 —0. 0005 +o .038

15 —0O, 0049 +o .017

40 —0. 0040 +0 .OII

44 —O. 0044 +o .015

These are the values given by Professor Schur in his catalogue

‘of the group, but they are not derived «(lirectly from a comparison

of his places with those of Winnecke. Systematic corrections

have been added to make the proper motion of the group as a

whole conform with observations by Bradley and by Tobias

Mayer; these corrections are:

—0.*0003 -+07’,039.

The necessity for such a large correction in declination is ac-

counted for by Professor Schur, by assuming that either in the

Bonn or in the Gottingen observations, or perhaps in both, the

declination of the group as a whole was incorrectly determined ;

we shall have occasion to refer to this circumstance later.

The plates were taken at practically only two dates, 1870.3 and

1877.3; applying the corresponding proper motions to the mer-

idian observations and reducing them to the equinox of 1875.0,

we get:

of the Rutherfurd Photographs. 237

For Plates I, II, III and IV,

da. ; Ad

Ae NW 2354 ISO!

5 —1220 .23 +1531 .02

15 fo) oO

4o +1459 .38 —1849 .36

44 +1948 .13 +1399 .16

My do

15 128°07/55/.26 +20°13/01”.26

For Plates V, VII, VIII and IX,

da Ad

4 —1723”.40 —1856”.81

5 —1219 .75 +1531 .17

15 oO o)

40 -+1459 .48 —1849 .40

44 +1948 .19 +1390 .15

My do os

15 128°07’51”.75 -+-20°13/01”. 38

4a and 4d are obtained by subtracting the right ascension and

declination of Star 15 from those of the five comparison stars.

The numerical work in the problem before us, namely, to deter-

mine the constants of the plates, will be greatly decreased by first

assuming an approximate scale-value and then determining how

much this is in error. Such an approximate value is furnished

by the reduction of Rutherfurd’s photographs of the Pleiades

where it was found that

I millimetre = 52.87

Let us suppose that this scale-value has been applied to the

measured coordinates « and y of each of the comparison stars,

giving X and Y; then the quantities X sec 0, and Y will be nearly

equal to the corresponding da and 40d respectively. The causes

of difference are the following :

a. Transformation Corrections (see below), Refraction, Pre-

cession, etc.

b. Orientation, use of incorrect scale-value, ete.

c. Errors of observation, both in the measured coordinates and

in the meridian places.

Let us first consider the causes of difference under a; we shall

then determine the orientation, true scale-value etc., by comparing

the corrected codrdinates with the corresponding values of da

ANNALS N. Y. ACAD. ScI., X, May, 1898—15.

238 Prexsepe Group; Measurement and Reduction

and 40d, eliminating the errors of observation as far as possible

by means of a least-square solution.

I. TRANSFORMATION CORRECTIONS.

An astronomical photograph may be regarded as a central pro-

jection of a portion of the celestial sphere upon a tangent plane.

The point on the plate which corresponds to the point of tan-

gency is the foot of the perpendicular let fall from the optical centre

of the object glass upon the plane of the plate. The rigorous re-

lations between the rectilinear codrdinates referred to this point

as origin, and the right ascension and declination of a star, were

given in simple form by Professor Turner in Vol. XVI,-of “ Ob-

servatory,” page 374. Previous to this, however, Ball and Ram-

baut gave these relations in the form of series in their paper “ On

the Relative Positions of 223 stars in xy Persei,” Transactions of

the Royal Irish Academy, Vol. XXX, page 247. In our notation

these formulas would be

Aa— X sec 6) = (X sec 4) Ytand,—4 (Xsec 5))? + (Xsec 0) Y tan? d,

Ad —Y =— }(Xsec 0)? sin 20, —$ V3— 3 (Xseed))? VY

The elegance of these formulas lies in the fact that the coefticients

of the powers and products of X and Y, are functions of 6, only,

and are therefore constant for a plate, or indeed for an entire

zone. For most plates these series are sufficiently accurate, but

when the declination or the measured coordinates are large they

fail; in such cases we do not need to resort to the rigorous for-

mulas but we have ‘merely to extend the series to higher terms,

as was done by Professor Jacoby in a review of a paper by Pro-

fessor Donner, in the Vierteljahrschrift for 1895, page 114. In

the same place, formulas are also given in which Jaand 4d appear

in the second members, instead of X and Yas above. Omitting

terms of higher degree than the third, which is permissible for the

Presepe plates, these formulas may be written

Aa — Xsec6,= Aa - Ad - tan d, —4 4a? (1 —3 sin? d,)

46 — Y=—+} 4Aa?- sin 2 6, —} Ae”: Ad - cos 26, —¥ A083

The use of these formulas presupposes a knowledge of the ap-

proximate values of 4a and 4é for each star. They possess two

points of advantage over the inverse forms: first, there is one

term less in the expression for 4a — X sec 6,; and second, they

give slightly more accurate values for the corrections as they do

of the Rutherfurd Photographs. 239

not involve errors of orientation, scale-value, etc., such as would

be incurred through the use of the measured X and Y in the sec-

ond members. I have therefore used the latter expressions for

computing the transformation corrections given in Table VI, em-

ploying the heliometer values of da and 40 given by Professor

Schur. It will be remembered that Rutherfurd was careful to

make the central star 15 coincide with the foot of the perpendicu-

lar let fall from the optical centre of the object glass upon the

plane of the plate. As our measured coérdinates are referred to

this star as origin, Table VI applies equally to all the plates.

TABLE VI.—TRANSFORMATION CORRECTIONS.

Star. Aa—X sec 6 As— VY Star. 4a— X see 8p As—Y

ze “i Mt “é

I —2.83 —3.01 24 —0.85 —0.22

2 0.66 —2.80 25 —0.34 —0.26

3 +3.15 —2.58 26 —1.60 —0.23

4 +5.75 —2.23 27 —Oo 4I —o.28

5 —3.33 —I.22 28 0.23 —0. 29

6 —I.31 —0.77 29 + 1.68 —0.36

7 +1.49 —0.52 31 —I.O1 —0.35

7A -+o.21 —0.27 32 —2.92 —0.39

8 —o.84 —0.29 33 —3.08 —0.53

10 +0.36 —0.23 34 —0.34 —0.65

our +-0.60 —0.19 35 +3.24 —o.89

14 —0.02 —0.OI 36 +1.13 —0.98

15 0.00 0.00 37 —I.41 —0.97

16 —o.16 +0.05 38 +0.45 —1.38

17 —0o.20 —0.O1 39 +1.28 —I1.47

18 —0.31 —0.03 40 —4.84 —1.59

19 +0.54 —0.06 41 —I.24 —2.24

20 —0. 36 —0.04 42 —1.35 —2.54

22 -+0.51 —o. 10 43 +1.19 —2.89

23 +0.53 —0.15 44 +479 3.05

23A +0.67 —o.18 45 5}. 12 —3.66

II. Corrections ror REFRACTION.

Formulas for clearing rectangular codrdinates of the effects of

refraction were first published by Dr. Rambaut in the ‘ Astro-

nomische Nachrichten,” No. 3125. Professor Turner has shown

how these may be much simplified by employing the coordinates

of the zenith as projected upon the plate.* His formulas, how-

ever, will not serve in the transformation of rectangular codrdi-

nates into right ascensions and declinations unless we apply an

* Monthly Notices, R.A.S., November, 1893.

240 Presepe Group; Measurement and Reduction

extra correction for orientation. (See note at the end of this

paper.) The formulas that I have preferred to use are those given

by Professor Jacoby; * while these are not quite so simple as

those of Professor Turner, they take into account the orientation

correction mentioned. Let |

¢g = the latitude, + 40°44’ in this case.

0 — a,= the hour angle of the centre of the plate, from Table I.

6, =the declination of the centre, + 20°13/

=the constant of refraction, computed in the usual way

and then multiplied by €2 to allow for the increased refrangibility

of photographic rays.

Now let us compute:

tan N = cos (?— a) cot»

G = cot (¢,+ N)

H = tan (6—aq) sin N cosec (6) + NV)

MB (1 4-H?)

N= 2 (G—tan 6)) H see 4,

M, = 3(G- tan 4) H cos 6)

N, = B (1+ G?)

Then the corrections for refraction take the form:

Correction for X sec 0, = M, . X sec 6, + Nz: Y

os BL Y=M,:.Xseo+N,: ¥

The coefficients of X sec 6, and of Y in the second members are —

constant for an entire plate. We may then construct Table VII,

in which the number of the plate is the argument.

TABLE VII.—REFRACTION COEFFICIENTS.

Plate. Mz Nx My Ny

I. 0.006356 | 0.000017 0.0001T4 0.000349

Il. 0.000423 0.000042 0.000174 0.000375

Ill. 0.000404 0.000031 0.006153 0.000373

IV. 0.000523 0.000086 0.000255 0.000424

V. 0.000357 0.000015 0.000110 0.000354

VII. 0.000423 0.000042 _ 0.000174 0.000375

VIII. 0.00049I | 0.000074 0.000233 0.000404

IX. 0.000377 | 0.000023 0.000131 0.000360

All the coefficients are positive.

* Astronomical Journal, No. 387.

{+ Bulletin du Comité Permanent, I, 464; and Scheiner and Rambaut,

Astron. Nach. 3255.

of the Rutherfurd Photographs. 241

III. PrRecEssIon AND NUTATION.

These merely change the position of the axes to which the

group is referred; it follows therefore that their differential ef-

fect upon X and Y is simply to rotate the coordinate axes through

a small angle. When we determine the constants of a plate by

comparing the measures of some of the stars with their true posi-

tions, it is evident that we need apply no corrections for preces-

sion and nutation to the measures of the comparison stars. Thus

if we employ the places of the latter as referred:to the equinox of

1875.0, then the value for the orientation which we shall get will

include the necessary correction for precession and nutation.

On the other hand, if we correct the places of the comparison

stars for precession and nutation, then it would not only be

necessary to apply the resulting orientation correction to the

other stars, but we should also have to apply to them aeeieguel

corrections for precession and nutation.

IV. ABERRATION.

It was shown by Bessel* that aberration changes the position

angles around a point equally,and changes the distances by a

constant factor, no matter in what direction the distance is meas-

ured. Consequenily, as in the case of precession and nutation,

we need apply no correction for aberration to the measures of the

comparison stars, since the resulting orientation and scale-value

corrections will be appropriately modified to include its whole

effect.

Thus we see that the coordinates of our five comparison stars

need be corrected only for transformation and refraction. We

must bear in mind, however, that the orientation and the scale-

value which we shall then obtain are not the true values of these

constants: the former must be corrected for precession, nutation

and aberration, and the latter simply for aberration.

We are now ready to find the constants of the plates. Let

p=:the correction to the scale-value, so that the true scale-

value is 52’’.87 (1 + p).

r — the orientation correction, or the small angle through which

the axes are to be rotated in the direction of decreasing posi-_

tion angles.

* *¢ Astronomische Untersuchungen,’’ Vol. J, page 207.

242 Presepe Group; Measurement and Reduction

k — the number of seconds of arc of a great circle through which

the axes are to be translated in the direction of decreasing

right ascensions.

¢ =the number of seconds of arc of a great circle through

which the axes are to be translated in the direction of de-

creasing declinations.

The corrections to the rectangular coordinates arising from p

are then:

For X, +p:X

AG Carr Vek.

On account of the orientation corrections, remembering that r

is small, we have the corrections :

OSes aie OG

Finally, & and ¢ give the corrections :

For XxX, +k

A aC

Combining all these corrections, we have

For X, +t+p-X+r-Y+k

“ Y, +p: Y—r-X+e

Let us now compute n, and n, for each comparison star, from

the following equations:

n, sec 0, = X sec 0, plus corrections for transformation and

refraction, minus da.

nN, = Y plus corrections for transformation and refraction,

minus Ao.

Then for each comparison star we have two equations of the

following form from. which to determine p, r, k and c:

pX+r¥+k+nz=0

p¥ —rX+e+ n=0

Owing to the way in which the coefficients of the unknowns

are repeated in these equations we do not need to make the least

square solution in the usual manner, but as Professor Jacoby has

pointed out,* we may find the unknowns very simply. Thus, let

y = the number of comparison stars, and let us denote by square

. brackets the sum of v quantities.

* Monthly Notices of the Royal Astronomical adeicige May, 1896.

ey. “a

of the Puede Photographs. 243

Put

A—[EX]+[¥¥]—— ([4P+191)

C= [X- ne] +L ¥ +m] —= ([X] [ne] + [¥1l])

E=[Y-n.]—[X- my] —~ ({¥][n-]—[X][ny])

Then we have:

k —~([X]p+ [Y]r+ [n=]), with the weight, v — ee

c=—=((Fle—(XIr+im)), « « « o Bie

The following will be found a convenient check on the computa-

tions: the sum of the residuals for the right ascension equations

is equal to zero, and similarly for the declination equations.*

The above method of solution is rendered still simpler in the

present case, as we are going to use the same comparison stars

for all the plates. Hence all the terms in the expressions for A,

Cand £ are constant except those which involve n, orn, Thus,

selecting the codrdinates of the comparison stars from any plate

in Table V,and multiplying them by 52.87 we have, with suffi-

cient accuracy :

aXe We

4 —1620” —1850”

5 \ —I1I40 +1530

15 fo) fo)

40 +1370 —1850

44 +1820 +1390

Consequently, for all the plates,

* This is indeed a general check for any set of observation equations in

which one of the unknowns enters with a constant coefficient; if this unknown

is missing from some of the equations, then the sum of the residuals for those

equations in which it does appear is equal to zero. The theorem may be

easily modified to include the case of unequal weights.

244 Presepe Group; Measurement and Reduction

A = 20,080,000

C=[X- nme] +[Y + ny] — 86 [nz] + 156 [ny]

Bs [¥- nr] —[X- ny] + 156[nz] — 86 [ny]

C .

Lee 20,080,000 ’ weight, 20,080,000

E ce

UE Aneto 20,080,000

20,080,000

k=— 86p-+ 156r—o.20[nz]; weight, 4.96

e=+156p+ 86r—o.20[n,]; “ 4.96

It now remains to show how the right ascensions and declina-

tions of all the stars may be computed. The constants of the

plate give rise to the corrections:

For X secs, + p- Xsecd,+7r sec d,-¥+k sec J,

Sicha » +p-Y —r-X +e

The corrections for refraction are:

For X see 0p, + Mz - X seco, + Nz - Y

Soe ; + M,. X sec do, + N,: Y

We have still to add corrections for transformation, which vary

from star to star, but are the same for different plates. Now let

us define a, and 0, as the projected right ascension and declina-

tion respectively of a star, the true right ascension and declina-

tion being given thus:

a = a, plus the correction for transformation.

5 = 0, plus the correction for transformation.

Then collecting the corrections given above:

a,=(1+p+4+ M.) Xsecd,+(Nz+7 see 0) Y+ (aq +k see 4y)

Oh = sida Lil) 12 + (M,—r cos 6)) X sec Jy + (4) + €)

Hence, to get the projected right ascension and declination of

any star, the constants of the plate having been determined, we

need only compute the six coeflicients in the parentheses and per-

form the simple operations indicated. These coefficients, it is

needless to remark, are constant for an entire plate.

