Journal of the Washington Academy of Sciences

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JOURNAL

OF THE

WASHINGTON ACADEMY OF SCIENCES

Vou. 46

January 1956

No. 1

EDITORIAL

THE woRK of an editor is not only to read

papers, accepting some and tactfully reject-

ing others, but also to improve the service

rendered to both readers and authors. My

previous editorial (June 1955) was addressed

primarily to readers. These remarks are

directed to authors.

The cost of publication, especially of

scientific material, has increased tremen-

dously in recent years. The Academy has

been spending a large part of its income to

subsidize publication of the results of scien-

tifie research, by paying direct printing ex-

penses and supplying reprints at less than

actual manufacturing cost. Early this year

a cost accounting resulted in raising the

price of reprints to approximately their cost.

A strong protest was raised, but our Ways

and Means Committee was already in action

and had made some progress. An arrange-

ment has now been completed whereby

papers can be reprinted at less cost, by

starting each paper on a new page. This will

sometimes threaten large blank spaces; but

your editor will endeavor to avoid this by

inserting quotations or other material. Such

extraneous matter will not appear in re-

prints. The new price schedule for reprints

is given on the inside front cover of this

issue.

Unfortunately, no rearrangement of lay-

out will reduce the printing cost of the

papers themselves. Many scientific journals

offer authors’ institutions the opportunity to

partially defray this cost by honoring page

charges. Publication of results is a vital part

of any research project, and publication cost

should be considered part of the research

cost. Organizations financing research should

not depend on private charity for dissemina-

tion of results. The Board of Managers of

the Academy has therefore established a

voluntary publication charge; it is hoped that

our local scientific institutions, both private

and governmental, will be able to honor this

charge and thereby further the interchange

of information among the various fields

represented by the Academy.

SIXTEEN YEARS AGO

The following item appeared in the July

1939 issue of this JOURNAL:

The 1148th meeting was held in the Cosmos

Club Auditorium, Saturday, March 11, 1939,

President Brickwedde presiding.

Program: RicHarp B. Roserrs, Department

of Terrestrial Magnetism of the Carnegie In-

stitution: The splitting of uranium and thorium

nuclei by neutrons.—Several years ago Fermi and

collaborators observed that artificial radioactivity

is induced when uranium is bombarded by

neutrons. Recently Hahn and Strassman have

shown by chemical methods that among the

radioactive elements produced are barium,

cerium, and lanthanum. This observation was

explained by Meitner and Frisch as a fission of

the uranium nucleus into two roughly equal

parts with approximately 200 million electron-

volts of energy released in the process. This

theory was soon confirmed by observing the

ionization produced by these heavy and highly

energetic particles. Neutrons were also found to

be emitted in this fission process and these

neutrons might conceivably lead to an exothermic

chain-reaction. However, it appears very prob-

able that separated isotopes of uranium in large

quantities would be necessary to sustain such a

chain-reaction.

FEB > {) 1956

2 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

VoL. 46, No. 1

PHYSICS.—E ffect of defects on lattice vibrations, II: Localized vibration modes in a

linear diatomic chain.’ P. Mazur, E. W. Monrrouu, and R. B. Ports,? Uni-

versity of Maryland.

INTRODUCTION

The influence of defects or local dis-

turbances in otherwise regular media is a

subject of great current interest in physics.

The electrical properties of semiconductors

are mainly due to impurity levels from which

electrons can easily be excited into a con-

ducting state. The interaction of elementary

particles is the result of the manner in which

their existence disturbs the field of the

vacuum or ‘‘ether.”’

In a_ previous publication,’ hereafter

referred to as I, a discussion was given of

the effect of defects on the vibrations of

monatomic crystal lattices. Generally all

motions of a lattice can be expressed as

linear combinations of normal modes of

vibration. In a regular lattice these normal

or collective modes are plane waves. Gen-

erally normal modes of all frequencies in a

certain continuum band or range exist.

The lattice propagates driven oscillations

whose frequencies he in this band. But

frequencies which are outside of it are

damped out in a short distance. The higher

the frequency of such an oscillation the

shorter the distance required for a given

degree of damping. The motion of various

atoms contributes equally to the component

of a thermodynamic quantity (say free

energy or heat capacity) derived from a

particular mode.

It was shown that certain types of defects

in a crystal lattice give rise to localized

normal modes whose associated atomic

motions are concentrated in those atoms

that are near the defects. The corresponding

vibrational frequencies form a discrete set,

which is displaced out of the continuum of

frequencies of the perfect crystal. The atoms

that participate in localized modes are

responsible for more than their share of the

1This research was supported by the United

States Air Force through the Office of Scientific

Research of the Air Research and Development

Command.

2On leave from the University of Adelaide,

South Australia.

3 Monrrouu, E. W., and Ports, R. B., Phys.

Rev. 100: 525. 1955.

internal energy of the crystal. Hence the

region around the defect is equivalent to a

“hot spot” in the lattice. A localized mode

(either in the interior or on the surface of a

crystal) might catalyze physical and chemi-

cal processes which would not normally occur

at the existing temperature of the crystal.

Local surface defect modes might also excite

molecules adsorbed on the surface by having

a frequency almost equal to a vibrational

frequency of the adsorbed molecule.

It was also pointed out in I that attrac-

tions or repulsions occur between defects.

These are due to both the localized modes and

to the slight displacements which occur in

all the lattice frequencies. We shall show in

another paper that the pair theory of nu-

clear forces is essentially equivalent to the

continuum limit of the interaction between

two holes in a erystal lattice.

It is the purpose of the present paper to

discuss the effect of defects in a linear

alternating diatomic lattice. Although the

general method developed in I is used,

the diatomic lattice introduces several new

features such as the well-known splitting of

the frequency band into two bands, the

acoustical and the optical, separated by a

gap of forbidden frequency levels. It is

necessary to cover a wide range of masses

since in the alkali halides, for example, the

mass difference may vary from as little as 1

or 2 per cent to as great as a factor of 20.

Our results are analogous to those of

Saxon and Hutner* and Koster and Slater®

for localized wave functions and impurity

levels in semiconductors.

PERFECT LATTICE

Consider a chain of 4N + 1 particles of

masses either m or M arranged alternately

such that those at the ends are of mass m.

Let each particle be connected to its nearest

neighbor by a spring of stiffness y. The

equations giving the 4N — 1 normal modes

of longitudinal vibrations of the chain are

‘Saxon, D. S., and Hurner, R. A., Philips

Research Reports 4: 81. 1949.

> Koster, G. F., and Siatrer, J. C., Phys. Rev.

95: 1167. 1954.

JANUARY 1956

mea u(n)

+ y[u(n + 1) — 2u(n) + u(n — 1)] = 0

m= 0, +2, ---, QN — 2)

Mou(n)

+ yfu(n + 1) — 2u(n) + u(n — 1)| = 0

(2.1)

al, +3, ---, QN — 1)

u(2N) = u(—2N) = 0

i =

where w is the normal frequency and u(n)

the displacement of the nth particle from

its equilibrium position. We have postulated

the end particles to be fixed. The solutions

of these equations are

u;(n) = A sin (2N + n)e; n even

22)

uj(n) = Bsin (2QN + n)o; n odd

with

~; = jr/4N janinteger (2.3)

and

A is Qy — Mw _ 2 cos Pi (2.4)

B 27 COS 9; 2y — mo

There are 2N symmetric (1.e., u(—n) =

u(n)) modes with frequencies given by

MAZUR, MONTROLL, AND POTTS: LATTICE VIBRATIONS. II 3

i wow. =m+M

+(m? + M’? + 2mM cos 29;)°

; i (PG)

= [m + M + 2(mM)’ sin ¢;]’ (2.6)

+[m + M — 2(mM)* sin ol

where

i jn /A4N,

fe I,gose DN = 1, (Om)

Also there are 2N — 1 antisymmetric

(i.e. u(—n) = —u(n)) modes, with fre-

quencies given by (2.5) and (2.6) with

go; = jn/AN,

and in addition the frequency given by

REO 650 IV HD OR)

2) j 2 1

ee ) w= 2(m) for m<M (29)

ay; 7

Seni

e ) w, = 2(M)'. for m>M (2.10)

In the unusual terminology, the frequencies

gree J

I Ses Sa ey

AS ———--———-2 AS 2

OPTICAL

BAND

S 2W-/ S Nex

Ses a ee AS 2N

GAP

AS @N ee enera-=--

ACOUSTICAL

(7) m™<mM

(4) m>M

Fra. 1.—Normal frequency levels for the vibrations of a perfect alternating lattice, S = symmetric

modes; AS = antisymmetric modes.

+ JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

w? w

2g(m-+M) 2g(m+m)

mM nm

OPTICAL

BAND

245/m 2y/m

GAP

24/mM 2y5/m

ACOUSTICAL

BANO

3) Oo

(a) m<mM

Fic. 2.—Plot of w? versus defect mass m’ for frequencies that emerge from the bands

w, form the optical band and the w_ the

acoustical band (see Fig. 1). Note that in

both cases a level at the top of the optical

band, viz.,

JN}

(2M a, = 2m + a) ean

avi

and the level » = O at the bottom of the

acoustical band are missing.

ONE ISOTOPIC DEFECT

(a) Effect on the frequency levels

We now consider the effect of replacing

the central particle of mass m by one of

m’ = (1 — e)m. Four possibilities will be

considered since m’ may be greater or less

than m and m may be greater or less than M.

The only change in the fundamental equa-

tions (2.1) is that the equation for n = 0 is

replaced by

1 — e)mw u(0)

\ @ail))

an ylu(1) = 2u(0) + u(—1)} = 0)

The 2N — 1 antisymmetric modes of

the perfect lattice, since they force u(0) = 0,

are unchanged by the change in the mass of

VOL. 46, No. I

(6) m>M

the central particle. Hence the only altera-

tion is to the symmetric modes. This ob-

servation enables one to predict the effect of

the isotope on the frequency levels; for

noting that reduction of the mass increases

the frequencies and vice versa one can

predict that for m’ < m < M the top S

level will rise out of the optical band but

for the acoustical band the top S level

cannot rise above the AS level above it;

for m < M and m’ > m the S levels are

lowered and the bottom S level of the

optical band falls into the gap. For m > M

and m’ < m one level raises out of the

optical band and another from the acoustical

band and for m’ > m > M no levels come

out of the bands (see Fig. 2). These pre-

dictions are confirmed from the following

detailed analysis.

Since we are concerned only with the

symmetric modes we try for the solution of

(3.1)

u(n) = A, sin (2N ¥ n)e

Dy 604, Oy B)

u(n) = B, sin (2N ¥ n)g Ce)

ey cs | LOR = i)

JANUARY 1956

Apart from the connecting equations we get,

as before,

(mwa _ 27) (Ma — 2y)

ee (3.3)

— 4y cos ¢ = 0

and the connecting equation with n = 0 is

(1 — e)mw’A, sin 2N¢

+ 7[2B, sin (2N — le

— 2A, sin 2N¢] = 0

(3.4)

or using (2.4)

[1 — e)mw — 2y\[Ma — 2y]

—4y’ sin (2N — 1)e cose = 0.