As an example of the above methods I have set down the de-

tails of the computations for the constants of Plate VIII.

of the Rutherfurd Photographs. 245

Right Ascensions.

Star 4 5 15 4o 44

% : (Table V), —30.6580 —21.5809 o +25.9804 +34.4505

X sec 0) = 52.87 sec 0) - 2, —1727.31 —1215.89 O 4-1463.77 +1940.98

M,- X sec 6): (Tab. VII),— 085 — 60 0 + 0.72 + 0.95

N,- Y: (See below), — om + 1.2 0 — of + O12

da—X sec 6): (Tab. VI), + 5.75 — 3.33 0 — 484 + 4.79

— da : (Page 237), +1723.40 -+1219.75 oO —1459.48 —1948.19

Nz SEC Oo : + 08 + 005 0 + 0.03 — _ 1.36

Me * + 080 + 005 0 + 003 — _ 1.28

Declinations.

Star. 4 5 15 40 4A

y : (Table V), —35.0520 +28.9675 0 —34.9240 +26.3259

== SAS Ge —1853.20 4 1531.51 fe) —1846.43 +1391.85

NV, :-X sec 6,: (See above),— 0.40 — 028 o0 + 0.34 +. 0.46

Ad — Y : (Table VI), = 2123) 1.22) 0 = 59 == 3105

— Ad : (Page 237), +1856.81 —I153I1.17 0 -+1849.40 —1I390.15

Ny : + 023 — 054 0 + 097. — 0.33

[X - n,] =—3650 [Y-: nz] =—3240 [nz] =—0%.40

[X-nm]=+ 980 [Ym] =—3510 [ny] =+ 07.33

p = + 0.000352 =£0,000030

r = -+ 0.000211 =£0.000030

k=-+ 0.08 =0.”061

e=-+0.%o01 0.061

Having found the constants, we may now proceed to get the

right ascension and declination of each star on the plate. For

this purpose wé compute the coefficients :

For Right Ascensions. For Declinations.

52.87 (I+ p+ WM.) see 0) = 56.3887 52.87 (1 +p+ N,) = 52.9100

N+ 7 sec 55 = +0.000299 M, —r cos 5) = +0.000035

a + & sec dy) = 128°07/54”.84 6) + ¢ = 20°13/01”.39

A slight change has been made in the two coefficients in the

first line, our formulas requiring (1+p+J/,) and (1+p+W,).

This change, however, merely amounts to combining two multi-

plications into one; thus, instead of first computing X sec 0, and

then multiplying this by (1+p+J/,), we may apply the factor

52.8711 + p+) sec 0, to x# directly. The formulas require that we

246 Prexsepe Group; Measurement and Reduction.

know X sec 0, in computing the correction to the declination,

but for this purpose we may use 52.87(1 + p+ M,) sec 4, - #, the

quantity which we have just computed and which is practically

equal to X sec 0, for this purpose. Similarly in the declination

we may compute at once 52.87(1 +p + NV).

Employing these coefficients for Star 7 we have:

Right Ascension: Declination :

x: (Tab. V), — 14.6960 y: (Tab. V), — 19.0252

52.87(1+p+W,) see 0):x :— 828./69 52.87(1+y+WN, )-y: — 1006.62

= — 13/48.69 = —16/46”.62

(N.+r sec 5))-Y: — 0.30 (M,—r sec 5,)- Xsec dy :— 0.03

a)+k sec dy : 128°07 54 .84 ° dote: +20°13 oI .39

qq = 127°54/05”.85 0 = +19°56’14”.74

These give the projected position; the true right ascension and

declination are found by adding the transformation corrections

from Table VI, giving:

@ == 127°54/7".34 , 0 — + 19°56" 14”. 22,

which are corrected for refraction, precession, nutation and aber-

ration, and are referred to the mean equinox of 1875.0.

Vv.

Results.

Least-square solutions entirely similar to that given in detail

in the last section lead to the following values of p, 7, etc., for

the various plates :

ConsTANTS OF THE PLATES.

Probable Probable

Error of Error of

porr. kore.

0.000037 =£0.075

45 0.092

22 0.066

4I 0,082

22 0.044

24 ==0.049

30 0.061

24 0.048

+0.001054

+ 844

409

1435 |

211

326

be Ht He He He Ut H+ He

The average probable error of p or r is

0.000032

which corresponds to an uncertainty of about o/’.06 in the codér-

dinates of the outlying stars. The great diversity in the values

of ris due in small part to corrections for precession, nutation

and aberration, but chiefly to the accidental position in which

the plate was inserted in the measuring machine.

The following are the residuals for the five comparison stars,

used in computing the values of p,r, and ¢ given above.

Residuals from the Right Ascension Equations:

Plate. Star 4, Star 5. Star 15. Star 40. Star 44,

I 0.00 +0.03 —oo! +6.07 ~ —o.09

II — .24 + .31 — .18 + .42 — .31

Iil — .14 + .20 — .23 + .28 — .II

IV — .19 ais (TR .00 + .39 — .33

V — .OorL + .13 — .06 + .25 — .31

VII — .07 + .09 + .02 + .14 — .18

VIII — .08 + .05 + .08 + .21 — .26

IX + .10 — .09 — .06 + .12 — .08

Means, — .o8 + v.11 — .06 + .24 —.2I1

247

248 Presepe Group; Measurement and Reduction

Residuals from the Declination Equations:

Plate. Star 4. Star 5. Star 15. Star 40. Star 44.

Hi —o.1 B 40.20 40.0 I akg 10 —o.18

II — .03 +. .20 — .15 + .II — .13

Til — .07 SE gil — .06 + .16 — .16

IV — .00 + .23 — .04 + .07 — .26

Vi — .09 + .34 .0O — .oI — .24

VII — .10 + .22 — .04 + .08 — .16

VIII — .08 + .25 + .o1 + .04 — .22

IX — .02 + .23 — .O1 + .03 — .23

Means, — .06 + .22 — .03 +. .07 — .20

Employing the constants in the manner described at length in

the last section, we obtain the quantities a, and 0, which have

been tabulated in the following pages. It will be remembered

that a, and 0, are the projected right ascension and declination of

a star respectively ; the transformation correction being the same

for all the plates, may just as well be applied to the means;

and it is evident that this procedure does not affect in any way

the comparison of the right ascensions or declinations of a star

as derived from different plates. The columns headed “ At Epoch

of Plate” give the codrdinates uncorrected for proper motion.

The calculation of the latter is very simple in this case as the

plates were taken at practically only two dates, 1870.3 and 1877.3;

hence the annual proper motion is obtained by subtracting the

mean of the places on plates of the earlier date from the mean for

the later date, and dividing the difference by 7. The columns

marked “ P. M.” give the correction for proper motion necessary

to reduce the place of the star to the epoch 1875.0.

Probable errors are given for the right ascension and the dec-

lination of each star, and also for the proper motions; they were

calculated thus :

Let m = the number of plates of date 1870.3 on which the star

| was measured.

nm = the number of date 1877.3.

[vv] =the sum of the squares of the residuals obtained by

subtracting the mean from the separate observations

reduced to the epoch 1875.0.

Then the probable error of a quantity having the weight unity

IS =

of the Rutherfurd Photographs. 249

0.6745 Va

The weight of a right ascension or a declination at the epoch

1875.0 is

4gmn

22.1m-+ 5.3”

For a proper motion the weight is

49mn

m+n

Most of the stars appear on all eight plates ; for such we have

simply,

Probable error of a, or of 0, = =£0.103 V [vv]

““ of proper motion = 0.028 V [vv]

Two of the stars were observed only on plates taken in 1877,

and consequently it was not possible to reduce them to the epoch

1875.0 by using proper motions determined from the plates them-

selves, as has been done for all the other stars. The proper mo-

tions used for these two stars are those given by Professor Schur

on page 208 of his memoir, and are as follows :

Star. P. M. in Right Ascension. P. M. in Declination.

AI —0o”.042 +0”.012

42 —o .066 +o .036

These were used for an interval of only 2.3 years.

250 Prexsepe Group; Measurement and Reduction

STAR I.

Right Ascension : Declination :

dank er At Epoch| At Epoch of At Epoch

Ypocn O oe wpoch oO

Plate. Boat 1875.0. Plate. BER 1875.0.

I | 127°35/31//.25 | —0’’.43 | 30’7.82 | 20°26/52’’.60 | +0/7.15 | 52/7.75

II BO) 80) P= 1B a7) 47\/+ .15 -62

Til 30 .94 |— .43 51 52 ape nl, .67

IV Bit gi |} == ofl a7 64)/+ 115 -79

V 30 .46|+ .21 .67 .84|— .07 Si

VII BONA ae .68 -79|— .07 ae

VIII BO eAS | =k .66 .60|/— .07 -53

Ix RO PA Se wit 43 .90|— .07 83

Mean, 127°35/30//.61 Mean, 20°26/52//.71

Probable Error, =E.041 Probable Error, +.026

Proper Motion, —0.09I 0.011] Proper Motion, -+-0.032 0.007

STAR 2.

Right Ascension : Declination :

Plate.

E f AtE At Epoch of At Epoch

Ps Pia : Bo ait lee : Plates Bent 1375.0.

1 | 127°36/26/’.17 | —o’’.31 | 25’7.86 | 20°10’02/’.04 | +0’7.15| 2//.19

iQ | 26 .21 |}— .31 90 GG) IS uc 25

Til AS (68) |= oil oD .06/+ .14 .20

IV AS iy pT .84 -I4|}+ .14 .28

V 25 .74/+ «15 .89 .26|— .07 .19

VII 25 .65 | + .15 .80 422) ——s OW, .25

VIII 25 .60/+ «15 -75 -24|— .07 G7

IX 25 .7I | + «415 .86 -40}/— .07 3Be

Mean, 127°36/25/7.83 Mean, 20°10/02//,23

Probable Error, =£.018 Probable Error, -E.015

Proper Motion, 0.066 0.005} Proper Motion, -++0.03I =-0.004

of the Rutherfurd Photographs. 251

STAR 3.

Right Ascension : Declination :

At Epoch of At Epoch At Epoch of

Plate. at 1875.0. Plate.

Tee 2o 20 4 : 19°57/10/7.51

.50

-49

++44 | |

Mean, 127°37/27//,66 Mean, 19°57/10/",43

Probable Error, ==OR2 Probable Error, = 021

Proper Motion, —o.081 --0.009] Proper Motion, +-0.002 0.006

STAR 4.

Right Ascension: Declination :

‘ieee At Epoch of AtEpoch| At Epoch of ‘At Epoch

i t tk

Plate at Mh ate eee | hia7a08 Binte.. | eee 1875.0:

I} 127°39/06/7.16 | —0’’.29 | 5/7.87 | 19°42/06/7.67 | +-0/’.01| 677.68

II .92 |— .29 .63 .72|+ .O1 3773}

IiI 6..04.|— .29 75 .68}+ .or .69

IV 5 .97|— .29 .68 -74\-+ .o1 275

V 5 .60|;+ .14 74 .66 .00 .66

VII 5 Gl cts bil .68 -70 -00 -70

VIII 5 .52;/+ .14 .66 d7/Ghi| 00 73

Ix 5 .71|+ .14 285 .77|— .O1 .76

Mean, 127°39/05/’.73 Mean, 19°42/06/7.71

Probable Error, =£.024 Probable Error, =+,010

Proper Motion, —0o.06I1 +0.007 | Proper Motion, -+0.002 0.003

2 Presepe Group; Measures and Reduction

STAR 5.

Right Ascension : Declination :

AtEpochof | py |AtEpoch| At Epoch of

Plate. | | 1875.0. Plate.

20°38/33/7.84

33-71

33-64

33-74

3) SY |.

33-99

34 .O1

Mean, 127°47/38/7.41 Mean, 20°38/33//, 91

Probable Error, =£.022 Probable Error, =+.015

Proper Motion, —0.030 0.006 | Proper Motion, +-0.037 0.004

STAR 6.

Right Ascension : Declination :

At Epoch of p.m, |At Epoch] At Epoch of

Plate. 1875.0. Plate.

127°51/33//.81 | —0/’.32 | 33/7.49 | 20°25/33//.46

.66 HBP : .16

i aCe

97 “22

2AT, .16

-34 -16

.26 16

.20 .16

Mean, 127°51/33//.48 Mean, 20°25/33//.57

Probable Error, =+.031 Probable Error, ==.03i

Proper Motion, —o.069 =0.009| Proper Motion, -+-0.044 +0.009

of the Rutherfurd Photographs. 2538

Right Ascension : Declination :

At Epoch of _M. ch| At Epoch of At Epoch

Plate. 875.0. Plate. vk 1875.0.

127°54/06/7.35

6 .36

Mean, 127°54/06/7,00 Mean, 19°56/14//.74

Probable Error, +.025 Probable Error, ==.024

Proper Motion, —0.07I 0.007 | Proper Motion, —o0.006 +-0.007

Srar 7A.

Right Ascension : Declination :

At Epoch of p.m, |AtEpoch| At Epoch of

Plate. | 1875.0. Plate.

127°57/58//.00 | —0/’.47

Fo. .26) || 47

7 OE, |) eee 82 57 F 61

Sa lae 622 F 34 : 38

Mean, 127°57/57//.66 Mean. 20°09/42//.50

Proper Motion, —o.100} Proper Motion, —0.019

ANNALS N. Y. ACAD. ScI., X., June, 1898—16.

254 Presepe Group; Measurement and Reduction

Star 8.

Right Ascension : Declination:

po) TE araain a At Ep ch| At Epoch of At Epoch

| ocnh o

pet | ea Megs) Maint | eas |S

I | 127°57/50/7.38 moe 34 | 9/704 | 20°26/12’7_54 | —-o-i2) aaa

II 59 .38 | 34 | .04 51;/+ .12 .63

III 59 .64 | — .34 | 30 (031) = aera -75

IV 50) dl Pa 84) .08 69 + .12 .81

V 59 .08 |+ .17 n25 -79)| = "sao SWB

VII 58 .90 | + .17 | .O7 .69 — .06 63

VIII ie) ol) | SS | 03 -70|'— .06 .64

IX SS. Os bar oy | 5 .88;— .06 .82

Mean, 127°57/5Q//.12 Mean, 20°26/12//,71

Probable Error, =£.028 Probable Error, aE O22

Proper Motion, —0.072 0.008 | Proper Motion, +-c.025 +0.006

STAR I0.

Right Ascension : Declination :

oo Ena | |AtEpoch| At Epoch of At Epoch

| |

T | 127°58/48/7.65 =e 19 | 4877.46 | 20°06/50/7.40 | --0/7,14 50/7254

II -76 19 | 57 -33 | ee ta -47

III 83 |— .29| 64 :27)|\—- oar 41

IY 77 \— .19| .58 ~34.| 20) Sa eee

Vv 47 )+ .09 56 52) =o 45

VII 34 |-F .09 | -43 -58.|-— >) Oral .51

VIII 427) 09) 51 -48|— .07 4I

IX 67 | + .09 | .76 .56 | — .07 -49

| | |

Mean, 127°58/48/7,.56 Mean, = 20°06/50/7.47

Probable Error, E=O25 Probable Error, =E.012

Proper Motion, —o.040 0.008] Proper Motion, -++0.029 0.003

of the Rutherfurd Photographs. 255

STAR II.