Use of (3.3) then gives the characteristic

equation

cot 2N¢e — « cosec 2¢ Ki (6) = 0 (3.5)

with

K.i(¢) = [M + m cos 2¢

(3.6)

+ (m’ + M’ + 2mM cos 2¢)'|/m

the solutions of which are to be inserted

into (3.3) to give the required frequencies.

It can be easily verified that for the special

MAZUR, MONTROLL, AND POTTS: LATTICE VIBRATIONS. II D

to that considered in I (see eq. A.8). The

solution of (3.5) can be investigated from

the graphs of cot 2N¢ and of

file, €) = € cosec 2g K,(¢). (3.7)

For the case m < M these graphs are

sketched in Fig. 3.

For m’ < m or € > O one intersection of

the f, curve with the cot 2N¢ curve is

“Jost”’ or is given by ¢ = ip and this corre-

sponds to the discrete frequency rising from

the top of the optical band. For m’ > m

or € < 0 the “intersection” ¢ = 7/2 + w

corresponds to the discrete frequency falling

into the gap from the optical band. This is

as illustrated in Fig. 2.

For the case m > WM the graphs are

sketched in Fig. 4. For m’ < m or € > 0

the intersection on f, at ¢ = 1 corresponds

to the discrete level emerging from the top

of the optical band and that of f_ at g =

a/2 + ip to the level emerging from the

top of the acoustical band. For m’ > m or

e < 0 there are no discrete levels; this is as

illustrated in Fig. 2.

(b) Evaluation of the discrete frequencies

The discrete frequencies can be calculated

for the limiting case N — o. For the inter-

case M = m the equation (3.5) reduces section ¢ = zy equation (3.5) becomes with

f+, E>0

th # na

5 TT/4N T

~ eae

f+, €<O f

Fic. 3—The graph of the function fi(¢,€) with m < M given by (8.7) and cot 2V¢. The intersections

give the solutions of (3.5).

6 JOURNAL OF THE WASHINGTON

~|_ f+, €>0

fe) ea ee

Hata ae

f+, €<O

Vike

ACADEMY OF SCIENCES VOL. 46, No. 1

f-, €<0

sae ~_la

' SS =a 2

f-, €>0

Fia. 4.—The graph of the function f+(¢,€) with m > M given by (3.7) and cot 2N¢. The intersections

given the solutions of (3.5).

coth 2NYy — lasN > ~

m — e€ cosech 2¥[M + m cosh 2y

+ (m’ + M* + 2Mm cosh 2y)*| = 0 oe)

(1 + &*) sinh 2y — 2¢e cosh 2y

=2eM/m

(3.9)

For the level emerging from the top band

(1.e., for the cases m’ < m with m < M

orm > M)

eS) 2

——— W =

OY;

+ (m + M* + 2mM cosh 2y)?

= m+ m(e” sinh 2y — cosh 2p)

m+ M

(3.10)

which gives, on using (3.9),

=) oem Os aye

-{2M + [m1 + «’)

+ 42 (MW — m)}?}.

The special case IZ = m gives

(m/y)o = 4(1 — &) (3.12)

as obtained in I, (A.10). Also, for small ¢,

(3.11) gives

(3.11)

w = wi[l + (M/m)e + O(c] (3.13)

where w, is the top of the optical band

(see 2.11). This equation shows that as

€ — 0 or m’ — m, the discrete level returns

to the top of the band.

For the intersection ¢ = 7/2 + wa

similar analysis leads to the result

(2 2

(62) —

Te (en ie

; {2M — [m°(1 ae e) (3.14)

+ 4e2 (M? — m’)}*}.

This formula gives the frequency level which

falls into the gap from the top band when

m’ > m and m < M and the level which

rises into the gap from the bottom band

when m’ < m and m > M. For small e,

(3.14) gives

ico 2

ays

-(m — M) & + O(e’)

so that as e > 0, (mM/y)w — 2M from

below if m < M and from above if m > M:

in the first case w = (2y/m)? is the bottom

of the optical band and in the second case

it is the top of the acoustical band.

A special case of some interest is when

2M + 2(M/m)

(3.15)

JANUARY 1956

e€—1 orm’ — 0. Then (8.11) and (3.14) give

(mM /y)o = (2M + 2M)(1 — &)*

im += M + 00 — e).

The top signs (corresponding to the fre-

quency emerging from the top of the

optical band) give w — ~ as ¢— 1 and the

bottom signs (for the frequencies in the gap)

= wo = M+ ™m.

This value of w: is half that of w:, and also

the average of w for the bottom of the top

band and the top of the bottom band. This

result has an interesting interpretation for

the case m’ < m and m > M. As m’ > 0

one frequency — ~ (accounting for the

loss of one degree of freedom) and the

frequency given by (3.17) is a so-called

surface frequency. The effect of m’ — 0

is to reduce the lattice to two chains each

with one end fixed and the other free.

This problem is being considered in detail by

Wallis.”

In the case m < M and m’ > m the

limiting case ¢e = 1 — m’/m > —~& corre-

sponds to the central mass being infinite

and hence fixed, the lattice dividing into

(3.16)

(3.17)

® Wats, R. F., private communication.

“O53

‘05

ZAE

A (2 4/my?

MAZUR, MONTROLL, AND POTTS: LATTICE VIBRATIONS. II if

two separate lattices with fixed ends. From

(3.14), as €e — —«, w — (2y/M) which

corresponds to the top frequency of the

bottom band. Hence the level in the gap

falls from the bottom of the top band to

the top of the bottom band. The bottom S

level of the bottom band has meanwhile —

w = O accounting for the lost mode.

The frequency levels given by (3.11) and

(3.14) are plotted in Fig. 2.

ZERO-POINT ENERGIES

(a) Perfect lattice

The zero-point energy of the perfect lat-

tice with m < Mis

Ey = Sotho (4.1)

with w given by (2.6) and (2.9). Hence

ui = (m+ M)?{m + (m + M’)

ahr

2N—J

> fh = 4¢nmyd + my? 42)

Fai

. sin’(jr/8N)}’}

and in the limit as N — , Ey can be ex-

pressed in terms of an elliptic integral of

the second kind:

2 3 4

M/m

Fie. 5.—Self energy of an isotope plotted as a function of I/m for fixed m

8 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

2 nn 8

INA(Qy/m)! = [1 aE (m/M)") —

a/4

[ (1 — 4(mM)?(m?+ M?)? (4.3)

-sin’ 6} dé.

(b) Self energy of an isotope

The change in zero point energy when the

central particle of mass m is replaced by an

‘Gsotope” of mass m’ can be calculated

using the method of contour integration

as discussed in I. The starting point is the

formula

AE _ 1 fy @d

thor Qn c o+ Wr dz

-In &,(z, €) dz

(4.4)

where from (3.6),

&,(z, €) = 1 — e tan 2Nz cosec 2z K(z)

= 1-4 ¢ tan 2Nz (4.5)

—(e/y) tan 2Nz cosec 22 wi. (z)

and C is the contour which is a rectangle

with corners -ia, 7/2 + ia. Since this

integral cannot be evaluated in closed form,

two extreme cases will be considered, firstly

when m M and secondly when m > M.

Gi) my M

In this case we assume M = m(1 + yn),

n small. For the contour C we can let a> «

so that the only contribution to the intergral

comes from the integration along the imagi-

nary axis, using w_(z) and ¢_(z, ©) giving

for large N.

NE —]

Tho, m(2m + 2M)!

{[m> + M? + 2Mm cosh 2t]' (4.6)

s—

where

,(t) = 1 — « tanh/

+ ¢ cosech 2¢[(m? + M’

+ 2Mm cosh 2)? — (M + m)]/m.

(4.7)

VOL. 46, No. 1

Using M = m(1 + 7), we obtain

[((m? + M? + 2Mm cosh 2t)? — (M+ m)}?

(2m + 2M)? (4.8)

= sinh 3¢ + O(n’)

and

In @,(¢) = In (1 — eé tanh 3?)

+en tanh 3 sech t(1 — e tanh 3f)~

+ O(n’). (4.9)

When these are inserted in (4.6) the term

without 7 gives precisely the result obtained

in I(4.15) for the monatomic lattice while

the term in 7 gives, after integration by

parts, the contribution

en [ ss tanh 2¢ dt

4n Jo cosh t — € sinh t™

This integration can be reduced to standard

integrals by writing

tanh 2¢

cosh t — € sinh t

(4.10)

2, sinh t — € cosh ¢

1+ = cosh 2¢ eu)

€

ze cosh t — € sinh |

and the final result is

Ce Ey = 2

shay

‘(m+ 2sin™ ©) + (8x) (1+ &)*

(4.12)

- en[2v/2 In (1 + V2) — V2 ex

SL = Sy 26 Oa e)| + O(n’)

(i) m > M

In this case we let M = &m, & small.

In the contour C we now eannot let a > «

but rather a — 0. In (4.4) we have to insert

w/o, = 1 — 3€ sin’ 2 + O(€/) (4.13)

w/o, = &sin 2[l — 11 + cos 2)]

+ 0) (4.14)

$.(z,€) = 1— e(1 + #) tan 2Nz cotz

+ O(€') (4.15)

JANUARY 1956

@_(z,e) = 1+ <(1 — &) tan 2Nztanz

-_ (2), Ga6)

For small a only the integration along the

horizontal sides of the rectangle C contribute

to the integral giving

ABE 1 [*’ > ose — 1a)

Yo, 2ni Jo zr Wr

. Gin &,(x — ia, e) — w(t + 1a) (4.17)

qx Or

aE In &,(x + 2a, €) dz.

In the limit of large NV

tan 2NiG@ == 7a) — 327 (4.18)

with considerable simplification of formulae

(4.15) and (4.16). In evaluating (4.17) for

the limiting case a — 0 two features are

important. Firstly to get the correct value

for AF the cases e > 0 and e < 0 have to

MAZUR, MONTROLL, AND POTTS: LATTICE VIBRATIONS. II 9)

be distinguished because in the first case

the discrete levels above both bands (corre-

sponding to 2; = a and z. = (1/2) + te)

have to be added while in the second case

there are no discrete levels which have to

be allowed for (c.f. Fig. 2b). The formulae

(3.11) and (3.14) give for the levels coming

out of the top and bottom bands respectively

w aes 4

ee 1 T 34 = 2) ap WO)

f= - ey - 30-28]

OL (4.20)

+ O(€).

The second important feature is that in

some of the integrals which arise, the

integration has to be performed before the

limit a — 0 is taken. A useful check on the

integrations is afforded by putting w = w,

so that the contour integral counts (the

number of levels in the band for the im-

perfect lattice) minus (the number of levels

ala @

.4 5G 8

= /{ — (msm)

Fra. 6.—Self energy of an isotope plotted as a function of ©

10 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

in the band for the perfect lattice). For

each band this is 0 or —1 according to

€ < QO ore > O. The final expression for the

self energy is

= e[-t+ta —@y"

2 L oe

(1/2 + sin | + TL = &)

3| 1 € 2)\-1 5

+e[t-£a-2 (4.21)

en a Qs 8) “Gy gia «|

+ 0(€')

Two equations, (4.11) and (4.21), have

been derived giving the self energy of an

isotope, the first valid for m ~ M and the

second for m > M. With these two expres-

sions the complete range of values of MW

can be covered for ¢ as large as 0.7, the

connection between the two results im-

proving the smaller the value of e¢. For

example, for « = 0.2, (4.11) gives AF =

(const.) 0.980 for 7 = —0.64 or M = 0.36m,

whereas (4.21) gives, for the value — = 0.6

or the same value of WM = 0.36m, AH =

(const.) 0.980. As WM — «, AH — (const.)