Right Ascension : Declination :

Bade SOAGwpocn of |At Epoch} At Epoch of | | At Epoch

pines eee) BIGIONO, pinta | |e Y a eeroto:

| |

I | 127°59/36/".89 | —0/’.35 3677.54 | 20°01’46/’.90 | +0/’.10 | 47//.00

Il 36 .86 — _ .35 51 46 .86/+ .10|46 .96

III RS) O16) pS) | .61 46 .80/+ .10}| 46 .90

IV AG; Ol) |J—— BS | 73, 46...76|-+- .10|46 .86

V 20) .63) |) . 17 80 46 .95 — .05| 46 .90

VII BO) oO a ey 53 46 .96 — .05|46 .o1

VIII 260-40) | a a7 57 46 .83|— .05|46 .78

IX | AS AS) ae aly/ 46 AG. TO) | OF, Ap ake

| | | | |

Mean, 127°59/36/7.59 Mean, 20°01/46/7.93

Probable Error, =E.032 Probable Error, ==. 027,

Proper Motion,

—0.075 -£0.009}| Proper Motion, +-0.02T --0.008

STAR 14.

Right Ascension : Declination :

Mame! | At Enoch of At Epoch] At Epoch of | | At Epoch

och o oc och of | Ep oe

Plate. Ee Me 1875.0. Plate. | eee | 1875.0.

| | |

NA 6928°0 7745/06) |) O77 20) "A477 SGN 20°31/26/ 4.10 | Oks) 29/7;23

1g 44.81 |— _ .20) 61 29 .0O0|-+ .13| ae

IDOE 44.98 |— _.20 | -78 2805288 | seeks | OL

IV A5 315 | —, .20 .95 20 Oley 14

V 44 .82|}+ .I0 .92 29 .07|—_ +.06| .OL

VII Ade 60) || 5) Sos -70 29 .I9 — .06 5a

VIII 44.75 |-- .I0 85 29.23, — ~.06) a1

IX 44 .64|;+ .I0} -74 29 .26/— .06) -20

| | | | |

Mean, 128°07/44// 80 Mean, 20°31/20//.13

HACE IONE Lae, mor Probable Error, =+.022

Proper Motion,

—0.042 --0.009] Proper Motion, +-0.027 -£0.006

256 Prexsepe Group; Measurement and Reduction

STAR 15.

Right Ascension : Declination :

tcl Iemeoetase [At Epoch] At Epoch of At Epoch

Fate, (0 (ieee oe sarees Plate | oh ie Biae

I | 128°07/55/’.19 | —0’’.25 | 54/”.94 | 20°13/01/’.26 | +0/7.12| 1//.38

II BOOT ta 225 | 4uenoe Ir;/+ .12 22

Til Bi (O28 ia a Sy) a .20)| +) 212 22

IV 55 .26)— .25/55 .o1 .23/-+-+ «12 35

W BA 74) =) fre | 54386 .39|— .06 33

VII SAS Tol oe Ck2| 54s .34|— .06 28

VIII 54 .84|/+ .12/54 .96 .39|— .06 38

IX 54 .69 | + -13 | 54 82 .37/— .06 ail

Mean, 128°07/54//,88 Mean, 20°13/01// 32

Probable Error, == O22 Probable Error, B= Ole

Proper Motion, —0.054 --0.006} Proper Motion, ++0.025 +0.003

STAR 16.

Right Ascension : Declination :

At Epoch of | _M. |AtEpoch} At Epoch of

Plate. 1875.0. Plate.

128°08/44/7.80 -34 | 4477.46 | 19°42750//.00

50 .08

49 .91

49 .85

49 -97

50 .00

AQ -95 |

50 .08

Mean, 128°08/44// 48 Mean, 19°42/49/7. 99

Probable Error, =.028 Probable Error, =E.021

Proper Motion, —0.073 -+0.008} Proper Motion, ++-0.006 0.006

of the Rutherfurd Photographs.

STAR 17.

257

Right Ascension :

Declination :

Plate.

Se | 2 Me eecaee| Augen er |, Pian: | At econ

I | 128°10/05/7.46 | —0’’.27 | 5/’.19 | 19°48/46/’.81 | +-07’.09 | 46’’.90

II Bl > 327 || AL OO .83|/+ .09 .92

Il 5 .26|/— .27/ 5 .0o9 .8r;/+ .08 89

IV 5 oF |= 27 | Seo 75|/+ .08 83

V Sn O2) |= 2 Tats. LO .88|/— .o4 84

VII GE OO) te eT StS) |. T9 .g0|— .04 .86

VIII Fee Ole ates Ay espns LA .93/— .04 .89

1x A SS [a= il || ah sy) 39s) to 95

Mean, 128°10/05//,12 Mean, 19°48/46/’.89

Probable Error,

Proper Motion,

—0.058 =£0.010

=k.035

Probable Error, =-.O1I

Proper Motion, +-0.018 0.003

STAR 18.

Right Ascension : Declination :

fae TR Aniicien of | At Epoch| At Epoch of At Epoch

| t

Mili eine ee Ul ier: Pinte | «Meee ele ie7sios

IE |) Weare ee Si (—0!.22 32//.22 | 19°59/31/7.64 | +-0//.10 | 3177.74

II BA PAS) || = 2D BD OVil -53/-+ .I0 63,

Ill 22) (20 = sei | Bit “eye .44/-+ .10 54

IV 62 2S = al | BD AO .48|/-+- .10 58

V 32h7.05))| 1) Blu sen. 16 -74|— .05 .69

VII 3-95 | +) Le ise), .06 .60;}— 05 655

VIII 2a) SOM a gate | 2a aii .64/— .05 59

IX Bila SON cata wal len leayline 7 .69}/— .05 64

Mean, 128° 11/32//,08 Mean, 19°50/31//.62

Probable Error, =—.024 Probable Error, =£.019

Proper Motion,

—0.046 -0.007| Proper Motion, +0.02T 0.005

258 Presepe Group; Measurement and Reduction

STAR 19.

Right Ascension : Declination :

Plate.

At Epoch of | p.m, |AtEpoch| At Epoch of P.M. | At Epoch

Plate. es 1875.0 Plate. : 1875.0.

Il | 128°r1736/%.06 eas 135/781 | 20°35’50/.68 | +0//.09 | 50’7.77

64 |

IV | 36.37 |—. .25 | 36) exe 4 09 73

V 35 .95 | + .12|36 .07 .69 — .04 65

VII 35 .86|}-+ .12|35 .98 .87|— .04 .83

VII 35. .72.| 4-12) | 350 04 .82/— .04 .78

Mean, 128°11/35/7.96 Mean, 20°35/50/’.75

Proper Motion, —0.053| Proper Motion, --0.019

STAR 20.

Right Ascension : Declination :

At Epoch of |At Epoch| At Epoch of At Epoch

Bigg of | pm igen] at Bpoeh of | me AIS

T | 128°11/51/7.88 | —0o/’.20 | 51/7.68 | 19°58/50/’.40 | +077.08 | 50/7.48

II | il hes -20 | 57 .42\|+ .08 -50

III 47/5) (== 1D)! 55 ~ .39/+ «08 47

iy -77.|— .20 | .57 -40|-- .08 48

Vv .49 |-+ .I0| 59 -50)| —) 04 -46

VII 42 |}-+ 10) 52 ay |= Ou Rag

VIII 51 |-+ .I0| .61 50 — .04 46

Exe 58 | -- TO | .68 68 — .04 -64

Mean, 128°11/51//,60 Mean, 19°58/50//.48

Probable Error, +.016 Probable Error, _=£.023

Proper Motion, —0.042 -+0.004| Proper Motion, +-0.016 --0.006

of the Rutherfurd Photographs. 259

STAR 22.

Right Ascension : Declination :

mace | SAcrpeen of | At Epoch| At Epoch of At Epoch

oc |

elctes i Eo | 1875.0. Plate. Foe 1875.0.

I | 128°12/43/’.03 | —o/’.32 | 42/’.71 | 20°26/50/7.07 | +0/7.13 | 50’7.20

II AD $f) |= oA | 38 sal a= oii 25

Il 42 .98 |— _.32 .66 .0o4|/-+ .13 .17

IV | Aes (Os) | 42 .76 o4|/-— .13 oly)

Wel AD AS | ae tld | 52 .20|— .06 14

vali AD BR | olllS | -49 .20;/— .06 SIAL

VIII | 42.57 |+ .16) fe .35|/— .06 249)

IX | 42 .63 |-—- .16| 79 -28|— .06| —22

Mean, 128°12/42// 63 Mean, 20°26/50//,20

Probable Error, --.040 Probable Error, =£.015

Proper Motion, —o.068 0.011} Proper Motion, +-0.027 --0.004

STAR 23.

Right Ascension : Declination :

Pai Li Ae Rpock of At Epoch| At Epoch of At Epoch

t t

Plate. se lez 0! Place, | |e at | isva00.

I | 128°14/60/7.24 | —o/’.23 | 6077.01 | 20°34/39/7.08 | ++-0’/.19 | 39/7.27

15 59 .92 |— .23159 .69 38 .93|-+- 19 .12

Il 59 .8I |— .23|59 .58 38 .gI|-+ .19 .10

IV 60 .20|— .23|59 .97 38 .94|+ «19 ai}

Vv 58 8G | ar okt | Se) sold 39 .21;— .09 a2

VII BO) 254) |-a) = SEN5Q) 65 39) -18)|——) = .09 | .09

Vil BOM 7s) neha SO Oe 39 .18|— .09 .09

IX 59 .69 |+ .11 | 59 .80 39 .41|— .09 522

Mean, 128°14/50/7,81 Mean, 20°34/39/’.16

Probable Error, =.044 Probable Error, =£.025

Proper Motion, —0.049 0.012} Proper Motion, +-0.040 0.007

260 Presepe Group; Measurement and Reduction

STAR 23A.

Right Ascension : Declination:

So Pee eanaay oe a At Epoch | At Epoch of At Epoch

oc J; (og) 0c.

Plate. Ee We ieyetos Plate. | tet | sce

I | 128°15/57/7.80 | —o/’.32 | 57/.48 | 20°26/03’’.10 | +0/’.09| 3//.19

II -74.|— «32 42 2 .80/+ .09| 2 .89

III 7O || = 482 38 2 .0o|/-+ .09] 3 .09

IV .96 |— .32 .64 2° .96| 4-9 .6o)\ ar res

V AD Loe oi 58 oo) (= OH |) 2 05

VII 220 =) eho -A4 3 .09/— .05| 3 .04

IX .29;+ «16 45 2) .12)||— 054 aon

Mean, 128°15/57//,48 Mean, 20°26/03//.06

Probable Error, =.024 Probable Error, ==.022

_ Proper Motion, —0o.069 0.007} Proper Motion, --0.020 0.006

STAR 24.

Right Ascension : Declination :

ic sepa epock ce |At Epoch} At Epoch of

och Oo 2

Plate. pe 1875.0. Plate. ; ee

I | 128°16’58/7.57 | —o/’’.21 | 58/7.36 | 19°58/19/7.27 | +-0/7.07

II 58 .24|/— .21/58 .03 -16/-+ .07

Til 58 .57|— .21/58 .36 22|+ .07

IV 58 .67 |— .21/58 .46 Tet eOr

V GUC) | See oO S219) 29/— .03

VII Se 688) | ap) XO | 5/7 *.) 24) oO

VIII 58 .32;}+ .10|58 .42 27|— .03

IX 58 .38|}+ .10/58 .48 38|— .04

Mean, 128° 16/58//,30 Mean, 19°58/10//,26

Probable Error, + ,O51 Probable Error, -+.016

Proper Motion, —0.045 0.014 | Proper Motion, -+0.015 --0.004

of the Rutherfurd Photographs. 261

STAR 25.

Right Ascension : Declination :

|| At Epoch of At Epoch| AtE f |

t t h At Epoch

feet wits |} PPE mia o: Bite, |) Bones etree

| | |

He 25251722377, 03) —— O17, 25) 31/778 gope ne 37779) +-0//.07 | 36’7.86

II 7 On| 25 -45 .67/-+ .07/) 74

iit Bit esi | AG a2 60 | + 07 | 2677

IV 6 On |= 225) -70 . 6g | ge .07 | -76

V Ai, SEO NS oe -51 YS = oe .70

VII Bit Ezy Se gil -50 -82|— .03 -79

AVAL | 3r .38|+ «12 -50 -75|— -03| .72

IX Ait p59) |) Se ole 72 500) OA 82

Mean, 128°17/31/7,56 Mean, 20°07/36//.76

Probable Error, =—=.043 Probable Error, ==.016

Proper Motion, —0.054 +0.012] Proper Motion, +-0.015 0.004

STAR 26.

| Right Ascension : Declination :

Plate l

At Epoch of p.m. (|AtEpoch} At Epoch of le P.M. | At Epoch

Plate. 1875.0. Plate. | 1875.0

| |

Mees on 7 2374229027, 201 2OKaOR NL LO Wei oF | +0’. 03 20/7 .94.

II | 36 .92|— .30 .62 |/-+ .03/2I .o4

Til 36 .98 |— _ .29 .69 a & |-+- .03| 20 .86

IV Bi oie Il Gao .83 20 .76;-- .03/ 20 .79

We 36 .49|-+ «14 | 63 20 .82;/— .02| 20 .80

VIII | BIO Seat ols 94 20 .89'— .02)| 20 .87

Ix 36 .56|/+ «15 7D: 21 .09;— .02 21 .07

Mean, EASON TCS B77 5 Mean, 19°47/20//.91

Probable Error, =.034 Probable Error, =.028

Proper Motion, —0.063 =-0.009 | Proper Motion, -+0.007 --0.008

lor)

Presepe Group; Measurement and Reduction

STAR 27.

Right Ascension : Declination :

Pal tale ff | At Epoch} At Epoch of AtE

t h | t tE t h

Plate. | iene 1875.0. Plate. eo 1875.0.

| | |

T | 128°17/52/.80 | —o’’.17 | 52/7.63 | 20°06’36’7.49 | +0//.15 | 36’7.64

II 5B Solty .18 .67\/+ «15 .82

Tit 56 |— .16 .4c 5sol+ .15 65

IV yea") 2 LO 55 43/+ .15} 58

V 42 |}+ .08) .50 70|— .07 -63,

VII 34 |}+ .08 .42 73|— ..07 .66

VIII 30 |+ .08 -38 71 | —— | 207 .64

1X 39 |+ .08 47 86|— .08 78

Mean, 128°17/52//.44 Mean, 20°06/36/7. 68

Probable Error, =.037 Probable Error, =.022

Proper Motion, —0.035 0.010] Proper Motion, +0.032 +0.006

STAR 28.

Right Ascension: Declination :

POAC noch Ghia At Epoch| At Epoch of At Epoch

| t t

Biste,.. Mgt el asaton Plate. || 2 a ieee

I | 128°18/06/7.53 | —o’’.19 | 6/7.34 | 20°16/31//.01 | +-0/7.07 | 3177.08

II 26 |/— .19 .07 30 .96/+ .07/31 .03

iil AAD ero | .25 30) -79)|--) seO7ml eOmEOy

IV 58 |— _ «19 | 39 20 .93/-+ .07/3I .00

V 21 |}+ .09 -30 30 .98|— .03]|30 .95

VII .0o3 | + .09 st) 20) .97)/—— 7203) |Bomeo#

VIII .22/+ .09| nel 31 .08|— .03/31 .05

IX 22) + .09 | aout 31 .06/— .04]|31 .02

{ I 1

Mean, 128°18/06/7,26 Mean, 20°16/30/7,99

Probable Error, =+.030 Probable Error, =+.020

Proper Motion, —o.040 +0.008| Proper Motion, ++-0.015 --0.006

“—

of the Rutherfurd Photographs. 263

STAR 20.

Right Ascension : Declination :

ame | Tat Epoch of 'AtEpoch} AtEpoch of | "At Epoch

: oc | c J |

Bibi, oo) fous | 1875.0. Plates | | EoneD | 187508

| | i

I | 128°18740’’.95 | —0o’’.29 | 40/7.66 20/7.52 | -+0//.17 | 20/7.69

II Ao .52|— .29| .23 2a Jy | .48

III APS. | 26) 58 “On hee 17 57

IV 4I .08 |— .29 | -79 37) + 17 | 54

V go .50|/+ .14 -64 .48 — .08 .40

VII 4o .30|)-+ «.14} 44 71 |—— » -08 63

VIII AG oO | qe oll 64 .62 |— .08 54

IX 4o .38 |-+- - 14. | 52 81 | — .08 | a8

| | :

Mean, 128°18/40//_56 Mean, 20°37/20//.57

Probable Error, =+.046 Probable Error, =-.030

Proper Motion, —0o.062 0.012] Proper Motion, ++-0.036 0.008

STAR 31.

Right Ascension : Declination :

Bae. Ae Fuoct of ‘At Epoch| At Epoch of | | AtE

t |At Z t h

Pe Ue Miya cane AT Tnener ies aro (Atapte

| | |

I | 128°19/12/’.34 | —o/’.27 | 12/7.07 | 19°59/06/.84 | +0/7.10|} 6//.94

II 12S hee 7 Od SO) pete) |S 9 GMOS ers)

iD in .93)|—. .27/) EE .66 6 .93/-+ -10| 7 .03

V rae ey Pt 5re) ie a yP7l 6 .94/— .05| 6 .89

VIII TM BU) Mea) egy | 2 ahs) 6 .88|— .05| 6 .83

IX Iie Bo || Go gill ate BOYS) ii Sur SON OZ

Mean, 128° 10/11//,92 Mean, 19°59/06/7 92

Probable Error, == OAT Probable Error, O27]

Proper Motion, —0.057 -:o.o1I} Proper Motion, -++0.022 0,008

264 Prxsepe Group; Measurement and Reduction

STAR 32.

Right Ascension : Declination :

At Epoch of .M. |AtEpoch} At Epoch of p.m. |At Epoch

Plate. 1875.0. Plate. j 1875.0.

128°20/56//.93 : 5 19°38/06/7.20 | +-0/’.03 | 677.23

.02 : : 35 ba 16203

.98 28 | : I7/+ .03

.20 : : 05 03

-51 j ; .28 .02

.61 : : S27 .02

aq : . II .Q2

64 : : | 22 -02

Mean, 128°20/56//,76 Mean, 19°38/06//,22

Probable Error, =+.026 Probable Error, =+.028

Proper Motion, —0.059 +-0.007 | Proper Motion, -++-0.007 --0.008

Sma 23:

Right Ascension : Declination :

pert) ae peer ot AtEpoch| At Epoch of At Epoch

ie ee ae Plate. | Ee Me aya

I | 128°22/30/7.50 | —0//.34 | 30/7.16 | 19°40/09/’.34 | +0/7.04) 9//.38

i 30.37 |=. =34 | 30.03 Yi [aim Oe -61

III 30 .14 |— .34]| 29 .80 34/+ .04 38

IV 20 53 | ——, 234.1 30) 19 32; + .04 36

VII 29 .92 |+ .17| 30 .09 -50|— .02 48

VIII BO) 4OB | Se oH || BO aK) .29|— .02 2a

IX 29 .71|-+ .17/| 29 .88 -57|— .02 55

Mean, 128°22/30//.05 Mean, 19°40/09/7,43

Probable Error, == .048 Probable Error, ==.037

Proper Motion, —0.072 +0.013] Proper Motion, -++-0.009 -ko.o10

of the Rutherfurd Photographs. 265

STAR 34.

Right Ascension : Declination :

At Epoch of p.m. |At Epoch] At Epoch of At Epoch

Plate. 1875.0. Plate. i ae 1875.0.

128°23/08/7.33 | : 8/7.06 | 20°09/37’’.37

| 8

Mean, 128°23/08//_09 Mean, 20°00/37//.44

Probable Error, =£.029 Probable Error, =—.012

Proper Motion, —o.058 +:0.008] Proper Motion, +-0.022 --0.003

STAR 35.

Right Ascension : Declination :

plate At Epoch of | ‘At Epoch} At Epoch of | | At Epoch

peice Cree uibtemoedl o Piate. Mee Arh lynn

| |

T | 128°25/03/7.01 | —0’’.27 | 2//.74 | 20°42/28//.84 | +-0/’.14 | 2877.98

II 2 .92 |— .27 .65 28 .80|/-+ .14|28 .94

III 3 .04|— .27 oy 28 .86'+ .14|29 .00

IV 2B Oil D7 74 28 .82/-+ .14/28 .96

Vv | By fs |S 5s -gI 289-86) O7) | 29 879

VII 25S) | = eels 71 29 -I2|— -.07|29 .05

VIII 2 .59/+ .13 a2 29 .00|— .07/ 28 .93

JOx¢ 2 AT | ee EA 55 2OR ot = 07) | 29-10

Mean, 128°25/02//,72 Mean, 20°42/28//.97

Probable Error, =.028 Probable Error, =.025

Proper Motion, —o.058 -ko0.008} Proper Motion, -+-0.030 0.007

266 Prexsepe Group; Measurement and Reduction

STAR 36.

Right Ascension : Declination :

site At Epoch of At Epoch| At Epoch At Epoch

och 0 (0) och of oc

Plate. pat 1875. re Plate. ne | Bah 1875.0.

I | 128°26/25/7.18 | —0’7.45 | | oye. 2022252 7) | +0/7.16 | 35/7.89

II 25 ib) = 45 .69 -67 | | -f- .16 83

Il 25 0b] | Aa he 59 fe a5 -74

IV 25 .40 | — Ad | .96 .63)/+ .15 -78

Vil BUN 5S) | ae P| SI 11) |—= Ge .88

VIII | 2A Agana on -76 -78 | — .o08 7G:

IX | 24 .54 | + ca 76 92 | — .08 .84

Mean, 128°26/24//.78 Mean, 20°22/35// 81

Probable Error, =.028 Probable Error, =+.022

Proper Motion,

—0o.095 +0.007] Proper Motion, +-0.033 --0.006

STAR 37.

Right Ascension : Declination :

Fae At Epoch of At E h}| At Epoch of | At Epoch

oc och oO O¢.

Plate. i | Eat 1875. 0. Plat te. Ere 1875.0.

t282o67217eon le —o//.28 | ar 53 | 20°01’19/’.38 | +0/7.05 | 1977.43

II 61 23 | Ba 56 + 05 .61

Ill 250 | — 28 22 31|/+ .05 -36

IV 531) |= 25) | 61 .28|)-+ .05 aR

Vv 28 )+ .14 42 .42|/— .02| .40

VII .29;+ .14| -43 3G ha .03 31

VIII 232 |-+ .14| .46 49 — .03 46

IX .27 | + “14, -4I .58|— .03 o55

Mean, 128°26/31//.43 Mean, 20°01/10//.43

Probable Error, ==7082 Probable Error, =£.029

Proper Motion,

—0.059 0.006 Proper Motion, -+-0.011 +-0.008

of the Rutherfurd Photographs.

Declination :

Right Ascension:

Plate. |

Probable Error,

Proper Motion,

=E.031

—0.045 0.008

Probable Error,

Proper Motion, -+-0.016 --o.008

At Epoch of |AtEpoch | At Epoch of 7. | At Epoch

Plate. Be 1875.0: Plate. Be a arya,

I | 128°20/56/7.44 | —0!/,21 | 56/7.23 | 20°16/19/7.07 | 4-0’7.08| 19/7.15

ati ofa) | ea | QA | SAT Ig .16|+ } .08| 24

IV .66 | — .21 | -45 18 .93/+ .07 .0O

VII 17 |-+ .10| a Ig .0o8 — .o4 .O4 |

VIII 15 |+ .I0| 25 I9 .I7 — .0O4 mk

IX Beam eisd)|| .42 Ig .24|— .04 20

Mean, 128°29/56/7.32 Mean, 20°16°19/’.13

== .030

Right Ascension :

Plate.

| At Epoch of

Plate.

STAR 309.

Declination :

, |AtEpoch| At Epoch of uM. | At Epoch

Se metaysi: Plate. eee iee0)

I | 128°30/39//.00 |

—=617735)/ 307-05) || 209217527734 |

II SD | 25 337, SRM = Gir -4I

III 38 82 |— .35 | 47 .22/-- .07| -39

IV 30) OL |= 335 | .66 -24|/-+ .07 Bil

V 38.44) 17 61 .30'— 03 .27

VII 880533 eer ka 50 42, — .03 39

Vill Bye Gaevle alte | 51 -38 |—~_ .03 35

IX | oraeeyabaea) ally) | 50 56 = ery -52

Mean, 128°30/38/7.53 Mean, 20°21/52//.38

Probable Error, =k.027 Probable Error, =E.021

Proper Motion,

—0.075 =+0.008} Proper Motion, +-0.015 0.006

STAR 40.

Right Ascension : Declination :

Paw At Epoch of At Epoch| At Epoch of At Epoch

) 0c.

Plate. Day cern) Plate. | foal aes

I | 128°32/19/7.74 | —0’’.42 | 19/7.32 | 19°42/13/7.48 | ++0/7.05 | 137.53

II .92 |— .42. .50 .60/-+ .05 .65

Til st p= > A .36 65|/+ .05 -70

IV [O20 42 .50 541] = 85 59

V 14 |+ .21 “35 .67;/— .02 65

VII .22:|- 21 43 .65/— .02 63

VIII | .29-|-+ .21 | 50 .61;/— .02 59

IX 620) ||P se oflit 61/— .02 59

| |

Mean, 128°32/19//.42 Mean, 19°42/13//.62

Probable Error, == 020 Probable Error, =+.014

Proper Motion, ' —0.090 -ko0.006] Proper Motion, ++-o.010 -£0.004 |,

STAR 4I.

Right Ascension: Declination :

Ty dS ag poen ee | 'At Epoch| At Epoch of | At Epoch

At Epoch o pee poch o {poe

Plate. ie asiey Plate. | Be Me isgeos

VII | 128°06/08/7.44 | +07’. _ 877,54 | 20°06’21/7.68 | —0” Os) ari aes

VIII 20 a .IO .40 TO Se .03 75

Mean, 128°06/08//, 47 Mean, 20°06/21// .70

STAR 42.

Right Ascension : Declination :

re At Epoch of At Epoch| At Epoch of At Epoch

poch o : poe poch o Cie ale poe

Plate. | se 1875.0. Plate. = 1875.0.

VII | 128°38’00/7.16 | +-077.15 | | o0/”, 31 | 20°06/1677.46 | —o’’.08 | 16/7.38

VIII 59 .83 ioe 15 59 "98 .29|— .08 20

Mean, 128°38/00//,14 Mean, 20°06/16/7,30

of the Rutherfurd Photographs. 269

STAR 43.

A a

Right Ascension : pains ‘| Declination :

gD Aiciipoon of At Epoch |

och 0 | AtE

Plate. Bc cane miata cera

I | 128°3947’7.04 | —0/’.46 | 46’’.58 | 20°10/06/’.94 | +0//.03) 6/7.97

I AGES, AON ata 25 Tse onl) | So

Tit 46 .88|— .45 43 72|+ .03 78

iy) AZ, 05) —— 9-45 .60 56)+ .03 .59

Ne Ao =325)| =) -22 54 68 |= 2) 66

Vil 46 .27|)+ .22 -49 .82/— .02| .80

VIII AG -32)| 45-22 54 .95|/— .02 203

IX 46 .06 + -23 | -29 -74 | — .O2 2

Mean, 128°39/46/7.46 Mean, 20°19/06//.78

Probable Error, ==.036 Probable Error, =.035

Proper Motion, —0.097 -+0.010] Proper Motion, +0.007 --o0.010

STAR 44.

Right Ascension : Declination :

/ | oc e: och o oc

Plate. 4 Eee: 1875.0. Plate. | aes 1875.0.

I | 128°40/18/.28 | —o/’.23 | 18/7.05 | 20°36/14/’.23 | --0//.07 | 147.30

II iS 627 |/—=" 623 || 1S) (OA 133) == 207, .40

UI 1G Ale) p—= (22 | WS (27/ .31|/-—- .07 38

| IW iS 226 ||— 122) 18) -of4 .21\-+- .07 .28

Vv To) .O5 | Lhe o> «Lo .40'— .03 13a)

VII W7.O5 | -1-e aeenh LS .O0 -42|/— .03 .39

VIII 7) ey Se ett |) 77 “ees 36/— .03 nae

Ix 18 .o8 |-+ .11/18 .19 BR |= oul .29

Mean, 128°40/18//, 10 Mean, 20°36/14/’.34

- Probable Error, =—.027 Probable Error, a= O12

Proper Motion, —o.048 0.008} Proper Motion, +-0.015 --0.004

ANNALS N. Y. ACAD. Scr., X, June, 1898—17.

eed sats!

270 | Presepe Group; Measurement and Reduction

STAR 45.

Right Ascension : | Declination :

SH | PANNE DOENO At Epoch| At Epoch of At Epoch

poch o poe Epoch o poe

Plate. Ea 1875.0. ou

Plate. ; 1875.0.