{(m/m’)? — 1} which is merely the difference

in zero point energy between two oscillators

because the lattice degenerates into a series

of uncoupled oscillators.

In Fig. 5 the self energy is plotted as a

function of (J//m) for constant m, and in

Fig. 6 as a function of ¢ for various values

of M.

TWO ISOTOPIC DEFECTS

If two isotopes of mass m’ replace the

two particles of mass m at the positions

numbered +2/ then the characteristic equa-

tions are

cos 2Ne¢ cosec (2N — 2l)e

— 2¢ cos 2le cosec 2¢ Ki(y) = 0 (5.1)

sin 2N¢ cosee (2N — 2l)e

— 2e sin 2ly cosec 2g Ki(v) = 0. (G2)

As in the analysis given in I and in 4(b)

above, the energy of interaction V between

VOL. 46, No. 1

two isotopes 1s given by the contour integral

V bie 1 w(z) d

Sher, Write = wy, az

In Pi (z, €) dz (5.3)

with

viz) = 1 — &Ki() sm’ ON = Qe

[2 sin 4Nz sin’ z — e€ sin (2N — 2l)z

- sin (2N + 2))z Ki(z)f. (6.4)

As in (4.6) the contour integral reduces to

the single integral

Vinge =I

m(2m + 2M)!

. | (On? + M? + 2Mm cosh 28)? (5.5)

thoy,

— (m+ M)} = In y(t) dt

where

w@ =1— 2

{M + m cosh 2t

— (m? + M? + 2Mm cosh 2t)*}

exp. (—4lt)

m sinh 2t — {M + mcosh 2t

— (m? + M* + 2Mm cosh 2t)*}

(5.6)

We can obtain an expansion for V valid

for large distances by expanding the inte-

grand as a power series in ¢ and exp (—/f).

This yields

Vi _ —2(e’m’)(M m)? 1

a(M +m)? (8i)8

3em

il il

[i+ ea to(s)|

In the case m =

Vo —-2e 1 3¢€ ,)

tho, «© (16/1)? E tap G | (8)

in agreement with I (5.3b).

An important consequence of the result

(5.7) is that it proves that V is negative

or the interaction between the isotopes

attractive regardless of the relative magni-

tudes of m and J. In the more general case

tha,

©)

M this expression becomes

JANUARY 1956

of isotopes of masses (1 — €:)m and (1 — e2)m

the energy of interaction is proportional to

€€. and hence is repulsive if ¢; and & are of

opposite sign. Also if one isotope is of mass

(1 — «)M replacing a particle of mass MW

then in the equation (5.7) the factor em

becomes ¢V/. Thus for the interaction be-

tween two “M”’ isotopes, em’ is replaced by

(e:eM) and for the interaction between an

““m” and an ‘“‘7”’ isotope, the factor becomes

(eeomM).

CONCLUSION

In a perfect alternating lattice the normal

frequencies fall into two bands separated

by a gap. It has been shown in the present

work that, as for the monatomic lattice,

localized modes can occur with discrete

frequency levels out of the bands when the

lattice contains defects such as isotopes.

For the alternating lattice, four interesting

eases arise. When one of the lighter masses

“m”’ is replaced by an isotope ‘“‘m’’’, then

if m’ < m one level jumps out of the optical

band into the region above, whereas if

m’ > m one level jumps from the bottom

of the optical band into the gap between

the two bands. When one of the heavy

masses is replaced by a lighter isotope one

frequency jumps out of the top of the

acoustical band into the gap while at the

same time a second level jumps out of the

top of the optical band into the region

above. Finally, when one of the heavy

MAZUR, MONTROLL, AND POTTS: LATTICE VIBRATIONS. II 11

masses is replaced by a heavier isotope

then no frequencies emerge from the bands.

The defect level which rises out of the

top of the acoustical band into the gap is

of special interest. As the defect mass ap-

proaches zero the level approaches the

level at the center of the gap. This level

could be interpreted as due to a surface

mode.

The self energy of an isotope has been

computed, and the series solutions obtained,

one valid for m M and the other for

m >> M, together cover the whole range of

variation of the masses. The interaction

energy between two isotopes is proportional

to the inverse cube of the distance of separa-

tion and is attractive for two light or two

heavy isotopes and repulsive for a light

and a heavy isotope.

Although this paper has been concerned

with only the one-dimensional lattice, the

general features will be similar for the more

realistic three-dimensional lattice. Thus one

will expect surface modes, a phenomenon

not arising in monatomic lattices. Also

the attractive and repulsive character of

the forces between isotopes will be of special

interest in the two and three-dimensional

lattices; a particle of mass intermediate

between m and M will “appear” as a light

isotope to one set of masses but as a heavy

isotope to the others, depending on its

position. The detailed analysis of the two

and three-dimensional lattices will be given

in a following publication.

Citius emergit veritas ex errore quam ex confusione.—FRancis Bacon, Novwm Organwm.

12 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

vou. 46, No. 1

MATHEMATICS.—Numerical experiments in potential theory using orthonormal

functions. P. Davis and P. RasrnowitTz,! National Bureau of Standards.

EDITORIAL NOTE

In potential theory and vibration theory much

use is made of a complete set of orthonormal

solutions appropriate to the domain of the

problem. The solution of the particular boundary

value problem at hand is represented as a linear

combination (generally an infinite series) of these

orthonormal functions. One property of ortho-

normal expansions is that if the infinite series is

approximated by its first n terms, the least

square error fit is always obtained.

This approach is related to much work that

has been carried out in the last generation but

which has so far been limited to theoretical dis-

cussions and applications to geometrically

simple domains such as circles and rectangles.

In practical problems, different methods have

been preferred, e.g., relaxation techniques. The

numerical experiments described in the following

paper show that the advent of high-speed auto-

matic digital computing machines makes the

method of orthogonal functions feasible.

INTRODUCTION

We describe in this paper three computa-

tions that were carried out on the National

Bureau of Standards Eastern Automatic

Computer (SEAC) and which made use of

a multiple purpose orthonormalizing code

recently developed for this machine [ef.

Davis and Rabinowitz (/)]. These com-

putations can be described briefly as fol-

lows:

(a) Computation of the system of orthonormal

polynomials for a ‘‘bean shaped”? domain

(Fig. 1).

(6) Solution of a Dirichlet Problem for this

“bean shaped’’ domain.

polynomials for the square.

For the theory of orthonormal functions

as applied to problems in conformal map-

ping, boundary value problems, etc, the

reader is referred to Bergman [2], Szeg6 [3].

The orthonormalization code employed

possesses the following features and limita-

tions:

(1) Inner products of the type [ fg ds

(of

are replaced by an integration rule

1 Now at the Weitzmann Institute, Rehovot,

Israel.

[fos D wis (Pog Po)

(2) The orthonormalization itself is car-

ried out by the Gram-Schmidt process.

(3) The code is of single precision type.

That is, the computation is carried out with

44 binary digits (11+ decimal digits).

It will be useful to specify the ortho-

normalization process more precisely. Let n

vectors, f;, of dimension N, have com-

ponents Yi, Y2, °°: , Yin, ¥ — 1,2, --- ,n,

TABLE 1.—LEAST SQUARES SOLUTION FOR

DrirIicHLET PROBLEM FOR BEAN-SHAPED REGION

| eS Po| A

38 | ee 3 a> | 2a

Ay < fo) 5 fQ a

1 -000} .110}.01414) .76089|/—.0030 || Boundary Value =

2 |—.050) .108).01427) .72025|—.0031 e™cos y + log

3 |—.100) .115).01963) .66721|—.0032 {Ql — y)2+ 22]

4 |—.160) .150).02300| .55236)—.0034

5 |—.220) .205).03897| .40068|—.0032 || Least Square Har-

6 |—.320) .300|.02792) .17014/—.09006|| monic Polynomial

7 |—.400) .358).03324) .06949| .0044 1.0017261087

8 |—.500) .420).01483) .02006| .0069 || +-.997339446 Re (z)

8 |—.550) .436).01423) .04590) .0023 \|—1.991187716 Im (z)

10 |—.600) .430).01505) .12037|—.0042 ||+1. 48065453 Re (z2)

11 |—.644! .400).01483) .22850|—.0069 || —.00949996 Im (z?)

12 |—.660| .350).01420) .33248)—.0026 || +. 1889575 Re (Zz)

13 |—.655| .300).02881) .41180) .0014 || +.6236775 Im (23)

14 |—.635| .200/.03043) .56168) .0038 || —.355600 Re (z4)

15 |—.595|} .100/.03076) .70060) .0009 || +.024526 Im (2)

16 |—.552| .000).03311) .84177/—.0019 || —.11960 Re (25)

17 |—.500;—.105|.03175| .98915|—.0023 || —.28034 Im (z5)

18 |—.440|—.200|.01809/1.12198} .0001

19 |—.400)—.250).01998)1.19326) .0018

20 |—.350)—.300).01882|1.26792| .0029

21 |—.300|—.344|.03140)1.33734) .0027

22 |—.204|—.400|.03450/1.44504; .0000 || Discrepanciesat Points

23 |—.100|—. 436|.02846/1.54875/—.0025 Interior to Bean

24 -000|— . 448) .02831)1.64168|— .0017 x Discrepancy

25 - 100|— . 442).03860/1.73582) .0015 4 +.0009

26 230) — . 400} .02431/1.85882) .0037 56) —.0001

27 - 300} — . 350} .02059/1.91643) .0014 32, —.0007

28 | .353|—.300].03566)1.95563|— .0013 oil —.0013

29 - 430|— . 200) .03122)1.99206| — .0030 0.0 —.0017

30 -477|—.100}.02975/1.96611| .0004 —.1 —.0017

31 -510} .000).02846)1.89648) .0041 —.2 —.0015

32 -522| .100).01696/1.75623} .0030 =} —.0011

33 -520) . 160).02330)1. 63625) — . 0006 —.4 —.0010

34 -500) .240).02102/1. 41224) — 0057 oH) —.0014

35 -456) .300).01795)1. 14765] —.0038

36 | .400) .330/.01147) .91523) .0028

37 | .360) .337!.01762| .78912) .0058

38 | .300} .320).01648| .68785| .0054

39 | .250) .290).01901) .66231) .0027

40 | .200) .245).01901| .69067|—.0001

41 - 150) .200).01809) .72694|—.0017

42 | .100) .160).01677) .75642'—.0025

43 -050) .128/.01501) .77202|—.0028

JANUARY 1956

and let one additional vector f have com-

ponents yi, °°: , Yn.