II | 128°44/17/’.78 | —o/’.33 | 17/7.45 | 19°51/23/’.45 | +0//.08 | 23/7.53

.62 .38| + 8

Ill — .33 .29 .O .46

IV .98 |— .33 | 65 .22|/+ .08 Ako)

V 5208 |-|= 216 .42 -44);— .04 -40

VII 34 |+ .16 .50 .56;/— .04 52

Vill 39 |+ .16 55 -45|/— .04 -4I

Ix e230 |tat- 2) ak" 39 ‘43 | —) 8049) 39

Mean, 128°44/17/7.46 Mean, 19°51/23/.43

Probable Error, ae On Probable Error, a= .022

Proper Motion, —0.070 0.009] Proper Motion, -+-0.017 0.006

The final results of the measurements have been collected on

the next page; the right ascensions and declinations are ob-

tained from «a, and 0,, which are printed in the foregoing pages in

slightly bolder type, by adding the transformation corrections

given in Table VI, page 239. The magnitudes are those of the

Bonn Durchmusterung.

of the Rutherfurd Photographs.

271

Catalogue of the Relative Positions and Proper Motions of

42 Stars in the Priesepe Group.

Mean Equinox of 1875.0.

Epoch 1875.0.

fe) d al | dd fo) / My 4d |

I 8.8 127 35 27.78 —o.091 | +20 26 49.70 | +0.032 8

2 8.2 36 26.49 | — .066 | +20 09 59.43 | + .031 8

3 8.4 37 30.81 — .o81 | +19 57 07.85 + .002 a

4 Woe 39 11.48 — .061 | +19 42 04.48 | + .002 | 8

5 8.0 47 35.08 | | RO) +-20 38 32.69 |-+- .037 | 8

Geer 51 32.17 | — .069 | +20 25 32.80 + .044 8

FN NEKO) 54 07.49 — .071 | +19 56 14.22 | — .006 8

7A | 8.9 57 57.87 +20 09 42.23 4

8 9.0 57 58.28 —':072 | |} 20 20 12:42) -- 025 | 8

10 8.0 58 48.92 | — .o40 | +20 06 50.24 | + .029 | 8

II 8.8 127 59 37.19 — .075 | +20 or 46.74 |-+ .o2t | 8

14 8.0 128 07 44,78 — .042 | +20 31 29.12 | + .027 8

15 7.0 07 54.88 — .054 | +20 13 01.32 + .025 . 8

16 8.0 08 44.32 | — .073 | +-19 42 50.04 |-+ .cc6 | 8

17 U2 IO 04.92 | — .058 | +19 48 46.88 |}+ .o18 | 8

18 8.2 Il 31.77 | — .046 | +19 59 31.59 |-+ .o21 | 8

LOW i 9:0 II 36.50 +20 35 50.69 | eet

ZO Oi2 IX 51.24 | — .o42 | +19 58 50.44 |-+ .016 | 8

225780) °| I2 43.14 — .068 | +20 26 50.10 |}+ .027 8

23 7B) 15 00.34 | — .049 | +20 34 39.01 | + .o4o 8

23A | 9.0 | I5 56.81 — .069 | +20 26 02,88 | + .o20 8

24 | 8.2 | WS By | == ONG | Sele) Ge Mayon |e ons |S

25 8.5 | I7 31.22 — .054 | +20 07 36.50; + .o15 | 8

26 FIO) 4 I7 35.17 —.003 | +-19 47 20:68 | -- ‘oo7 | 8

27 Te 17 52.03 | — .035 | +20 06 36.40 | + .032 | 8

28 8.5 18 06.49 | — .of0 | +20 16 30.70 | + .o15 8

29) 1 8.8 18 42.24 | — 062 | +20 37 20.21 + .036 8

31 | 19 10.91 | — .057 } +19 59 06.57 | + .022 8

32 9.0 20 53.84 | — .059 | +19 38 05.83 | + .007 8

Ba 8.2 22 260.07 — .072 | +19 40 08.90 + .009 Fi

24. Fal 23 07.75 — .058 | +20 09 36.79 + .022 8

35 8.7 25 05.96 — .058 +20 42 28,08 | + .030 8

36 9.0 26 25.91 — .095 +20 22 34.83 | + .033 7

37 TPs 26 30.02 — .059 | +20 or 18.46 + .oII 8

38 9.0 29 56.77 — .045 ! +20 16 17.75 | + .016 6

39 8.6 30 39.81 = 075 || q-20 2 Gesehe | a= yeuss 8

40 8.7 32 14.58 — .090 +19 42 12.03 + .o10 8

4I 9.5 36 07.23 +20 06 19.46 2

42 9.3 37 58.79 +20 06 13.76 2

43 75 39 47.05 | — .097 | +-20 19 03.89 | -- .007 8

44 8.9 40 22,88 — .048 | +20 36 11.29 | + .o15 8

45 8.4 | 128 44 12.34 | — .o70 | -+-19 5I 19.77 | + -.O17 7

Vin

Discussion of Results.

Let us first ascertain what is the probable error of a measured

coordinate, being careful not to let personalities in the observing

enter into our result. Hach codrdinate was measured completely,

that is in both the direct and in the reversed positions, by two

observers. The difference between the two complete measure-

ments will be free from personalities and may be ascribed

to errors of observation. This difference, which I shall call v,

may easily be computed from Table III; say the two observers

are Schlesinger and Kretz, then subtract (S—) direct, from

(S—K) reversed and the difference is double the amount by which

one observer’s complete measurement differs from the other’s, or

2v. The probable error of a final coordinate is then given by,

4-0-6745 4 |[ev]

ne 2 n

Proceeding in this way for all the plates we obtain the follow-

ing probable errors. Only those stars were used, thirty-three in

number, which appear on all the plates.

Probable Error of a Probable Error of a

final z. final y.

Plate I =£0/7.034 =-0/7,031

II .036 .029

II -023 .023

IV .024 .020

Vv .020 .027

VII .034 .020

VIII 032 .025

Ix .037 5027)

Means, ==0// 030 -£0/7,025

The greater uncertainty in right ascension is due to the fact

that the images are usually elongated in that direction and

are therefore more difficult to bisect. The elongation was caused

by the failure of Rutherfurd’s clock to keep pace exactly with

the diurnal motion of the group, sometimes lagging slightly or

sometimes moving too rapidly.

272

The Rutherfurd Photographs. 273

In the tabulation of results the probable error of each right as-

cension and declination is given. We may compute the prob-

able error of right ascension of a star as derived from a single

plate by the expression

-EO, 674s fer = C08 Oo

where [vu] is the sum of the squares of all the residuals in right

ascension for the thirty-three stars which appear on all eight

plates; the factor cos 0, serves to reduce the probable error to

are of a great circle. The expression for the probable error of a

single declination is identical with the above except that cos 6,

is omitted. In this way we obtain the probable errors,

In Right Ascension. In Declination.

=£0/7,081 =£0/7,058

If we do not confine ourselves to the thirty-three stars as above,

but use all the stars, we get

-—0’’.080 +0//,060

Thus it appears that the uncertainty in a right ascension or in

a declination is considerably greater than that in the correspond-

ing measured codrdinate. We may conclude from this that when a

large number of plates is available, better results will be attained,

for a given expenditure of time oe labor, by measuring a ee

number of plates rather than measuring a few with all the

elaboration used in the present research. But for the Ruther-

furd photographs such elaboration is amply justified by the very

limited number of existing photographs of so early a date.

It might appear at first as though a large part of the discrep-

ancy between the two sets of probable errors, namely, those for

the measured coordinates, and those for the resulting right ascen-

sion and declination, could be accounted for by the uncertainty

of the constants used for the several plates. That such is not the

case appears from the following considerations: the residuals

for the five comparison stars, given on pages 247 and 248,

exhibit a remarkable uniformity, showing that the greater part

of these residuals is due to inaccuracies in the meridian observa-

tions. It follows, therefore, that the probable errors given for

the constants p,7r, and c, are due not so much to errors in

274 Presepe Group; Measurement and Reduction

measuring the plate as to errors in the meridian places. To ob-

tain more precise information on this point, let us correct the

meridian places of each of the comparison stars by the mean of

the residuals for that star, and suppose we have effected thes leat-

square solutions anew, using now the corrected meridian places.

It can easily be shown that the new solutions would lead to ex-

actly the same values of the constants as had been first obtained,

but now each residual will be altered by a certain quantity,

namely, the amount of the corresponding correction to the mer-

idian place. We may then subtract at once the mean of the re-

siduals for a star, from the corresponding residual in each least-

square solution and then compute the probable errors of the

constants. The results of such a computation are as follows:

Probable Error of Probable Error of

p Orr. kore

Plate if -+0,0C00T3 -+0’’.026

Il 24 .049

III Igy .032

IV 16 .032

V I5 .030

VIL 08 .O16

VIII II .022

IX 20 .O4I

Means, 0.000015 =£0/7 031

The former means were

-£0.000032 =k0/’.065

and these must be regarded as indicating the uncertainty in the

absolute values of the constants; if the constants which we have

obtained are in error, then there will be a decided tendency to

error in the same direction on different plates, and the smaller

probable errors given above indicate how much we should expect

the adopted values of the constants to differ from each other as

obtained for different plates. Consequently only a small part of

the discrepancy between the probable errors of the measured co-

ordinates and of the right ascensions and declinations can be due

to uncertainties in the adopted constants.

The discrepancy is probably caused by inaccuracies, and in

some cases neglect, of instrumental corrections. For example,

the difference between the two complete measurements of a coor-

of the Rutherfurd Photographs. 275.

dinate is independent of errors in the determination of the division

corrections, because the two observers always used the same

lines; but not so with the differences of the right ascensions

or declinations as derived from different plates. Similarly, the

corrections for temperature and straightness of the scale, which

we have neglected, do not affect the agreement of the measured

coordinates. Possibly too, there have been distortions of the

film, but the smallness of the probable errors on the whole must

rather be taken as evidence against such distortions. It is im-

portant to note that the close agreement of the right ascen-

sions and declinations for different plates affords a striking con-

firmation of the permanence of the Rutherfurd plates, which in

the present case have been measured a quarter of a century after

they were made.*

If we consider the probable errors of the measured coordinates,

we see that the uncertainty is considerably greater upon some

plates than upon others. Notwithstanding, equal weights have

been assigned to all the plates, since it appears that the uncer-

tainty in a measured codrdinate forms only a small part of the

uncertainty in the corresponding right ascension or declination.

Let us now compare the photographic results with those of the

heliometer. In his memoir upon the group, Professor Schur has

given the places of forty-five stars referred to the mean equinox

and epoch of 1875.0, which are the same as those used in the

present paper. Of these stars all but five appear on the photo-

graphs. The following table gives first the uncorrected or direct

differences obtained by subtracting the right ascension, declina-

tion and proper motion of each star in our catalogue, from the

corresponding quantities in Schur’s. The differences in right

ascension and in proper motion in right ascension have been

multiplied by cos 0, to reduce them to arc of a great circle.

* See, in this connection, ‘‘On the Permanence of the Rutherfurd Photo-

graphs,’’ by Harold Jacoby, Annals of the N. Y. Acad. of Sciences, Vol. IX.

276 Presepe Group; Measurement and Reduction

COMPARISON WITH HELIOMETER RESULTS.

HELIOMETER minus PHOTOGRAPHS.

Right Ascension. Declination. Proper Motion. a ;

0.0

Direct Corr’d. Direct Corr’d. Diffs in Diftain | > @tes

Diff’s. | Diff’s. DIAS: ae Ditties: RAs. Decks

—o.04 | +0.07 +o.40 —o.08 | +0.016 | —o.015 8

— .03 — .02 + .46 | — .o4 | — .o14 | — .020 8

—. — .24 + .61 + .10 | + .o1r | + .004 7

+. + .09 Sa Tie) + .20 | — .o19 | + .005 8

=. + .03 + .67 + .13 | + .o21 | + .oo1 8

=. + .06 + .55 — .02 | — .o1I | — .032 8

+. + .06 + .67 + .07 | — .004 | + .o18 8

=. + .o1 + .50 — .1I0 | — .004 | — .020 8

+. + .12 + .72 + .10 | — .030 | — .022 8

—. — .03 + .67 == .04. |) =" .002 "sore 8

—. — .10 + .74 + .o8 | — .032 | — .008 8

ae — .06 + .52 | —.I5 | — .o19 | — .008 8

+. + .25 + .57 | —.12 | — .007 | + .oo1 8

4, See eae Sor ES ey |) Jans 8

+. + .13 + .62 — .08 | — .023 | — .028 8

=. | — .09 + .71 | + .04 5

+. | .0O + .66 | — .o4 | — .035 | — .022 8

—. | — .07 + .67 1:02) 007) Ol 8

—. | + .04 + .79 + .09 | — .020 | — .o31 8

=e | — .09 +i1.o4 | + ..3r | — .o16 | — .orI 8

= OR | 100) | =2).62)) == ao, Longin] = aronan 8

+. | + .10 + .69 — .05 | — .o14 | — .006 8

+. | + .Io + .87 + .14 | — .032 | — .033 8

— .2 — .18 = OS) |) —— 04 O28 cian 8

—. — .31 + .73 | + .02 | — .004 | — .026 8

+. — .o2 | + .80 + .06 | — .007 | — .oI7 8

+. + .17 + 80 | + .04 | — .014 | — .002 8

+. — .07 + .74 | — .02 | + .009 | — .orl 7

+. + .II + .94 | + .1I9 | + .co2 | — .oro 8

=. — .09 + .66 — .08 | — .009 | — .026 8

—. — .02 + .79 + .03 | + .037 | — .030 7

—. — .07 + .68 — .I0 | — .oor | — .906 8

—. + .03 + .93 | + .14 | — .o18 | — .008 6

—. — .03 + .77 | — .o2 | + .0o08 | — .o1o 8

+. — .04 + .57 — .25 | + .028 | + .oor 8

—. ee) | Peak | = 105 2

—. — .20 + .66 | — .18 2

— .06 + .91 KO | aeoest ||| —— Cow 8

+ .09 + .71 = 2h OL, .000 8

— .13 259) = .O) ta} OLS meat amen 7

The corrected differences in right ascension and declination

were obtained by adding systematic corrections and also by modi-

fying the scale-value and orientation of the photographs. That

of the Rutherfurd Photographs. 277

constants of the plates would have to be changed so as to secure

the best possible agreement between the two catalogues. Each

star gives two equations of the form,

Xdp+ Ydr+dk+da=o

Ydp — Xdr+de+dd=o0

where da and dé are the uncorrected or direct differences in the

table. The least-square solution may be carried out in a manner

entirely similar to that previously used. The differences for stars

18, 20, 24 and 25 were not used because these stars were not in-

cluded in Schur’s triangulation, but each was merely located by ~

position angle and distance from the nearest star in the triangula-

tion. Stars 19, 41 and 42 were also excluded in making the least-

Square solution because of the small number of plates on which

‘they appear. The remaining stars, thirty-three in number, give

the following corrections to the contents:

dp = -+ 0.000011 + 0.000009

dr = + 0.000098 =: 0.000009

dk =-+0/.047 +0//.014

== WA, SEO OIL

The probable error of one equation is

=E 07.080

a quantity which speaks well for the accuracy of all three re-

searches concerned. The corrected differences in the table are

now obtained by adding to each uncorrected difference

X.dp + Y-dr + dk in the right ascensions,

and Y-dp — X-dr + dc in the declinations.

From the above value for dp we see that the meridian observa-

tions gave a scale-value which agrees very closely with that ob-

tained from the heliometer places; the largest effect that dp has

on either coordinate of any star is only about 0’’.02. On the other

hand the value of dr, or the change in the orientation constant

is quite large, corresponding to a correction of about o’’.20 in the

coordinates of outlying stars. The meridian observations which

we used to determine the orientation of the group, were also em-

ployed by Schur for the same purpose, and were found by him to

give results which practically agreed with those obtained by an

independent method. As we have adopted Schur’s proper mo-

tions for the comparison stars, to reduce their places to the epochs

278 Prexsepe Group; Measurement and Reduction.

of the plates, we can only conclude that the somewhat large value

of dr is due to the fact that the relative positions of these stars

with respect to the rest of the group have been differently deter- |

mined by the photographs on the one hand, and the heliometers

onthe other. This explanation is borne out by the comparatively

large values of the corrected differences for the comparison stars,

numbers 4, 5,15, 40 and 44. :

The large value for dk, or the systematic correction in declina-

tion, was to be expected. We have already remarked (see page

236) that the proper motions used for the comparison stars were

not derived by Schur from the direct differences between the two

heliometer determinations of the places of these stars, but that

systematic corrections,

+ 0%.0003 and — 0”.039

were added to the proper motions in right ascension and declina-

tion respectively. Hence we must expect the photographic places

to differ from those of the heliometer for the epoch of 1875.0, by

+ 0”.071 and —o”.612,

the proper motion having been used for an interval of 15.7 years.

These corrections agree quite well with the values of dk and de

respectively, as obtained above.

VII.

Orientation by Trails. Scale-Value.

An independent method for orienting a stellar photograph is

furnished by the “ trails ” or third images of some of the brighter

stars. The Rutherfurd photographs previously reduced depend

upon this mode of orientation, and the present research offers an

admirable opportunity for testing its accuracy. Four trails have

been measured and reduced on each Preesepe plate, and the re-

sulting values of the orientation corrections were compared with

the results obtained from a comparison with meridian observa-

tions, and also with those obtained with the use of the heliometer

places. On Plate II the trails were too faint to admit of measure-

ment, and on Plate V they were missing altogether.

The trails were measured in a different manner from that used

forthe other images. The plate was first set in the position

which it occupied when ‘‘y direct” had been measured for the

stars, and the micrometer was set and read on the east image of

a star whose trail was to be measured. Then, without touching

the microscope, the plate was moved along the cylinder till the

corresponding trail came into view. This was always possible

because the plate had been approximately oriented when first set

in the machine. Two readings were made upon the trail and the

plate was then moved back to the east image, which was read a

second time. The same operations were gone through for the

west image, and the mean of all the readings on the images was

subtracted from the mean of the readings on the trail, thus giving

the offset in declination by which the trail differed from the

middle point between the two images. All the above operations

were repeated in the opposite position of the plate, namely that

corresponding to “ y reversed,” except that in the latter case the

mean of the readings on the trail was subtracted from that for the

images, so as to get the same sign for the offset as before. Hach

trail was thus measured by. two observers separately, so that in

all, sixteen readings were made on each trail, and eight upon each

of the images. The resulting offsets are tabulated below in mil-

limetres.

279

280

TRAIL MEASUREMENTS.

Prexsepe Group; Measuremeni and Reduction

23. ie 31. 37.

I —.0443 —.0193 —.0084 | +.0183

Ill —.0676 —.0404 | —.0398 | —.0292

IV —-0535 —.0312 —.o169 | +.0070

VII —.0772 | —.0422 | —.0499 | —.0294

Vu —.1054 | —.0766 | —.0718 —.0510

IX —.0850 —.0568 —.0356 | —.0070

The distance from each trail to the middle point between the

corresponding images was measured approximately as follows,

being practically the same for all the stars upon a plate:

Ieee IU TOUR IY) WAU WA000 ID

8, 35.0, 35-1, 35-0, 39.3, 48.1, 39.4 millimetres.

We shall now consider what corrections must be applied to the

above offsets in order that the true orientations of the plates may

be computed from them. ’

Instrumental Corrections. The only correction of this kind

is that for rotation, the data for which have already been given in

Table II. Using the same notation as before the correction to the

offset is

—s. 7. sin 1/’

which is the same for all four stars. Having applied this connec-

tion, the offset may now be converted into seconds of are by mul-

tiplying by the approximate scale value, 52.87.

Transformation Corrections. For the present purpose it will

be convenient to use Ball and Rambaut’s formulas quoted on page

238,in which X sec 0, and Y appear in the second members instead

of da and 40. We need only the second of these formulas :

Ad — y=— ¥X (Xsec d))*sin 20, —4 Y3— (Xsecd))? VY

. For the trail, X sec 0, is diminished by

2 = 52.87 -s- sec 0p,

while Y remains practically unchanged. Hence the correction to

the offset is,

+ ¥ sin 20) -2: (ez — 2X secd,) + 2: (2— 2X secd)) Y

Refraction Corrections. The trails were taken somewhat later

than the principal images of the group, and as the zenith distance

of the Rutherfurd Photographs. | 281

changed in the interval, the refraction-coefticients will also be

changed. Denoting by IM,’ and N,’ what these coefficients be

come for the trails, we have the correction to the offset,

WM’. 2+ (M,— M,’) X sec oy + (Ny — N,’) ¥

The first term is constant for all four stars, and the two remain-

ing terms are small. To calculate M,’ and N,’ we must know how

much the hour angle has changed in the interval between the ex-

posures for the principal images and that for the trail. As each

of the former lasted six minutes and as the exposure for the trail

was much shorter, we may safely adopt seven minutes of time as

the change in the hour-angle. J,’ and N,’ may then be calculated

with sufficient accuracy by interpolating in Table VII.

After these corrections have been applied it will be convenient

to transform the offsets into position angles, which may be done

by the formula

offset \

== 27 Oo i |

P (nig tt \s cos Jy

Precession, Nutation and Aberration. Formulas for correct-

ing position angles for these were deduced in convenient form by

Bessel* ; let

a! = 20! sec dy sin a

B! =see 0p COS a

y/ = tan 0 cos a

0’ = tan 0, sin a

A, B, C, D= Bessel’s star-numbers, tabulated for each day

in the year in the ephemerides.

The true position angle at the beginning of the same year is

found by adding to the observed position angle the correction,

(— Aa! + BB! + Cy’ + Dd)

Then to reduce this to beginning of another year we add

+ 20/7.06 sec 0, Sin a: t ;

where ¢ is the integer corresponding to the difference of the years,

and must be considered positive if we are reducing an observation

to a later year than that in which it was made.

As an example of the reduction of trail measurements, I have

set down the calculations in detail for the trail of Star 23, Plate I.

* “ Astronomische Untersuchungen ’’ Vol. I., pg. 202.

282 Presepe Group; Measurement and Reduction

Offset, —0.0193 millimetres

Rotation Corr’n., -+ 0.0005

— 0.0188

Tn are, 107,99

Transf. Corr’n., +1 .75

Refraction +o .24

Corrected offset + 1//.00

Position Angle, 270 + 111//.9

—(Aa! + BB’ + Cy’ + Do), = 2" 26

20.06/’ sec dp sin a -t, + 84 .0

True Position Angle, 270° + 1098//.5

Consequently we have from this star,

Tr = -++ 0.000963

Similar calculations for all the trails gave the following results

in which r has been multiplied by 10° throughout.

ORIENTATION BY TRAILS. VALUES OF r X 108.

Star. | 3 | 3 31. |

oe 15. DD We iSBe | 7 1 37.

I +954 | | +963 |. +8400 | eeans

Ill +334 | +390 +118 +288

LN clei SEIT | _ 757 eves

VII | —128 | +186 | —1r40 | — 52

VIII +122 | +152 III | +113

IX —360 | ite —248 | —254

[ | | .

Taking the mean for the four stars on each plate and setting

down again the values of 7 previously obtained by comparison

with the meridian observations, we have,

Orientation by Orientation by

Trails. Merida. Obs.

Plate I + 0.000908 -+ 0.001054

Tit + 282 + 409

VG Gest His hoe dS

WALD ober BA 35

VIil + 7244 + 211

IX — 301 —_— 326

Means + 292 + 458

In comparing these it will be remembered that a difference of

0.000100 corresponds to about o”.20 in the coordinates of the out-

lying stars of the group. The results are decidedly adverse to

of the Rutherfurd Photographs. 283

the accuracy of this mode of orientation, especially as a compari-

son with the heliometer places indicates a further correction of

++ 0.000098

to the orientations obtained by using the meridian places. T!

large discrepancies are probably due to jarring of the plate duri 2

exposure, caused by stopping and starting the clock-work severa:

times ; the large difference for Plate 1V admits of no other obvious

explanation.

Let us now examine the scale-values of the different plates.

The values of p given at the beginning of Section V include aber-

ration and temperature effects. Formulas for the former cor-

rection are thus given by Bessel :*

d =-+ (cos 0p COs a)

Then the true distance is found by adding to the observed dis-

tance s,

—s(Cy+ Do),

C and PD being as before, the Besselian star numbers.

We may also correct the values of p for the temperature at

which the plates were measured by adding

+ 0.0900017 (7— 65°),

T being the temperature in Fahrenheit degrees at which the plate

was measured, given in Table IJ. This expression is easily de-

rived from the value of v on page 223. Corrections for the tem-

perature at which the plate was exposed ought also to be applied,

but sufficient data to establish a connection between this quantity

and the scale-value are lacking. After a greater number of Ruther-

furd’s photographs have been reduced we may have more definite

information on this point.

The true scale-value S (so far as it can be obtained without the

last correction), is given thus,

S= 52”.87 [1 + p— Cy— Do + 0.0000017 ( T°? —65° J]

The following table gives the corrections and the resulting scale

value for each plate. The corrections for temperature are very

small and might well have been neglected. The last two columns

give the readings of the thermometer attached to the telescope

and of the “ focus,” which have been copied from Table I for con-

venience of reference.

* * Astronomische Untersuchungen,’’ Vol. I, page 208.

284 Presepe Group; Measurement and Reduction

ScALE-V ALUE.

Cor. f Cor. Cc ted

ED: peraten. for nihSearoy Seale-valiie. BOL bes. ODE

I —0.000099 0.000000 52,8701 +58° 8.4

es 99 | + 2 52.8715 58 8.4

Ill — Too | — 3 52.8712 53 8.4

IV — roo | + 4 52.8760 53 8.4

Vv — 98 | + 3 52.8788 48 7.8

VII —- 99 | — 2 52,8827 58 fe)

Vill = 99 | — 5 52,8831 58 7-7

IX — 98 | — 2 52.8840 48 7.8

The mean of the scale-values is

52/!.8772

and if we adopt the correction of + 0.000009 as indicated by

comparison with the heliometer places, this becomes

52//.8776.

However, either of these must still be regarded as only an ap-

proximate value, since the separate values for the different plates,

as given above, vary in a way that cannot be fully explained bya

connection with the readings either of the telescope thermometer

or of the ‘ focus.” 4

The above investigations on the orientation and on the scale-

value lead to the same conclusion ; it will usually be better to de-

_ termine all the constants of a plate by comparing the measures of

some of the stars with their positions as known through meridian

observations or otherwise, than to attempt to reduce them by

means of a predetermined scale-value and orientation. In any

case it is necessary to appeal to such known positions to deter-

mine the values of & and ¢, or the absolute place of the group in

the sky. The positions of two Stars are theoretically sufficient to

determine all four constants, but in most cases it will be possible

to find enough stars to eliminate errors of observation to a large

extent.

In conclusion, I wish to acknowledge my indebtedness to

Messrs. Kretz and Hays for assisting me in the measurement of

the plates, and to Professor Jacoby, who has kindly explained to

me the methods used by him in the measurement and reduction

of stellar photographs, and who has also suggested some improve-

of the Rutherfurd Photographs. 285

ments in the paper in reading over the proofs. Finally I desire

‘to express my thanks to Professor Rees, Director of the Ob-

servatory, for the interest he has shown in my work, and for

securing its publication.

Note on Refraction Formulas for Photographic Plates.

Formulas for correcting the measured rectangular coordinates

of a star upon a photographic plate for refraction, may be easily

derived from the well known general formulas of Bessel. On page

166, Vol. 1. of his ‘“‘Astronomische Untersuchungen” he gives the

following corrections to the differences of right ascension and

declination :

A (a’—a)=s- k [tan® ¢ cos (p—q) sin g—tan ¢ sin qg tan 0) cos p

+ sin p] sec 95

A (0'—d)=s-k [ tan? ¢ cos (p— q) cos q+ tan ¢ sin g tan 0) sin p

+ cos p]

Substituting

X—=s sin p

Y=s cos p

G=tan ¢ sin q

H= tan ¢ cos q

we obtain

A (a! —a) =k X seco, (I+ BH?) +k Y (G—tan 4) Hsec

A (6/—6) =k X¥(G@4+tand)H +kY (I+ @?)

These formulas become identical with those of Professor

Jacoby when we change & into fin order to allow for the in-

creased refrangibility of photographic rays.

One point in the above deduction deserves mention; the quanti-

ties 0,, etc., were intended by Bessel to be the means of corre-

sponding quantities for the two stars whose distance along the

are of the great circle joining them has been measured. We have

treated them as though they referred to one end of that arc;

however, this merely amounts to neglecting terms in the second

and higher powers of s, which may be done for most photographic

plates.

If we omit the middle term in each bracket in Bessel’s formulas

we obtain the formulas given by Professor Turner; the omis-

sion of these terms, as has been repeatedly pointed out, corre-

ANNALS N. Y. ACAD. Scr., X., June, 1898—18.

286 Prezsepe Group; Measurement and Reduction.

sponds to a rotation of the axes, and is, therefore, of no impor-

tance when we determine the constants of a plate by comparing the

measured coordinates of some of the stars with their known places.

Turner’s formulas are

AX=kX: (1+ H*) +kY-GH

AY=kX-GH + &Y: (1 + @2)

These formulas may be simplified when we use the above method

for determining the constants, as I pointed out in the Astronom-

ical Journal, No. 480; rejecting so much of the correction for re-

fraction as may be regarded as either an orientation correction

or 4 scale-value correction, we have remaining

AX = kX. ( H? — G?)

AY= kxX-2GH

These formulas might have been used for the reduction of the

Preesepe plates, but as we wished to know the true orientation and

scale-value for each plate, extra corrections to these constants

would have been necessary. Only four of the comparison stars

used need corrections for refraction; so that in the present case

nothing would have heen gained by the use of the last formulas.

When, however, the number of comparison stars is greater, or

when we do not care especially to know the true orientation and

scale-value of a plate, these formulas will save some labor.

GENERAL INDEX TO VOLUME 4%.

Names of authors are in wy face type.

in italics.