Let

gd: = anfi

go = Anfi + Anfe

$3 = Gufi + Ayvfo + Assfs

where the vectors ¢; have components

21,22, °°° , 2in and are orthonormal in the

sense that

(¢:, ¢;) = ee Wr ik Zin = Oi.

The least square approximation to f is

given by

po Dy, (f, dudo: = > dk fx

k=1 k=1

where d; = yee Gi Pi) Ax; 5 J a IL, 2, 2925. 4s

a.; = 0, k < j. The discrepancy in this ap-

proximation is defined by

5=f- LU, dnlde

=f-Ddihe.

The input and output of the code may be

indicated diagramatically as follows:

Vector Input Vector Output

weights fi ja tp f og gt ohn 6

Wr Yu Ya Yni Yi ie 221 Zn 1

ONY

Wn Yin Y2n Ynn YN \(21n 22N Znn On

Q it @ O- —@ Qy1 21 Oni —dy

0 0 1 0 0 0 a22 An2 —do

0 O 0 0 0 0 O An3 —d3

nr . . . . n . . .

0 O 0 1 0 0 O Qnn —dn

The high-speed capacity of the code is given

by the inequality (n + N) < 150.

COMPLEX ORTHOGONAL POLYNOMIALS

Let B designate a simply connected region

lying in the complex z-plane whose boundary

C is rectifiable. Let w(z) designate a positive

and continuous weight function defined on

C (or on B + C). In the space of analytic

DAVIS AND RABINOWITZ: ORTHONORMAL FUNCTIONS 13

functions which are regular in B + C, we

may introduce the inner product,

2) (fa) = | feq@wl) as

and orthonormalize the powers 1, 2, 2,

z, -+: with respect to this inner product.

Designate the polynomials which arise in

this fashion by

(3) ONO) = Ne” ae 9° 83

Designate by ¢(z) the function which maps

the exterior of C conformally onto the

exterior of | w| = 1,¢(2) = 0, ¢/(0) = 1.

If z is exterior to C, we shall have

ce 0:

(nA Bel) — 4G

(5) ue e2 ee = Ie

where c is the transfinite diameter of C.

These results are independent of the weight

function w(z).

Let (z) map the interior of C conformally

onto the interior of | w| = 1. Let the weight

w(z) = 1, then

6) Lapa = Wevor

where LZ is the length of C. For details on

these matters and for some information as to

the rapidity of convergence see Szegd [3],

pp. 355-366.

ORTHOGONAL HARMONIC POLYNOMIALS

If the set of harmonic polynomials 1;

Re(z), Im(z); Re(z*), Im(z’) --- are ortho-

normalized with respect to the inner product

(f,.0) = | He, Dale, ») as;

(7) : ; :

ds = dx + dy,

there is obtained a system of orthonormal

harmonic polynomials p,(v, y) Which is

intimately related to the harmonic kernel

function, the Greens’ function, and other

potential theoretic domain functions for B.

See Bergman [2]. To determine a harmonic

function in B with boundary data f(x, y)

on C (the Dirichlet problem) we may write,

14 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

h(a, y)

_ Ss lf flu, v)pr(u, v) as| Dace y)

n=0 Cc

and each finite segment of (8) provides a

harmonic polynomial which fits the bound-

ary data best in the sense of least squares.

(8)

DIRICHLET PROBLEM FOR A BEAN-

SHAPED REGION

A bean shaped region (see Fig. 1) was

obtained from a free-hand drawing on co-

ordinate paper. The region itself is “‘defined”’

by means of 48 points on the contour (see

Table 1). These points are not distributed

equally on the boundary, but somewhat

more points were placed where the curvature

is greatest.

Although there are certain theoretical

difficulties which occur when non-convex

regions are employed, we were interested in

testing the process for a fairly intricate

region. Since the region was not specified

analytically no attempt was made to

incorporate into the weights w, (see eq.

(1)) a very exact line element ds or a very

exact rule of numerical integration. For this

region, weights w, were taken proportional

to the distance between the successive points

given on the contour. These are listed in

column 4 of Table 1.

As boundary value data, we used the

VoL. 46, No. 1

values of the harmonic function

(9) u(x, y) = Re(e? + log (2 — 2))

at the 43 points on the boundary. These

are listed in column 5 of Table 1. This

boundary data was approximated by linear

combinations of the 11 harmonic functions

1, Re(z), --- , Re(z’), Im(2’).

The input data for this problem was ac-

cordingly, w; = the weights of column 4,

Table 1, yx, = {22 (a + ty:)?,

(10) fr = Re(e™***” + log(a, + iy — 2)).

Column 6, Table 1 lists the discrepancy

between the specified values and computed

(least square) values along the contour.

It will be seen that the highest deviation is

0.0069. If one knew that this were the

greatest deviation over the whole contour

then the maximum principle for harmonic

functions would tell us that this is also the

greatest deviation in the interior. Un-

fortunately, it is impossible theoretically to

make such a conclusion, but one feels

that in the interior these deviations are also

of the same order of magnitude. We have

computed the deviations at ten points along

the real axis in the interior of the region

and have listed them in Table 1. These

results bear out this feeling.

? For a theoretical discussion of this point see,

ci KK. Payne and H. F. Weinberger [4] and Nehari

[5], [6].

Fic. 1.—Bean-shaped region used in computation

JANUARY 1956

ORTHOGONAL POLYNOMIALS FOR A BEAN-

SHAPED REGION

The input data here was as follows,

w; = the weights of Column 4, Table 1,

Yjr = (t + tyr)’, y = arbitrary. As part

of the output data we obtained the co-

efficients of the orthonormal polynomials,

and the values of each orthonormal poly-

nomial at each of the 43 points on the

contour. We obtained the orthonormal

polynomials up to and including those

of degree 21. For reasons which will be

explained presently, it is not felt. that the

polynomials of degree greater than 11 are of

great significance numerically.

TABLE 2.—DETERMINATION OF TRANSFINITE

DIAMETER OF BEAN-SHAPED REGION

n Rn/Rpxr

485511

913294

503448

.903615

506216

006834

. 908043

-507085

.907510

-505941

508073

SCO ONOMOMPWNrH ©

pu(z)

Pro(Z)

ON THE BOUNDARY OF THE BEAN

TaBLE 3.—THE QUANTITY EVALUATED

Pt. No. | pu/pro | Pt. No, | pu/ Pio |

1 .882 23 .937

2 . 906 24 1.018

3 944 25 1.016

4 987 26 .968

5 .999 27 1.069

6 .983 28 .985

7 .992 29 .996

8 1.017 30 1.056

9 .993 3l .940

10 .980 32 1.050

11 1.019 33 1.026

12 .989 34 .976

13 .974 35 1.034

14 1.004 36 984

15 1.082 37 981

16 .994 38 1.029

17 943 39 1.057

18 1.089 40 1.083

19 1.040 41 981

20 .930 42 .928

21 . 962 43 .890

2, 1.067

DAVIS AND RABINOWITZ: ORTHONORMAL FUNCTIONS 15

Table 2 presents the ratios kn/kni1 for

Tie — Oe eel) ec cording tom)! these

ratios approach the transfinite diameter of

the region. The convergence of this sequence

is not too rapid, but the table suggests that

we have determined this constant to two

decimal places. We have computed these

ratios also for n = 11, --- , 20, but have not

tabulated them here. Their behavior is

steady for a while and then as n > 11, they

begin to increase rapidly towards one. This

is the result of two things. In the first

place, there is a considerable loss of sig-

nificance in the coefficients of high order due

to the fact that these values have to be

scaled down sufficiently so as to fit on the

machine. Secondly, since only crude integra-

tion rules were employed in computing

i 2"2" ds, the orthonormal polynomials

themselves tend more to those corresponding

to finite sum inner product as n approaches

the number of points on the contour.

According to (4), the ratio Pnsil2) tends

Prlé

to the exterior mapping function. We have

tested this out for = 10. The worst agree-

ment can be expected on the boundary of

the region, where a theoretical value of

|¢(z)| = 1, z€C, should be obtained.

Table 3 lists the values of | pu(z)/pro(z) |

on the contour C. A maximum error of

10% from the theoretical value of 1 was

obtained. The average error appears to be

about 5%. From the values of pio(z) on the

contour it was a fairly simple matter to

trace the variation in arg pio(z), 2 € C, and

to verify that all the zeros of pio(z) lie in B.

Thus, pu/pi is regular outside of B.

As might have been foreseen from the

behavior of the ratios ky41/k, for n > 11.

no improvement in the quantities

| Pn+t (2)/Dn (z) |

was observed for n > 11. We shall discuss

in a later paragraph how these shortcomings

‘an, In certain instances, be overcome.

We have not yet developed a code for the

rapid evaluation of the interior mapping

function through the use of (6) and so an

estimate of the quality of the convergence

of this formula cannot be given at the

present time.

16 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

vou. 46, No. 1

TaBLE 4.—ORTHONORMAL POLYNOMIALS FOR A SQUARE; SIDE = 1.4; Sum or GaussIAN WEIGHTS = 1.0

10000000000

1.2371791483 Z

1.4937246015 Z?

1.7603713248 Z%

2.2025044571 Z4 +0. 4230570561

2.6608221383 2° +0.7301295947 Z

3.220657584 Z® +1.1572896252 Z?

3.905515952 Z7 +1.7238789614 Z%

4.737815070 2% +2.4298575834 Z4

5.737742726 Z9 +3.3915415979 75

6.949286858 71° +4.645751758 Z°

8.416037589 Zl +6.274558086 Z?

10.19384526 Z +8 .381528538 2%

1234288234 Z +11.102777658 Z?

14.94442510 74 +14.597987726 Z1°

18.09361812 715 +19.073026420 711

.0188295964

0646244543 Z

. 2286090195 Z?

.§137415655 78

.9916706683 Z4

.7111406242 2%

2.782242918 Z®

+4 .339843064 Z7

+ .0261223727

+ .0433444223 Z

+ .0869122976 Z?

+ .1803740299 Z?

1G Eek |

ORTHOGONAL POLYNOMIALS FOR A SQUARE

For machine purposes, it is convenient

to have all distances from the boundary

to the origm <1, and so the side of the

square was taken to be a = 1.4. Since the

boundary of the square consists of ele-

mentary curves, it is not too difficult to

employ high accuracy integration formulas

in (1). In computing with the square, we

selected along each of the sides a 16 point

Gaussian integration formula. At the time of

computation, this was the highest Gaussian

formula available, though subsequently

Gaussian formulas of higher order were

computed. (See Davis and Rabinowitz [7]).

Inasmuch as the function z* = (a + iy)* is,

along either x = const. or y = const., a

polynomial in y or in x of degree k, this

Gaussian integration formula will produce

inner products which are completely ac-

curate, neglecting machine roundoff, up to

TABLE 5.—DETERMINATION OF TRANSFINITE

DIAMETER OF SQUARE; SIDE = 1.4

n Rn/Rn+

0 .808290377

1 828251169

2 848528137

3 .799258916

4 .827753357

5 .826173559

6 .824643305

Ul 824328492

8 .825728043

9 .825659214

10 .825719560

11 .825599896

12 825888555

13 .825918846

14 .825950067

the terms i 22" ds. No particular use of

(oj

the symmetries of the square was made

and the cyclic occurrence of many zero

coefficients in the orthonormal polynomials

served as a running check on the accuracy

of the process at the machine end of the job.

The orthonormal polynomials are listed in

Table 4. Table 5 lists the ratios k,/kn+1

which approach the transfinite diameter of

the square. The theoretical value for this

quantity [see Polya, Szegé (8), p. 252] is

1 2

~ 14 PQ _ 9 gogo38

Aq?

Thus, using orthonormal polynomials of

degree 15, we have secured this quantity to

three significant figures.

CONCLUDING REMARKS

The method of orthonormal functions for

the solution of problems in potential theory

is an attractive one from the point of high-

speed computing inasmuch as a single all

purpose code can, with suitable small

modifications, be made to cover a variety

of problems. The inputs for these problems

are especially easy to handle.

The accuracy that has been obtained in a

moderate amount (about 2 hours) of com-

puting time on SEAC is not great; about 2

decimal places. To obtain this, one would

make use of about 15 approximating func-

tions each of which is defined by its values

at about 50 points. In order to increase this

accuracy, we would need to increase simul-

taneously the number of orthonormal func-

tions employed and the number of points

at which each function is defined. From the

JANUARY 1956

machine point of view, this means that we

must employ double precision coding in

order to retain significance in the higher

harmonies. Accordingly, four place ac-

curacy might require about 24 hours of

computing time on SEAC.

The authors wish to thank the computa-

tion Laboratory of the National Bureau of

Standards for carrying out certain (hand)

computations necessary for the final prepara-

tion of this report.

BIBLIOGRAPHY

(1) Davis, P.,and Rasinowitz, P. A multiple pur-

pose orthonormalizing code and its uses. Journ.

DAVIS AND RABINOWITZ: ORTHONORMAL FUNCTIONS 17

Assoc. Computing Machinery, 1: 183-191.

1954.

(2) Beremans. The kernel function and conformal

mapping, New York, 1950.

(3) SzEGé, G., Orthogonal Polynomials, New York,

1938.

(4) Payne, L. E., and Wrinspercer, H. F. New

bounds in harmonic and biharmonic problems,

Jour. Math. and Physics 33: 291-307. 1955.

(5) Newari, Z., On the numerical computation of

mapping functions by orthogonalization, Proc.

Nat. Acad. Sci. 37: 369-372. 1951.

(6) Newari, Z. On the numerical solution of the

Dirichlet problem. (To appear.)

(7) Davis, P., and RapinowitTz, P. Abscissas and

weights for Gaussian quadratures of high

order. (To appear.)

(8) Pézya, G.,and SzuaG6, G. Isoperimetric inequali-

tues in mathematical physics, Princeton, 1951

NOTES AND NEWS

FELLOWS OF IRE ELECTED

The Washington Section of the Institute of

Radio Engineers announces the election of nine

members to the grade of Fellow. Presentation of

certificates will be made at the Washington Sec-

tion Annual Banquet by the President of IRE to:

ALEXANDER, S. N., National Bureau of Standards.

For contributions to the development and appli-

cation of digital computers.

Beutz, W. H., Carpr., USN (Ret.) For leadership

in improving the reliability of military elec-

tronic systems.

Cuark, A. B. (Deceased 14 Nov. 1955.) For early

development and leadership in the field of

telephonic transmission systems.

Corcoran, G. F., University of Maryland. For

contributions to electrical engineering educa-

tion and to the associated literature.

Davis, T. M., Naval Research Laboratory. For

contributions in the field of military radio

communication.

Dinetry, E. N., Jr., National Security Agency.

For contributions in the fields of electronic

guidance and detection systems.

Kaumus, H. P., Diamond Ordnance Fuze Labora-

tory. For contributions in the fields of electro-

mechanical devices and electronic measurement

instruments.

Paag, C. H., National Bureau of Standards. For

contributions to military electronic research

and development.

Rasinow, Jacos, Rabinow Engineering Co. For

contributions in the fields of electronic ordnance

and automatic control.

Special recognition will be given to Wilbur 8.

Hinman, Jr., Technical Director of the Diamond

Ordnance Fuze Laboratory, who is this year’s re-

cipient of the Harry Diamond Memorial Award

NEW MEMBER OF NATIONAL

RESEARCH COUNCIL

Ray P. Trrte, a member of the Photometry

and Colorimetry Section of the National Bureau

of Standards, has been appointed a member of

the National Research Council. He will represent

the Illuminating Engineering Society in the Divi-

sion of Engineering and Industrial Research for

a period of three years ending June 30, 1958.

Mr. Teele has gained international recognition

as a member of photometric fields. His work

covers the maintenance of the national photo-

metric units of luminous intensity (candlepower)

and luminous flux; developing and maintaining

standards of illumination and photometric bright-

ness; participating in the national and inter-

national standard comparisons; and evaluating

candlepowers of different colored lights by study-

ing the luminosity factors of the human eye.

Born in Washington, D. C., in 1903, Mr. Teele

came to the Bureau in 1923. He received his

bachelor of science degree in electrical engineering

from the University of Michigan in 1927, and his

master of science degree in physics from George

Washington University in 1929.

Author or coauthor of some 15 articles pub-

lished in his field of research, Mr. Teele also

holds a patent for a blackout automobile head-

light mask and another patent for a headlamp

for motor vehicles. He is a member of the Optical

Society of America, the Philosophical Society of

Washington, the Illuminating Engineering So-

ciety, the Washington Academy of Sciences, and

the American Association for the Advancement

of Science.

18 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

vou. 46, No. 1

ZOOLOGY —The ticks (Acarina: Ixodoidea) of the J. Klapperich Afghanistan

Expedition, 1952 and 1953. GEORGE ANASTOS, University of Maryland.

This report brings together the available

information on the ticks of Afghanistan and

extends to 14 the number of known species

from this country. None of the ticks recorded

from Afghanistan are endemic but also

occur in Iran, in India, and in the southern

part of the U.S.S.R. The records and

collections studied so far are too small and

often lacking in essential data to allow any

far-reaching conclusions to be drawn. Un-

doubtedly future collections will extend the

current list considerably since scarcely any

tick records are available for the extensive

wild fauna known from this country.

The earlier records of ticks in Afghanistan

were included only as incidental ones in

studies on the tick fauna of the surrounding

countries. Yakimov (1922) reported on the

Ixodidae in Russia and included one record

of Hyalomma aegyptium (Linné), 1758, from

Koscha on the Russo-Afghan frontier. In a

revision of the Indian Ixodidae Sharif (1928)

recorded males of Hyalomma aegyptium

dromedarii Koch, 1844 (probably H. drome-

darit Koch, 1844), on Hrinaceus megalotis

Blyth from Afghanistan and males of

Hyalomma_ syriacum Koch, 1844 (=H.

aegyptium (Linné), 1758), from Jugdulluk

on Testudo horsfieldi Gray. An undetermined

species of Ornithodoros was noted by

Avanesov (1938) in native dwellings in

North Afghanistan and Pavlovsky (1944)

later reported the occurrence of Ornithodoros

papillipes \irula, 1895 (=O. tholozani

(Laboulbéne and Mégnin, 1882). Pomerant-

zev (1946, 1950) recognized the occurrence

of H. dromedari and of H. aegyptiwm in

Afghanistan but was apparently citing the

records of Sharif.

In 1954 the author reported the results of

a collection from Afghanistan made by the

Third Danish Expedition to Central Asia.

In addition to Hyalomma aegyptium which

had been recorded previously the following

species were found to be new to Afghanistan:

Hyalomma excavatum (Koch, 1844, H.

schulzer Oleney, 1931, H. rufipes glabrum

Delpy, 1949, Dermacentor niveus Neumann,

1897, Ixodes redikorzevi emberizae Pomerant-

zev, 1950, Rhipicephalus sanguineus (La-

treille), 1806, and Haemaphysalis numidiana

Neumann, 1897 (=H. erinacei Pavesi, 1884).

In 1955 the author was fortunate to

receive another collection from Afghanistan

made by J. Klapperich, Bonn, Germany, in

1952 and 1953. This collection, though

small, contained four species new to Afghan-

istan: Argas persicus (Oken), 1818, Derma-

centor marginatus (Sulzer), 1776, Haemaphy-

salis sulcata (Can. and Fanz.), 1877/1878,

and Ixodes redikorzevi redikorzevi Olenev,

1927. It also expanded the range of four

species previously recorded from this area:

Dermacentor niveus Neumann, 1897, Hya-

lomma dromedari Koch, 1844, H. excavatum

Koch, 1844 and Rhipicephalus sanguineus

(Latreille), 1806. No host information was

given for the ticks in this collection.

REFERENCES

Anastos, G. The 3rd Danish Expedition to Central

Asia. Zoological Results 12. Ticks (Chelicerata)

from Afghanistan. Vid. Medd. Dansk Naturh.

Foren. 116: 169-174. 1954.

Avanesoy, G. A. Tick transmitted spirochetosis in

Afghanistan. Med. Paraz. Parazitar. Bolezni

7: 88-94. 1938.

Hooastraat, H. Notes on African Haemaphysalis

ticks. I. The Mediterranean-littoral hedgehog

parasite H. erinacei Pavesi, 1884 (Ixodoidea,

Ixodidae). Journ. Parasit. 41: 221-223. 1955.

Pavuovsky, E. N. Tick recurrent fever. Medgiz:

1-79. 1944.

PoMERANTZEV, B. I. Ticks, family Ixodidae. The

U.S.S.R. and adjoining countries. Opred.

Fauna §.8.8.R. Zool. Muz. Akad. Nauk.

Leningrad (26): 1-28. 1946.

———. Fauna of U.S.S.R. Arachnida. Acad. Sci.

U.S.S.R. 4: 1-224. 1950.

Suarir, M. A revision of the Indian Ixodidae with

special reference to the collection in the Indian

Museum. Rec. Indian Mus. 30: 217-344. 1928.

Yaximov, V. L. Contribution a Vétude des Ixodidés

de Russie. Bull. Soc. Path. Exot. 15: 41-46.

1922.

JANUARY 1956

ANASTOS: TICKS FROM AFGHANISTAN

COLLECTION DATA

Acc. No. Species Locality Date No.