PAGE PAGE

Aberration; correction of distances Begoniacex; stipules in, Clos,. 12

ii@ye’ 402) ove GO Aree Gon 79|Belopolsky; ref. ....... 159

Adanson; ref., Clos. ..... 16 | Belt; ref. note ‘ 41

Aesculus ; bud scalesin, Gobel,. 16 Bentham and Mueller ; note . Ast

Agardh, J. G., on stipules, 6| Bessel; refs. 159, 241, 283, 285

Agrimonia ; stipules in, - . 42) Besselian day-numbers ; logs of

Agrimonia striata Michx. embry- 59, 161

onic leaf forms in, 42, 43] Betulacee; bud scales in, Henry, 6

Ailanthus glandulosa Desf. leaf de- Betulites ; stipules of, Lesq., 20

velopment in,...... 30 | Bischoff, G. W.; on stipules. . 5

Althenia jiliformis Petit, leaf ‘de- Blastomeres ; dev. of isolated. . 50

velopment in, . . 35 isolation of Ascidian . 53

American Ephe: eris ; ‘day-num- Blastula ; complete .. . 55

berspicomyy og She. . 59, 161 Botanical Gazette ; quoted, Hol-

Angiosperme ; stipules in, Regel, 7| lick sy AotW Ae RT 21

common origin of, . 23) ‘ BRADLEY 3077 2? RUTHERFURD

relating to Gymnosperme, 23 PHOTOGRAPHIC MEASURES OF

primitive plant, ..... 24| THIRTY-FOUR STARS NEAR, 161

Angles, measures of ( Bradley 8077 ) General data, Table, . . 163

Table VI, 169 Corrections, Tables, . 164-7

Aracex, leat development i in, 32 Results, Tables, 2 9 9 WGSES,

ELLOS Ue eee ee at sha: 33 Mean results, Table, 186

Aralia racemosa ibe petiole, . .. 32 Proper motion, Table, . 184-5

Arisema triphyllum (L.) Torr. do. 34 Catalogue of stars, Table, 187

Argelander; on ‘‘ Bradley 3077,’ 162 | Bradley; observations of, 236

Artemisia vulgaris L.; leaf dev.in, 31]! Braun; ref. on stipules, . 10

ASCIDIAN HALF-EMBRYO, THE, Brongniart, Ad.; quoted on stip-

Crampton,...... Pee 5) ules; Rrecul, eas. 10

Ascidian egg ; blastomeres of, 50) Bryophyta; relation to Pterido-

Ascidiella; embryo, ..... 53| phyta, etc., gee 23

Tq CLD IY Ostici = veuel us Vicn es 54 | buds; leaf-buds ; primitive leaf ;

Aspidiophyllum ; basilarappend. of 20 forms UTNE ayy! ome Ma Pe oh 26

Astaix; on stipules, a a formation of, Linnzus, . 3

Aster undulatus L. leaf. dev. in. 31 kinds’ distinguished, De

Asterophyllites ; leaf sheath a Candolle, ie AS

Vuillemin, 17 in Ficus and Magnolia, ete 5

Authors ; review of, on stipules . 3 in Rosacex,. . 5

Auwers, ref., . 64, 71, 115, 148, 159 | bud-scales; Agardh, 6; Rossman,

ilal ¢ Gobel, Bre neha sstray APO 16

Balfour, F. M.; ref... .... 25 Burnham ; ref., AY aghetan eke a ale fatnt 158

Bal TOR Nas sai hop wale Sse 159

Baptisia tinctoria es ) Re Br; leaf California ; Platanus, Lesq.. . 19, 20

eve IM ean riots toma 39| Campbell; ref... ....... 23

adnate stipulesin.. ..... , 41-2 Candolle, De; on stipules, . 3-4, 10—

Barfurth, D.; ref... ..... 50 11, 15-16, 27

Generic and specific names

288

PAGE

Caprifoliacex ; stipules in, 38

Castle, W.E.; ref., ..... 52-3

Cauvet, D.; onstipules, . . 13-15

Cephalanthus occidentalis L., stip-

mes nyse) 32 aan eek kes Niels tet Bees

Chabry }"rel.7. sto 5) ee 50, 538-4

Characee; relation to Pterido-

JUMET, B@g oo 0 6 op oO 23

Chauvenet; ref., ..... 115

Chrysosplenium ; scales of rhizomes

in, Gobel,

Cistacex ; stipules in, Clos, . me 12

Cleavage of blastomeres, 6

Cliffortia graminea L., stipules in, 44

Clos, D.; on stipules, 10-16

LCS) Ae hd ei Tt 45

Colomb, G.; on stipules, . 17-18

Comarum palustre L., leaf dev. in,

Comparison stars, 123, 137

Compositz, leaf dev.in,. ... .

Comptonia peregrina, stipule of,

Constants of photographic plates

Prexsepe Group, - ,

Codrdinates ; probable error

measurements, .......

Corylus ; from HKocene, note,

Corrections ; ( Cygni) Distance

Measures, . 59, 61-62, 79, 64-5

of Position angle Measures,

. 66-70, 58-9, 79

of orientation variation, :

67-70, 106-108

41-6

Tangent, : 86 OUR ee)

(‘Bradley 3077 7) Seale va-

riation, . . . . 162, 184

orientation variation, . 162, 184

refraction.,...... - 164

precession, etc., . 167

MPancent,: wymatee ice es 167

(Presepe Group) Instru-

mental, . 216-25, 280

transformation, . 238-9, 280

refraction, . 239-40, 280

precession, etc., . 241, 281

aberration, (si. site near 241

scale value, ..... 284

Cosson, E.; on stipules, . . 12

Crampton, Henry E.; THE ‘As-

CIDIAN HALF-EMBRYO, . 950

Cratzgus ; stipules of, Lesq., a ey AD

Cretaceous ; leaf-forms, .... . 27

Cross-fertilization of eggs, 51

Crucifere ; stipules in, Krause, ; 8

Ctenophore egg ; partial dev. of, .

Cucurbitacez ; tendril of, as leaf of

axillary bud, ....,. .’. 3

De Candolle,...... 4

Gindleyj 2. ae eee 5

General Index.

Cucurbitacez ; Listiboudois,. . 6

Kirochleger, ...... 8

Theories stated, Clos, 10

Cupulifere ; bud-scales in, Henry, 6

CYGNI; RUTHERFURD PHOTO-

GRAPHIC MEASURES OF SIXTY-

FIVE STARS NEAR, Davis, 58

PARALLAX OF 61! CYGNI, DE-

DUCED FROM RUTHERFURD

PHOTOGRAPHIC MEASURES, .. 123

Cyperaceze ; stipulesin, .. . . . 33-4

Cosson, <4. 2 ieee 12

Dahlia; nodal girdles in, Haus-

tein, 6.4). Ae eee 11

Daphne mezereum L, buds of, DeC., 4

Darwin, Charles; quoted, note, 25

Davis, H.S.; RUTHERFURD PHo-

TOGRAPHIC MEASURES OF SIX:

TY-FIVESTARS NEAR61 CYGNI, 58

PARALLAX OF 61’ CYGNI,

ETO, eh. on Sage ee 123

THIRTY-FIVE STARS NEAn

“BRADLEY 3077,” ..) 3) -aenepelone

Davis, Mrs. H. S., ref.. . 153

De Candolle; on stipules, 3-4, 10-11,

15-16, 27

Dentaria; scales of rhizomes in,

Gobel i: (ices 17

Deutzia; stipulesin,. ..... 45

Devonian Crategus; Lesq.,. .. 20

Dicotyledons: relation to Mono-

cotyledons, etc.,... . . . 23-4

Dipsacus ; nodal girdles 1n, |, EXins-

teil}... 5. bss s 2 eee il

reversion toward Monocot., 46

Distance Measures, 60, 80, 125-7, 168

corrections of, 59, 61-2, '79

Dixon; Alex., on stipules, as 14

Driesch, H.; ref oh a 50, 51, 53-6

Duchartre ; on stipules, : 11

Du Petit-Thouars, ref. ... 15, 16

Dutaily, G.; on stipules,. ... 13

Duval-Jouve, J.; do.,..... 13

East India;Wagnolia fuscata Andr.,

Meehan,...... ieee) 3

Echinoderms ; development in, -» 26

Eggs ; Ascidian, + Tals sot co) ene ate nmapcemmemneL

Ctenophore, .... . acre

Ciona, Molgula, ...:.. 52

cross-fertilization of, . . . 51

animal seriesamong, . . 51

Hichler, A. W.; on stipules, 12-22

EMBRYO ; THE ASCIDIAN HAtr, 50

specialized environment of, 26

production of half-embryo, 50

complete,...... .. 59

General Index. 289

PAGE PAGE

Embryology ; evidence of, on stip- Jacoby, Dr. H.; ref., . 58, 123-4, 224,

TALES Means reer a ute lie va, 6. & 25-6 240, 249, O75

Engler and Prantl, ref., > » 40) |(Johnsons ref, yo) ee ce 159

Eocene ; Corylus from, note... 27 Jordan, Dr. W.; ref.,. . . . 66, 118

Equisetum ; leaf sheath in, Juglandacez ; stipules ‘in, Sein apercal ate,

Colomb, ....... ,- + + 18] Juncacezx; ligulein,Duval-Jouve, 13

Erigeron annuum (L.) Pers., leaf Jussien, Adrien; on stipules, . 9

S@Nyey TOES Pe ae 31

Exposure of Rutherfurd Plates ; Kansas ; Betulites from, 20

data, .. ... . . . «58, 73, 190) Kapteyn; ref.,...... . . 160

Kirschleger, F.; onstipules,. . 8, 15

Fabre; onstipules,....... 10| Kofoid, C.; ref... ....... 51

Fagus; stipulesin,....... 39 | Krause,G.; onstipules, .. . 8

Ficus; ochrea in, Colomb.. . 17 | Kronfeld, M.; onstipules,. .. 17

buds i ms DCA ue 24 saith cs 5|Kutzing; quotedondo.,.... 15

Flint; ref., . . 160

Foliar buds ; “De ‘Candolle, 6 on 4| Labiate; scales of rhizomes in,

Foliola caduca ; Malpighi,.. . . 3 Gobel, lee

Fragaria; stipulesin, ..... 42-3 | Lamarck ; quoted on ‘stipules, 15

Francke, Martin; onstipules, . 22) Lamina, development of, in leaf,.. 29

Fulcral buds ; De Candolle, . . 5, Lamp; ref., : A iG eeeanrg Lt,

Fun % Smental Catalog; ref., 62| Laramie; Platanus, Lesq.,... 20

BAT Va raei ty iss syuegos Liskee . 55-6

Galium; stipulesin,. . . . . . 46-8) Lathyrus Aphaca L., stipules i in, 6) ets)

Gasparini; quoted on stipules, 10 | Leaf ; assimilative function, . . 24-5

Geology ; evidence of, in stipules, protective function; - = =) 4.7 25

24, 27 OMIM, 5 6 5 5 oo oc 26

Geraniacee ; stipules in, oar 10, 12 reduced, 28

Gobel ; cra saan oc. lly three main types of devel-

onstipules, .... 16 opment, oe es « 29-48

Graminex, stipulesin, ..... 32-4 relation of stipules to,

COSSODE Ssh tho lsiner cobs 12 Kronfeld,..... Bere albz/

(Goo 3h Gn 6 6 oO oO 6 17 origin of, Vinblemin, 7

Gray; Asa, quoted 13 | Leguminosz ; stipules of, 40-41

Gymnosperme ; relation to Angio- bracts of, Clos, ..... 10

SOME a 0 0.6) 00 oO 6 nO 23 | Le Maout; quoted onstipules,. 11

Ligule; origin, SBUECrD ve-

HALF-EMBRYO; THE ASCIDIAN, 50 nation, Tse eb oe

Hall, ref., > oo JY) corona of Silene BSi avs 6s 46

Haustein ; wT, on 1 stipules, : 11 conclusions relating to, 48

Heliometer: results compared with see review of literature on

photographic do.,. . . . 275-6, 278 StIpUl esi eae ee er os 3

Henry; A., on stipules, soy 6| Leptandra Virginica (ee) Nutt.

Henslow ; Rev. oe on ie stipules in, : 46

TUES ies bowls icele ss 114s 20 | Lespedeza capitata Michx. stipules

ref., eae Res sared LAE AA Aa TDS trcde star cle py cM ene aa ce, 40

Herting ; ref., aac sti sy ih siasth 5 CB) Lesquereux, L., on stipules, . . 20

Hicoria ; stipules i ls 0 Gg 6 OG O50 39 | Lestiboudois, Them ; onstipules, 6

Hilbure ; C.,onstipules,. ... 15 reference, . BY Sia senicrathtc 45

Hollick; Arthur, on stipule,. . 20 F.J., quoted, ... 11, 16

TOT ae ce ely oem Lier eed oso rem, = 24 | Lindley, John; onstipules, 5,11, 16

Hooker; quoted on stipules. . . 15|Link; quotedondo, ...10, 11

Humulus Lupulus ; stipules in, 48 | Linnzus, Carolus; onstipules, 3, 16

Hydroctyles; stipules,.... - 36, 45| Liriodendron ; primitive leaf in

Seeding isis oe ule eaten, 26

India East; Magnolia fuscata nodal girdles of, Haustein, 11

ANIOb ESS Hew A brea ell ae wan ene 13 abnormal leaves of, Hol-

Tsotesh wm ltomley Olver rants) ced 24 We 5 Go Oo o.oo a 12

290

PAGE

Lirviodendron; bud scalesin,Gobel, 16

Lloyd; quoted, . A 15

Logarithms ; Besselian day-num-

WET cask eee Ps eee 59, 161

Lubbock, Sir J ohn; on stipules,

19, 21

ref., j 28, 48

Magnolia ; stipules of, Meehan, .

ochrea in, Colomb, F

M. glauca L. , stipules of,

Lubbock, 5

Malphigi, Marcello; on stipules, 3

Malvacee ; stipulium of, Clos, . 10-13

Marrattiacer ; stipule a : 24

Martin, Miss Ida; ref., 58

Mass. ; New Bedford, 51

MEASUREMENT AND ’ REDUCTION

OF THE RUTHERFURD PHOTO-

GRAPHIC PLATES; PRASEPE

GROUP. . 192

Coe aCe ar)

Meehan, Thomas ; on stipules . 10

Melilotus alba Lam. ; stipule in,. 34

Mercklin, C. E. ; on stipules. . 8, 16

Meyer, Tobias; observations of, 236

Mirbel; ref. on stipules,. ... 11

‘Molyula manhattensis, . . . Sacto) o

Mollugo verticellata L., stipules i in, 46

Monocotyledones ; relation to Di-

cotyledones, ete, Sey re ie 23-4

sheathing petiole in,

stipules in, De Candolle, 4

Cauvietin sis tea a mk 13

Morgan; ref., a 51}

Mueller and Bentham, ref. “note, 41

Myrica ; absence of stipules in,. 45

Watadacee ; Visule im, . 2 = : 33

SIONOWUIES Wy 5g Gla ce wl. O4

Bischoff, .... 5

NATURE AND ORIGIN OF ‘STIP-

Loney BIS) S WIRstoy Ayre 5 GQ Sl 1-22

Naudin ; ref. on stipules, . 10

Nelumbium ; stipules in, Tricul, . 9

New Bedford, Mass. ; Molgula man-

QUESTS TIO, We een Wel hs se) Yat ea) ets 51

Newberry; J.S., ref., ; 27

Nodal girdles of Stellatee, ‘Haustein, 11

Nomenclature of cleavage, 51

Oaks; stipulesin,...... J .38

Ochrea, of Polygonacezx, 33, 44

of Palms, eae eens 36

relation to ligule and peti-

ole... . 48-9

of Polygonum, De Candolle 4

Bischoff, . . . : 5

Colombia enone 17-18

General Index.