EP-6 Argas persicus Kandahar 18-II-53 1 adult

DM-2 Dermacentor marginatus Do-Shak, Khinjan Valley, Hindu | 1-X-52 1 female

; Kush

DM-3 Dermacentor marginatus Larki, Sarekanda Valley, Badak- | 3-VIII-53 | 1 male

shan

DM-4 Dermacentor marginatus Walang, Salang Valley, Hindu | 29-IX-52 1 female

Kush

DM-5 Dermacentor marginatus Walang, Salang Valley, Hindu | 29-IX-52 1 male

Kush

DM-6 Dermacentor marginatus Sarekanda Mountain, Badakshan | 31-VII-53 | 3 females

DM-7 Dermacentor marginatus Sarekanda Mountain, Badakshan | 28-VII-53 | 1 male, 1

female

DM-8 Dermacentor marginatus Sarekanda Mountain, Badakshan | 29-VII-53 | 1 female

DN-2 Dermacentor niveus Sanglish Pass, Minjan Mountain, | 2-VIII-52 | 1 female

Badakshan

HSU-2 | Haemaphysalis sulcata Bashgul Valley, Nuristan 9-IV -53 1 female

HSU-3 | Haemaphysalis sulcata Bashgul Valley, Nuristan 8-IV -53 1 male

HSU-4 | Haemaphysalis sulcata Bashgul Valley, Nuristan 24-1V -53 1 male

HSU-5 | Haemaphysalis sulcata Pagman Mountain, 30 km. north- | 14-VI-53 1 female

west of Kabul

JD-1 Hyalomma dromedarii Bashgul Valley, Nuristan 11-IV-53 1 female

JD-2 Hyalomma dromedarii Kandahar-Kuna 22-1-53 2 females

JD-3 Hyalomma dromedarii Kandahar-Kuna 28-1-53 1 female

JD-4 Hyalomma dromedarii Kandahar 13-11-53 1 female

JD-5 Hyalomma dromedarii Vicinity of Kabul 20-III-53 | 1 female

JE-3 Hyalomma excavatum Kutiau, Nuristan 5-V-53 1 male

JE-4 Hyalomma excavatum Vicinity of Kabul 16-V-52 1 male

JE-5 Hyalomma excavatum Bashgul Valley, Nuristan 8-IV-53 1 male

JE-6 Hyalomma excavatum Bashgul Valley, Nuristan 24-IV-53 1 male

JE-7 Hyalomma excavatum Bashgul Valley, Nuristan 17-IV-53 1 male

IRR-1 | Ixodes redikorzevi redikor- | Pagman Mountain 6-VII-52 1 female

Zevt

RS-22 Rhipicephalus sanguineus | Bashgul Valley, Nuristan 12-V-53 1 male, 2

females

RS-23 Rhipicephalus sanguineus | Bashgul Valley, Nuristan 6-IV-53 1 male

RS-24 Rhipicephalus sanguineus | Jalabad, Nuristan 30-III-53 | 3 females

RS-25 Rhipicephalus sanguineus | Kandahar 22-11-53 1 female

RS-26 Rhipicephalus sanguineus | Kandahar 11-11-53 2 males, 3

females

RS-27 Rhipicephalus sanguineus | Kandahar 19-I1-53 1 male

RS-28 Rhipicephalus sanguineus | Kandahar 19-11-53 3 males, 6

females

RS-29 Rhipicephalus sanguineus | Kandahar 13-11-58 1 female

RS-30 Rhipicephalus sanguineus | Kandahar-Kuna 22-I-53 1 male

RS-31 Rhipicephalus sanguineus | Kandahar-Kuna 1-ITI-53 1 female

RS-32 Rhipicephalus sanguineus | Vicinity of Kabul 16-V -52 1 female

RS-33 Rhipicephalus sanguineus | Vicinity of Kabul 16-V I-52 1 male

RS-34 Rhipicephalus sanguineus | Kutiau 5-V-53 1 male, |

female

RS-35 Rhipicephalus sanguineus | Tchakaran, Wardush Valley | 1 female

20 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

vou. 46, No. 1

BIOCHEMISTRY .—Effect of cortisone acetate on production of liver and muscle gly-

cogen from C-14 labeled glycine and DL-alanine.! W. C. Hess and I. P. SHar-

FRAN, Georgetown University School of Medicine.

It is generally considered that the glycogen

formed in the liver of fasting rats, following

administration of adrenal cortical hormones,

is derived from protein (/—4). It has been

shown that cortisone acetate does not

increase the production of liver glycogen

after feeding glycine above the additive

effect of the individual actions of the two

compounds (5). However, cortisone acetate

does produce higher liver glycogen values

when DL-alanine is fed (6). The maximum

amounts of liver glycogen formed from

glycine and DIL-alanine, 2.6 percent in 16

hours and 3.3 percent in 6 hours, represent

conversions of 30 and 25 percent, re-

spectively, of the theoretical amounts of the

carbons of the 2 amino acids into glycogen.

Using glycine and DL-alanine containing

tagged carbon, several investigators have

reported that only 1 to 5 percent of the

isotope was present in the liver glycogen

(7-9). It would appear, therefore, that the

carbons of the formed glycogen do not

necessarily come from the amino acid fed,

at least as far as the particular tagged

carbons are concerned.

In a further study on the effect of cortisone

acetate on liver glycogen formation DL-

alanine and glycine tagged with C-14 in

carbons 1 or 2 have been employed to

determine whether there are differences in

the degree of glycogen incorporation of the

2 carbons before and after the administra-

tion of cortisone acetate.

Procedure for the administration of the

amino acid and estimation of liver glycogen

is the same as previously employed (5).

Rats, weighing 100 to 150 g, were fasted for

24 hours and then given either 500 mg of

tagged glycine or DL-alanine and sacrificed

at the end of 16 and 6 hours, respectively,

the periods of maximum glycogen pro-

duction for the 2 amino acids. The activity

of the labeled amino acids fed ranged from

1.0 to 1.5 X 10® counts per minute. Activity

1This work was supported, in part, by a con-

tract with the Atomic Energy Commission and

also by a grant from the Council on Chemistry

and Pharmacy of the American Medical Associa-

tion.

of aliquots of the isolated glycogen was de-

termined using a gas flow counter. In the

experiments with cortisone acetate 5 mg of

the hormone were given intramuscularly at

the end of the fasting period, and the glycine

or DL-alanine were fed 8 or 18 hours later,

so that, when the animals were sacrificed

at the expiration of 24 hours, the maximum

effects of the amino acid and the cortisone

acetate would be obtained. Muscle glycogen

was also determined on aliquots of the

gluteus maximus at the same time as liver

glycogen.

Results —Each experiment was conducted

upon 4 to 6 rats and average values and

standard deviations for each series are given

in Table 1. The percent of the administered

counts of the C-14 in the amino acids found

in the isolated liver glycogen is given in

column 2. The glycogen formed from glycine

1-C-14 accounted for 2 percent of the ad-

ministered counts, while 6.1 percent were

found when glycine 2-C-14 was fed. Barnet

and Wick (9) found 1.2 and 2.6 percent,

respectively, of the administered counts

from glycine 1-C-14 and 2-C-14 in the liver

glycogen. However, they found only 1.7

percent glycogen in the liver after 17 hours,

whereas our value at the end of 16 hours

was 2.6 percent. It might be noted that

Mackaye, Wick, and Carne (10) had

previously found 2.4 percent glycogen at

the end of 17 hours. The lower degree of

incorporation of the isotope reported by

Barnet and Wick (9) probably reflects the

smaller amount of glycogen formed. The

second carbon in DL-alanine yielded a

higher amount of the labeled carbon in the

glycogen than did the first carbon.

Since the glycogen formed accounts for 30

percent of the carbons of the glycine fed,

then if all the carbon in the glycogen comes

from glycine 30 percent of the counts should

have been present. The amount of labeled

carbon found in the glycogen accounts for

only 7 and 20 percent of the theoretical

amounts of the 1-C-14 and 2-C-14 glycines,

respectively. Similarly with DL-alanine

where the liver glycogen formed accounted

JANUARY 1956 HESS AND SHAFFRAN:

TasLe 1.—LIvER GLycoGEN FoLLowina INGEs-

TION OF CaRBON LABELED GLYCINE AND DL-AL-

ANINE WITH AND WITHOUT CORTISONE ACETATE

1 2 3 4* 5

Glycogen

ee Liver| Counts in} Total formed ree 100

wt | glycogen | glycogen| , 3 glycogen

acid

ercent

& Eee mg mg i KO

Glycine 1-C-

1 ae 4.2 | 2.0 + 0.4/105 + 10 1.9 + 0.4+

Glycine plus

CAR eo. 4.3 | 2.8 + 0.3/172 + 15) 90 + 15/1.6 + 0.5

Glycine 2-C-

TY eaten eerie 4.0 | 6.1+0.5) 99 +7 6.1 + 0.7

Glycine plus

CAG ses 4.4 | 8.8 + 0.7/170 + 15] 86 + 14/5.2 + 0.8

DL - Alanine

1-C-14...... 4.6 | 1.7 + 0.2/144 + 14 1.2 + 0.2

DL - Alanine

plus CA....} 5.1 | 3.3 + 0.4/270 + 19/173 + 8 /1.2 + 0.3

DL - Alanine

2-C-14......| 5.0 |10.7 + 1.1/160 + 14 6.6 + 0.9

DL - Alanine

plus CA....} 4.6 |19.7 + 1.8/266 + 20/179 + 10/7.4 + 1.3

* Column 4 is obtained by subtracting glycogen formed by

cortisone acetate alone in 24 hours, 1.9 percent, from column 3.

¢ Calculation of the t value of the difference for each pair

showed no significance.

tCA = Cortisone acetate.

TABLE 2.—MuscLE GuLycoGEN FOLLOWING INGES-

TION OF CARBON LABELED GLYCINE AND DL-AL-

ANINE WITH AND WITHOUT CoRTISONE ACETATE

Percent

Compound Rat we| CWC | Total | of count

amino acid

g percent mg

Wasting seen secieteetsrs asi 133 0.60 327

Fasting plus CA.......... 154 0.70 467

Glycine 1-C-14............| 187 0.62 341 0.5

Glycine plus CA......... 131 0.80 430 0.4

Glycine 2-C-14............ 135 0.59 330 0.6

Glycine plus CA......... 134 0.90 490 0.4

DL-Alanine 1-C-14....... 136 0.58 286 0.4

DL-Alanine plus CA..... 120 0.74 355 0.6

DL-Alanine 2-C-14....... 154 0.55 359 0.6

DL-Alanine plus CA..... 159 0.86 575 0.6

*CA = Cortisone acetate.

for 25 percent of the carbon in the amino

acid fed the counts in the liver glycogen

explained 7 and 43 percent of the theoretical

amounts for the 1-C-14 and 2-C-14 positions,

respectively.

When cortisone acetate was administered

prior to the amino acid the liver glycogen

formed represents the combined effects of

the two compounds. If the amount formed

by cortisone acetate alone in 24 hours, 1.9

LIVER AND

MUSCLE GLYCOGEN 21

percent (4), is subtracted from the total

amount produced the remainder may be

attributed to the amino acid. These values

are given in column 4. As previously noted

cortisone acetate depresses slightly the

amount of glycogen formed from glycine

while there is an increased glycogen pro-

duction from DL-alanine (5). The present

results are in accord with the previous ones.

The increase in glycogen formation from

DL-alanine induced by cortisone acetate

may result from the inhibition of glucose

utilization by cortisone suggested by Bout-

well and Chiang (//). Boutwell? has also

found that the administration of tagged

alanine together with cortisone acetate

produced an increase in the concentration

of the tagged carbon in blood glucose over

that produced by tagged alanine alone.

If the percent of the administered counts

from the C-14 incorporated into 100 mg of

glycogen is determined, column 5, to provide

a uniform basis for comparison, no signifi-

cant differences were found between the

‘results for each labeled amino acid with and

without cortisone acetate. In the experi-

ments with DL-alanine the cortisone was in

the animal for 18 hours prior to the ad-

ministration of the alanine, during which

period the liver formed glycogen (5) and the

period for the joint action was 6 hours;

never the less the results indicate an equal

dispersion of the labeled carbon in_ the

glycogen. It is conceivable that the amino

acids are converted into glucose that enters

the metabolic pool from which the liver

glycogen is synthesized. The glycogen

formed through the action of the cortisone

would come from the same pool as the extra

glycogen from the amino acid and conse-

quently contain the same percent of the

labeled carbon. Apparently cortisone acetate

does not influence the incorporation of the

carbons of the exogenous amino acids into

elycogen. The glycogen formed by cortisone

in the livers of fasting rats could come from

body protein (72) or as suggested by Kinsell

et al. (13) from body fat.

The results of the

muscle elycogen are given in Table 2. The

total glycogen is calculated from the

relationship of muscle mass to body weight

determinations of

2 Personal communication,

22 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

(14). While cortisone acetate did produce an

increase in muscle glycogen, as noted by

others (15), neither of the amino acids was

effective. On the average about 0.5 percent

of the administered counts were found in the

muscle glycogen and the administration of

cortisone acetate did not affect the value.

Summary.—Liver glycogen formed follow-

ing the feeding of glycine 1-C-14 or 2-C-14

to fasting white rats contained 2.0 and 6.1

percent of administered counts, respectively.

Similar experiments with DL-alanine 1-C-14

and 2-C-14 produced 1.8 and 10.7 percent

incorporation of the administered counts

respectively. When cortisone acetate was

injected prior to the amino acids the percent

incorporation of the labeled carbon in 100

mg of the glycogen was the same as in the

absence of the cortisone acetate. Cortisone

acetate produced an increase in muscle

elycogen; neither glycine nor DL-alanine

produced any change in glycogen content

either alone or in the presence of cortisone

acetate; less than 0.5 percent of the ad-

ministered isotopes were found in the muscle

elycogen.

vou. 46, No. 1

LITERATURE CITED

(1) Brirron, 8S. W., and Sitverre, H. Amer.

Journ. Physiol. 185: 657. 1954.

(2) Lone, C. N. H., Karzin, B., and Fry, E.

Endocrin. 26: 309. 1951.

(3) Lewis, R. A., Kunuman, D., DELBu, C.,

Koepr, G. F., and Tuorn, C. W. Endocrin.

27: 97. 1940.

(4) Locxrert, M. F., and Evans, M. M. Journ.

Endocrin. 7: 357. 1951.

(5) Hess, W. C., and SHAFFRAN, I. P. Proc. Soc.

Exp. Biol. Med. 88: 804. 1953.

—., Ibid. 86: 287. 1954.

(7) OusEN, N. S., Hemineway, A., and NieEr,

A. O. Journ. Biol. Chem. 148: 611. 1943.

(8) Gurin, S., Dettuva, A. M., and Witson,

D. W. Journ. Biol. Chem. 171: 101. 1947.

(9) Barnett, H. N., and Wick, A. N. Journ.

Biol. Chem. 185: 657. 1950.

(10) Macxaye, BE. M., Wick, A. N., and Carne,

H. O. Journ. Biol. Chem. 132: 613. 1940.

(11) Bourweui, R. K., and Curane, R. Arch.

Biochem. Biophys. 50: 461. 1954.

(12) Encen, F. L., Scurturr, S., and Pen7z, E. I.

Endocrin. 44: 458. 1949.

(13) Kinsey, L. W., Micnagts, G. D., Marcen,

S., Parrrivce, J. W., Bouine, L., and

Baucu, H. E. Journ. Clin. End. Metab.

14: 161. 1954.

(14) Donaupson, H. H. The rat. Mem. Wistar

Inst. no. 6. Philadelphia, 1924.

(15) Lronarp, S. L. Endocrin. 53: 226. 1953.

NOTES AND NEWS

NEW PUBLICATION ON COLORS

Publication of The ISCC-NBS method of desig-

nating colors and a dictionary of color names, by

Kenneth L. Kelly and Deane B. Judd, National

Bureau of Standards Circular 558, 158 pages,

has recently been announced by the Bureau.

The circular is designed to assist the scientist,

businessman, and layman to understand the dif-

ferent color vocabularies used in the many fields

of art, science, and industry. The dictionary

serves not only as a record of the meanings of

the 7,500 individual color names listed but also

enables anyone to translate from one color vocab-

ulary to another. For example, the dictionary

shows that griseo-viridis (biology) = serpentine

(fashion) = mint green (mass market), or in

ordinary language, a light green.

The terms by which this dictionary defines

color names are those of a refinement of the

method of designating colors outlined by the

Inter-Society Color Council (ISCC) and de-

veloped at the National Bureau of Standards.

The system applies not only to the colors of

drugs and chemicals, for which it was originally

developed, but to the colors of all opaque, clear,

cloudy, or fluorescent samples, whether viewed

by reflected or transmitted light, and to micro-

scopic structures.

The circular may be obtained from the United

States Government Printing Office at $2 a copy.

FORAMINIFERA CATALOG REISSUED

The Smithsonian Institution has recently

issued an offset reprint of Charles Davies Sher-

born’s An Index to the Genera and Species of the

Foraminifera. This monumental reference work,

long out of print, was originally published by the

Smithsonian in 1893 and 1896 in two parts. It

includes all species and genera of Foraminifera

published to 1889, giving both the original names

and any new combinations used by later authors,

as well as literature citations.

Systematic work on Foraminifera during the

past 40 years has received a tremendous impetus

from their economic value, especially that con-

cerned with the search for petroleum and more

recently with ecologic and paleoecologic studies.

Because of the daily increasing volume of pub-

lished material, it is difficult to keep abreast of

nomenclatural changes in current work. Recently,

Dr. Hans E. Thalmann of Stanford University

completed for publication an index of the Foram-

inifera from 1890 to 1950. This work continues

the earlier work by Sherborn, bringing it up to

date, but does not repeat the material of Sher-

born’s book. With the forthcoming publication

of Thalmann’s index and with the present reprint-

ing of Sherborn’s classic index, modern students

will have now available an invaluable tool in

their systematic work on the Foraminifera.

JANUARY 1956

PROCEEDINGS: PHILOSOPHICAL SOCIETY 23

PROCEEDINGS OF THE SOCIETY AND AFFILIATED SOCIETIES

PHILOSOPHICAL SOCIETY

1379TH MEETING, MAY 8, 1953

The Society was addressed by L. Marron, of

the National Bureau of Standards, on the sub-

ject Electron interferometry.

The early optics of electrons was geometrical

optics, the dynamic trajectories being analogous

to light rays. DeBroglie introduced the wave con-

cept of electron behavior in his famous disserta-

tion. The contrast between photon waves and

electron waves is due primarily to the fact that

the electron has a rest mass, hence a rest energy,

whereas the photon has mass only by virtue of

moving with the speed of light.

Experimental evidence of the wave-nature of

electrons was first given by the classical Davisson-

Germer electron diffraction experiment. In more

recent years, Fresnel diffraction has been ob-

served at the edges of objects in the electron

microscope.

Interference of light waves can be accidental,

as in oil-film effects, or Newton’s rings, or inten-

tional as in various interferometers. Inter-

ferometers may produce equivalent virtual

sources by wave-front splitting, as with two

slits or two mirrors, or amplitude splitting, as in

the half-silvered mirror of Michelson’s inter-

ferometer.

Similarly, accidental interference of electron

waves has been observed in thin crystal flakes,

and in blisters on iodine crystals. For an electron

interferometer, both wave-front and amplitude

splitting have been considered. A double slit

system turns out to have unreasonable dimen-

sions, so we turn to two mirror schemes. Un-

fortunately, electron mirrors are not available,

but we obtain a similar effect by the prismatic

action of diffraction gratings. The use of three

parallel gratings and suitable stops for the

unwanted beams will suffice. A fraction of the

incident beam goes straight through the first

grating, is deflected by the second and restored

to its original direction by the third grating.

Another fraction of the beam is deflected by the

first grating, restored in direction by the second,

and passed straight through by the third. These

two beams enter and emerge in the same direc-

tion, but jointly delineate a rhombus between

the gratings. The optical version of the arrange-

ment was studied by Carl Barus and lost in the

literature; it was set up and demonstrated to the

audience.

The electronic version has been built and

operated at the National Bureau of Standards.

The gratings were 100 angstrom thick gold erys-

tals, made by the epitaxial deposit of gold vapor

on the cleavage face of rocksalt crystals. The

interferometer can be used for measuring the

wavelengths of electrons, hence for determining

Planck’s constant.

Interference has been obtained with path

differences of as much as 6000 wavelengths,

despite the 200 wavelength limit predicted on the

basis of diffraction experiments. This raises an

interesting question as to the meaning of phase

velocity, a quantum mechanical unobservable.

It was also pointed out that free space is a dis-

persive medium for electron waves, since the

wavelength is related to the energy, hence to the

velocity.

1380TH MEETING, MAY 22, 1953

President Manan announced that there had

been a last-minute change of program, due to

the sudden illness of the scheduled speaker, that

two speakers were obtained on short notice from

the Naval Research Laboratory, and that the

Society was grateful for such fine cooperation.

The first speaker was RicHarp Tousry. His

subject was Rocket spectrographs for the sun in

short untraviolet and X-ray. Rockets are needed

for this work, because of the opacity of the

earth’s atmosphere. The lower wavelength limit

of balloon and mountain observations is 2860

angstroms. Some interesting problems in the use

and recovery of rocket-borne equipment were

explained.

Spectrograms taken at various altitudes were

shown, and the ozone density as a function of

altitude deduced from the changes of absorption.

Measurements down to 1900 A were made spec-

troscopically. At shorter wavelengths, the ther-

moluminescence properties of calcium sulfate and

manganous sulfate were employed. These phos-

phors are heated after recovery, and luminesce

in proportion to the amount of short-wave energy

they have absorbed.

Narrow wavelength bands were explored with

photon counters. Halogen filling reduces their

long wavelength response, and absorption win

dows reduce their short wavelength response,

24 JOURNAL OF THE WASHINGTON

leaving a band-pass characteristic. Soft X-rays

in the 5-10 A region were measured, and the

observed intensities were compatible with a cor-

onal temperature of one million degrees Kelvin.

The second speaker was JoHn P. HaGen,

Radio Observations of the Sun. He discussed radio

frequency measurements of the tenuous solar

atmosphere lying outside the photosphere. The

photosphere is transparent to visible radiation,

but not to radio frequencies. Such data yield

the temperature and pressure in the solar atmos-

phere.

Motion pictures of the 1952 Eclipse expedition

were shown. Eclipses are useful in this field be-

cause radio telescopes have poor angular resolu-

tion, hence the radial brightness distribution is

hard to measure. Effective resolution is obtained

during an eclipse by observing the radio fre-

quency intensity as a function of moon coverage

of the sun. Theory calls for limb brightening at

radio frequencies.