PAGE

Ochrea, of Platanus, Henry, . « 6

of Stellate, Regel, ... . ul

Onagracex ; scales of rhizomes in,

Gobel, !

Ophioglossacee ; stipule of,.. . 24

Orientation ; by Trails, 279

variation ; connection of, 67-70

106-8

Osmundacee ; stipulein, .... 24

Paleontology, evidence on stip-

ules, . 4, <430 ieee 24, 27

Palms; ochréa of, eee 36

PARALLAX OF 61! CYGNI, DE-

DUCED FROM THE RUTHERFURD

PHOTOGRAPHIC MEASURES, 123

various values of, . 154-5, 157-9

correction of distance meas-

ures for, 3 OGG 4ASS

correction of orientation

variation for,. . . . 67, 106

Parallax coefiicients; limiting

values of, 70

equations, "193- 5 "429- 44, 145-7

Parlatore; quoted on do. ; 15

Parthenocissus ; stipulesin, ... 45

Pastinaca sativa L. , Sheathing peti-

ole of, ! 36

Pax, F.; quoted on stipules, note, 13

Payer: do:j .... |. eee 15

Petals ; formation of, ‘Meehan, SS

Peters ; ref, .. + ee 159

Petioles ; dev elopment of, 29

of Composite, : . 31-2

sheathing, in Monocotyle~

dones, ss 4 scoot

conclusions, . . eae

buds, De Candolle, MES ss 4

appendages to, Hollick, 20

Phalaris arundinacea L. ; ligule, in, 34

Phallusia ; ref. Driesch, .... 55

mammillata, egos of, . . 5U

Photographic plates ; Refractive

formulas, . . 285

Phyllodium, related to stipules, ea

Pisum sativum; stipulesin,. . 38

Platanus ; ochreate stipules of,.. 36

ochrea of, Henry, .... 6

Cclomb;. -) 57302 eee 18

fossils of, Hollick, . . 20

nodal girdles in, Haustein, 11

basilar me of,

Ward, 19

stipules in, Lestib., F ‘ 6

Pleiades, Rutherfurd photographs

OL se

Poly ygonum ; ochrea of. .... 33

leaf developmentin,. .

General

Polygonum; stipulein,..... 4

Colomb, Ty Wihee tah lave 18

Postgeneration, . . 50-1

Potamogeton crispus 1.3 , leaf dev. in,

stipules in. Corson,

Potentilla fruticosa L. , stipule i in, 44-45

PRHSEPE GROUP; MEASURE-

MENT AND REDUCTION OF THE

RUTHERFURD PHOTOGRAPHS, . 189

exposure data,..... . 190

measurement,. ..... 192

daily records,... . 194-5

recording sheets, . 198-9

instrumental corrections, 216-25

corrected coordinates, 226

constants of the plates, . 241-6

catalogue of stars,. . . . 271

heliometer results com-

PALeU wee woe vicy eh 275-8

orientation by trails,. . . 279

Prantl and Engler; ref.. . 45

Precession ; correction for, 167

Primitive leaf,.......4. +s 26-9

Peritchard ret... Silas |. 159

Proper motion; correction of orien-

tation variation for, . 70-108

Projection errors, measurement of

Preesepe Group, . onneco)

Protective functions of leaf, . 24, 25

Prunus ; obscure venation of, she iA

bud scalesin, Gobel, . 16

Pieridophyta : relation to Sperma-

UO MATE, BO 5 Te Be geal 23

Pyrus Malus iia stipule i i, 42

Quercus rubra L., laminain,.. . 39

bud scalesin, Gobel,... 16

Rambant;ref.,..... 160, 239-40

Ranunculacexe ; leaf development

TICG Teer oot out es i Ae 34, 46

Ranunculus aquatilis ith: biay aca a Tne 21

Ranunculus bulbosusL.,. . .. 32

pees din ISTE oe es 58

Recording sheets, star measure-

urements, . . 198-9

Reference Books ; Parallax of 612

Cysni, >.) . 159

Refraction ; means of, . BOA Faw ABS Ie 58-74

corrections for, eMesmseu tena 164

formulas for photographic

plates ee a yee coals 285

Regel; H.,onstipules,.... 7

Repsold; ROP eA ie ins ist sites 224

Review of lit. on stipules, . neh 3

Rhizomes ; scales of, Gobel, . .

Rhodotypus § stipules Dy hsp Cans

Index. 291

PAGE

Richardia ; venation of ligule in, 33

sheathing petiolein,. .. 34

Right ascension and declination ;

probable error in, : 273

Rosa ; highest adnation ‘of stipules

TTA BPRS Me unt BM eS aha aa —3

Rosa humilis Marsh.,stipulesin,. 43

Rosa bracteata Lindley, bio a o-ke 9)

Rosacex ; leaf divisionin,. . . . 32

stipules in, . .. . 41-2, 44

buds in, De Candolle, . . 5

adnate stipules in, Lestib., 6

bracts of calyx in, Clos,. 10

Rossman; J., on stipules,. .. 11

Rotation corrections,. .... . 220

FLOUSSIVV TCLs oleic eo ot spars 50, 56

Rubia tinctorium’L. , Stipulesin,. 48

Rubiacee, do., . . ee “39, 46

Rubus occidentalis L. , stipules in, 42

villosus Ait., do., Bs 2 AD

Rumex ; leat development in, . 35

TEUGY ROS Cr i a ec 30

RUTHERFURD PHOTOGRAPHIC

MEASURES OF SIXTY-FIVE

STARS NEAR 61 CYGNI, 58

RUTHERFURD PHOTOGRAPHIC

MEASURES OF THIRTY-FOUR

STARS NEAR ‘‘BRADLEY 3077,’’ 161

Rutherfurd, Lewis M.; refs.

58, 60, 189

Sachs; ref. on stipules, .. . 15

Salix; stipulesin, Lindley,.. . 5

Sambucus; vestigial stipulesin,. 41

faustein’ oi (eee ole 11

Hubbock. 29 fh cee see Al

Sanguisorba Canadensis L., stipules

INS Peete eames ha ZAC)

Sassafras; leaf developmentin,. 30

Scabiosa ; nodal girdles in, Haus-

CELIA here es os 11

Scale-value ; approx. of, . . 237

corrections, Baie "920-4, 277-84

Scale variation ; correction of Dis-

tance Measures for, . . . 10/61

Scale-division errors,. . . 216-17

Schlesinger; Frank, THE PRZ&-

SEPE GROUP, F 5 dls)

Schur rete ence a 234 6, 277-8

Scirpus pol yphyllus Vahl. ; - ligulein, 34

Sedgewick; Adam, ref. Pe 25

Seedling ; primitive leaf-formsin, 26

Selagineila ; ligule of, ..... 24

stipulesin, 38

Seringe; ref. on stipules, iG, 11, 15

Seward; A.C.,ref.ondo.,... 24

Silene ; corona of, AUN aria laos ie 46

292

PAGE

Silphium ; nodal girdles in, Haus-

tein, . . ie Fi payne Heke

Smilax ; tendrils of, Steere 36

Lindley, BS Noriaki hiremae ste tite 5

Sto eilaiteny i heer 6

PERIGUIG cove) con meise, oer eines 9

theories stated, Clos, . . 11

Colomby ies ries ene 18

Socoloff:) ref... 9. cee LOS

Solidago juncea Ait.; leaf dev. in, 31

Spermatophyta ; relation to Pterido-

General Index.

Trails; orientation by,. ....

Trecul; onstipules,....

Treveranus ; ref., . » <) cee

Trifolium pratense L., stipules in, 44

Turner, Prof.; ref., . 239-40, 286

Tussilago; stipules in, Agardh, . 6

Tyler, A. A.; THE NATURE AND

ORIGIN OF STIPULES,

Umbelliferz ; leaf development in,

PM, BW a 5 5 6 23

Spergularia ech ed stipules | of, Vaccinium ; leaf development in, 30

Dixon, . Valeriana ; nodal girdles in, Haus-

Staphylea trifolia L., , stipules i in, . oe MARL ROEM oil ay ee 11

Stars; comparison, ..... 123-34 | Variation; orientation, correc-

Stellatz ; stipulesin, . .. . .39-46| tions for, . 67-70, 106-8

Mainnaeus) 9. 5. ae ee 3 scale, corrections for,. . . 61-2

ere iat shatinesaanl: 7| Vascular bundles ; deflection of,. 37

nodal girdle, Haustein, 11| Verbena; nodal girdles in, Haus-

Sternwarte,K., ..... 234-5 |) tein, a... 2 See eo aalih:

St. Hilaire; , Aug., on stipules, Viburnum ; stipules i IN; coca 45

Oye hes, Mee . . 6, 10-11, 16| Vines, S. H.; ref... . 2... 29

Stoks; ref. on stipules, seeihie 10, 15 | Viola obliqua Hill; stipules in, . 32-42

St. Pierre, G.; ref.do.,. .- . . 16) Vitis Labrusca L., stipules in, .. 45

Stipel, De Candolle, « « » «3, 40-1) Von: Baer's law, < Sasa 25

STIPULES; THE NATURE AND Von Mohl, ref., on stipules, . . 11

QORIGEN ORS S36 t eS epee 1| Vuillemin, P.; on stipules,. . . 17

Review of literature per-

taining to, ..... 938| Ward; L. F., on stipules, - 17, 19

synopsis of article, ... . 2 Tels, 5; caus - , 24, 27

conclusions relating to, . 48 | Weismann; A.., ref., 50

See authors’ names, and ge-

neric and specific names.

Willoughbya scandens (a, ) Kuntze;

stipules in,

Stipulium; Clos, ...... 10-12 | Wilsing; measures, 143, 152-3, eee

Struve ; ref., eee ee ee 159 16R

Sambucus Canadensis L. ,stipulesin, 40! Wilson; H. B.,ref., ..... 51, 56

Syringa vulgaris L., leat dev. in,. 30 Winnecke ; ref., oe @ (he peneedeeaG

bud scales in, Gobel, 16| Wood’s Holl, Marine Biological

Laboratory,. ...... 5t

Tangent corrections, . . . 60, 79, 167| Wydler; ref. on stipules, ... 15

Tassi; ref. on stipules, . . 10} Wyoming: Devonian of,. ... 20

Tendril ; of Cucurbitacex, 45

De Candolle,. ....-. 4| Xanthium spinosum L., spines of, 45:

TInGley;. ss ele tae 5

Lestoboudois, ..... 6 | Yellowstone Valley ; Platanus of,

SUDOLHAES Wal as folio. cee 36 Ward, ssi ss sue er ae LG)

Tertiary ; leaf forms in, SB)! Be

Thalictrum polygamum Muhl., . . 33-4| Zero corrections, mean of E. and

FRESE] ey etic Pople Spee tee 8 19

O90 Nell te fe-y foi io Te Salama e

ANNALS N. Y. ACAD. SCIENCES. VOL. X, PLATE I.

ANNALS N. Y. ACAD. SCIENCES.

VOL. X., PLATE ry,

ANNALS N. Y. ACAD. SCIENCES. VOL. X., PLATE V.

a a ee ee

ane fg

| Pe

ant

Ray

2 a as Ta Getben, ese. eee): Nos, 1-12.

ANNALS

OF THE

NEW YORK ACADEMY OF SCIENCES, —

LATE

LYCEUM OF NATURAL HISTORY.

Het Pork:

a PUBLISHED BY THE ACADEMY.

1898.

‘ if i He v iy) rf i AN {) : : p Vi J *

PUBLICATIONS

OF THE

_ NEW YORK ACADEMY OF SCIENCES.

[Lyceum or Natura History 1818-1876. ]

et ‘The publications of the Academy at present consist of two

ne series—The Annals (octavo) and The Memoirs (quarto). The

_ Annals, which opened in 1824, contain the scientific contribu-

tions and reports of researches, together with the reports of

oe meetings. The Zvansactions, in which the shorter papers and

_ business reports have hitherto appeared, are now abolished and .

«the matter appears inthe Annals. The complete volumes of a

: Annals will hereafter coincide with the calendar year, and be- ee

: ginning with the volume now in press will appear about April

30, August 31, and December 31.

The price of the Annals will hereafter be one dollar per part

_(three dollars per volume). By vote of the Academy, all pub-

lications will be sent free to members.

_ Subscriptions and inquiries concerning current and back cde

numbers of any of the publications of the Academy should be. oe :

addressed to the editor, Say

GILBERT VAN INGEN,

Columbia University,

New York City.

PRICES OF PUBLICATIONS.

Annals of the Lyceum (Vols. I—XI.), . . . . per Vol., $5.00.

poceeuiacs x athe (VIS lM). coe EE 5 .OOs

Trans. of the Academy (Vols. 1—-XVI.),.. . . “ “ 5.00.

we Adnals.. “ GVitler Veen sia 2 ised Cicamte el SOs

Memoirs « «“ Mol iro bart hice pce Mere ye OOs

‘Annals: “@.. « Mil OCU ep iseg ie! Aart Os

I.—The Nature and Origin of Stipules ; Plates iI. By. !

TYLER. . ‘ , : : 3 , :

_ CRAMPTON, Jr. i : 4 achat ; p s

III.—The Rutherfurd ene: Measures of ete er tive Stars near

61 Cygni. By HERMAN S. DAVIS (1°) 05 7

IV.—The Parallax of 61! Cygni, deduced from the Rutherfurd aPho

graphic Measures. By Herman S. rae cea 3

rs Bradley 3077.” By HERMAN 8. DavIs.

VI.—The Presepe Group ; Measurement and ‘Reduction we ‘

Rutherfurd Photographs. _ By FRANK SCHLESINGER. oe

IMPORTANT.

By resolution of the Council of the New York Academy of

Sciences, the committee on library was authorized to remove from

the Exchange List the names of libraries and institutions that

issue no scientific publications; and to add to the list the names

of one hundred societies that issue scientific papers.

_ Inaccordance with the above mentioned resolution institutions.

so dropped from the free list will cease to receive the future pub-.

lications of the New York Academy of Sciences after the issue of

Volume X. of the Annals. The series known as Transactions was

discontinued with the issue of Volume XVI (1898).

A revised list of exchanges will soon be printed and sent to all

on the present exchange list. Libraries and other institutions

whose names do not appear on the revised list may then become

subscribers to the new series of the Annals by payment of the

fixed price of three ($3.00) dollars a volume.

Beginning with Vol. XI. each volume of the Annals will coin-

cide with a calendar year and will be issued in three parts.

Subscriptions and communications should be addressed to the

Editor of the Annals.

GILBERT VAN INGEN,

Columbia University,

West 116th Street,

New York City.