The 1952 expedition made measurements at

wavelengths of 8 mm, 3 cm, and 10 cm. In all

cases, limb brightening was observed, i.e., the

sun appears to be encircled by a bright ring.

From this it 1s deduced that the temperature

rises steeply in the chromosphere, has a plateau

in the corona, and then falls off. (Secretary’s ab-

stract.)

1381ST MEETING, OCTOBER 23, 1953

Ricuarp L. Perrirz, of the Naval Ordnance

Laboratory and Catholic University, was intro-

duced by the President and spoke on Random

processes and noise in semiconductors.

The subject of the lecture was divided into

two parts: (a) Discussion of the relationships

between random processes in different fields of

study, such as physics, biology, and economics;

(b) application of random process theories to

noise in semiconductors.

Some of the basic definitions of interesting

random processes were given. Reference was

made to average values, probability functions,

correlation coefficients, and power spectra. The

Markoff process was discussed, and the relation

between branching processes in biology and

atomic bomb problems indicated.

In a semiconductor the number of electrons

contained in a conduction band is random.

When a current is going through the semicon-

ductor a noise is produced due to the fluctuation

of the number of electrons. Noise studies permit

the measure of certain parameters of the semi-

ACADEMY OF SCIENCES vob. 46, No. 1

conductors. The speaker described some experi-

mental methods used to determine the noise

spectrum. He discussed how the shape of the

noise spectrum is being related to the fluctuations

of lattice temperature and to the electron mobil-

ity in semiconductors.

1382D MEETING, NOVEMBER 6, 1953

James W. Davisson, of the Naval Research

Laboratory, was introduced by the Chairman

and spoke on Electrical breakdown wn crystals.

Most phenomena in crystal physics add sym-

metry to the crystal symmetry itself. In the

X-ray determination, the most important prob-

lem is to find out what is the symmetry of the

crystal. It turns out that electrical breakdown

phenomena, apart from crystal growth, are the

only ones which show symmetry of crystals under

all conditions. Electrical breakdown in crystals

generally leads to the formation of well-defined

paths. These lie in crystallographic directions

which depend upon the symmetry of the crystal,

the temperature, and the applied field. Both

negative and positive patterns vary with the

temperature. When one changes the polarity in

crystals which lack a center of symmetry, the

patterns are distinct and at no temperature come

together. Present theory, based upon anisotropic

electron scattering at the Brillouin zone borders,

explains some of the qualitative features of phe-

nomena. In metals, diamond, germanium, and

silicon, there is no polarization scattering but a

‘nonpolar’ scattering. Sulfur scattering does not

vary with temperature but presents still some

orienting influence. It looks as if, in sulfur, there

is a new type of asymmetrical scattering not de-

pending upon the Brillouin zone border. There

is, therefore, evidence that in addition to the

Brillouin zone effects there must be some other

source of asymmetrical scattering.

After a discussion on the subject of the lecture,

the meeting was adjourned for a social hour.

Twenty-one members attended the meeting un-

mindful of the snowstorm which fell on Wash-

ington with complete disrespect to the Weather

Bureau predictions.

1383D MEETING, NOVEMBER 20, 1953

SHIRLEIGH SILVERMAN, of the Johns Hopkins

University Applied Physics Laboratory was in-

troduced and assumed the chair for the technical

portion of the meeting.

The first speaker was JoHN Srronec, Johns

JANUARY 1956

Hopkins University. His subject was Interim re-

port on studies of infrared radiation from the moon

and the planets. Slides of the 8-14 micron infrared

spectra of Venus, Mars, and the moon were

shown, and surface temperatures deduced from

these data were given. The ingenious experi-

mental arrangement for comparing planetary

radiation with sky background and cancelling

effects of apparatus radiation, was explained.

One of the experimental results was that the

visually dark side of Venus is as warm as the

visually bright side, hence the day-night relation

being observed was sunset, rather than sunrise.

No carbon dioxide was observed on Venus, im-

plying that the observed stratosphere is above

the carbon dioxide layer. The atmospheric circu-

lation of Venus appears to be opposite to that of

Earth, for the poles of Venus were found to be

6° cooler than the equator, whereas an opposite

relationship is true on Earth (at high altitudes).

The earth’s atmospheric absorption was corrected

for by an ingenious scheme. The infrared radia-

tion from the moon can be computed in terms of

the moon’s temperature, in turn computed from

known solar constants. Comparison with the

observed lunar radiation yields the absorption in

the earth’s atmosphere.

The second talk was Line width and shape in

the Infrared, given by W.S. Benenict, of Johns

Hopkins University. This talk was centered on

the Lorentz law of collision broadening of spectral

lines. The predictions of this theory for line

peaks, troughs between lines, and extreme wings

of bands were discussed and compared with ex-

periment. The Lorentz law is good for CO,

except in the extreme wings, fair for CO except

in the wings and troughs, and no good at all for

HCl. The inadequacy for HCl is attributed to

polar intermolecular forces.

The final talk was Photo-ionization absorption

spectra of negatwe ions, by Lewis BRANSCOMB,

National Bureau of Standards. Negative ions

have a low binding energy of only 1 or 2 volts,

hence the photodetachment of the excess electron

involves infrared absorption. Most atoms do not

form negative ions; those that do such as hydro-

gen, usually have only one such state, hence do

not yield a line spectrum of absorption but only

a convergence limit of a continuous spectrum.

These ions are of interest as a possible mechanism

for storing electrons in the ionosphere. Experi-

mentally, the weak continuous absorption is al-

most impossible to observe. The speaker’s pro-

PROCEEDINGS: PHILOSOPHICAL SOCIETY 25

cedure was to observe by electrical means the

detachment of electrons from a beam of known

ion current. The experiments on negative hydro-

gen ions check with theory; negative oxygen

ions are still being studied.

1384TH MEETING, DECEMBER 4, 1953

The Society was addressed by K. K. Darrow,

of the Bell Telephone Laboratories, on The Hall

effect. He quoted a statement by Maxwell that

the current distribution is Not affected by a

magnetic field. Mr. Hall did not believe this

statement, and devoted his doctoral thesis to an

experimental proof of its falsity.

An electric current flowing through a ribbon,

whose plane is perpendicular to a magnetic

field, tends to be deflected against one edge of

the ribbon, in the direction of the resulting

mechanical force on the conductor. This trans-

verse virtual displacement of the streamlines of

the current produces a compensating transverse

electric field to compensate the displacement

force. The vector resultant of the applied longi-

tudinal electric field that motivates the current

and the transverse electric field of the Hall effect,

makes an angle @ with the direction of the ribbon.

The transverse equipotential lines are therefore

also rotated through an angle 6. This angle @ is

expressible as a function of the magnetic field

and the charge mobility, or as a function of the

field, the current, and the number of free charge

carriers per unit volume. Hence the Hall effect

offers a means of measuring either mobility or

free charge carrier density.

If a trace of arsenic, atomic number 33, is

present in germanium, 32, there are excess elec-

trons available for conduction, even at low tem-

peratures. As the temperature is raised, more

and more of the arsenic atoms release their excess

electrons, and the conductivity is increased.

These effects are demonstrated by the sign and

magnitude of the Hall effect.

Conversely, if the impurity is gallium, 31, there

is a deficiency of electrons, and the Hall effect

yields the density of apparent positive charge

carriers, and shows the increase with tempera-

ture; these two types of semiconductor material

are known as n-type and p-type respectively.

At sufficiently high temperatures, pure germa-

nium becomes a so-called intrinsie semiconductor.

The thermal agitation releases valence electrons,

and supposedly equal numbers of negative charge

carriers and apparent positive charge carriers are

26 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

present. Hall effect measurements yield the ratio

of the two mobilities. (Secretary’s abstract.)

1385TH MEETING, DECEMBER 18, 1953

The Society was addressed by GkorGrE GAMOW

on The arithmetic of life. Living cells are composed

of two types of material: the body of the cell is

made of proteins, the small nucleus of various

nucleic acids, generally abbreviated DNA. The

chromosomes in the nucleus are decomposable

into six building blocks; sugars, phosphates, and

four complex bases. The chromosomes somehow

carry the information for the synthesis of the

cell proteins.

DNA comprises long chains of sugars cemented

together by phosphates. To each sugar is attached

one of the four bases. The bases can hook to each

other in certain pairings by hydrogen bonding,

thus allowing two suitable long sugar chains to

be adjoined. The resulting dual chain chromo-

some has a helical structure, with a pitch of one

turn to ten sugar molecules. Chromosome division

takes place by splitting of the string of hydrogen

bonds. After the splitting, each of the bases can

attach a replacement from solution, and even-

tually restore the whole chromosome. In an ex-

cited state, some of the otherwise forbidden

hydrogen bond pairings can occur. Under these

conditions, the newly grown half of a chromo-

some may contain a few errors. Under subsequent

division, this error is propagated and becomes

permanent. This may be the explanation of

mutations.

The proteins of the cell are decomposable into

twenty different amino acids, as building blocks.

It is interesting to note that although amino

acids have both laevo- and dextro- forms, only

the laevo-acids have been found in living organ-

isms. Protein molecules are made of long chains

of amino acid groups. The problem is to explain

how the long chromosome chains of four bases

control the manufacture of the long protein chains

of twenty blocks. Analysis of the allowable

combinations of four adjacent bases in the chro-

mosome chains, in light of the hydrogen bonding

rules, shows that exactly twenty different ‘‘dia-

monds” can oecur. The twenty amino acids fit

into these diamonds, pointing in toward the axis

of the spiral, and approaching sufficiently close

to each other to join and make protein. These

protein molecules can then be stripped from the

mold, so to speak. Further combinatorial analysis

shows that the twenty diamonds cannot follow

vou. 46, No. 1

each other in arbitrary order, but still represent

essentially a radix four system. The diamonds

can be segregated into six classes: the first class

contains four diamonds, each of which can be

followed by any of fourteen, including themselves.

The second class is similar. The third and fourth

classes are similar, but the combining number is

seven, rather than fourteen. The last two classes

can each combine with only seven, and in each

case this seven does not include the members of

the class itself. If we represent each of the twenty

diamonds by a letter we have 196 allowable pairs

of letters, and each of these pairs allows only four

choices of the succeeding pair. Trying to identify

the various letters with the twenty amino acids is

a complicated problem in cryptography. The

structure of insulin is a known chain of 29 amino

acids, hence represents an allowable message in

our code. So far, the code has not been broken.

(Secretary’s abstract.)

1386TH MEETING, JANUARY 15, 1954

This meeting of the Society was the occasion

of the retiring Presidential Address on Some newly

solved and some unsolved problems in optics, by

Arcute I. Manan, of the U. 8. Naval Ordnance

Laboratory. The address has been published in

this JouRNAL 44: 165-194. 1954.

1387TH MEBTING, JANUARY 29, 1954

The Society was addressed by JEROME

WoLKEN, director of the Biophysics Research

Laboratory of the Eye and Ear Hospital, Pitts-

burgh, Pa., on Cellular growth, structure, and func-

tion. The structure of cells was described, in

idealized form. A relatively new technique of

electron microscopy of cells was described. The

cell is first ‘fixed’? with Osmium Tetroxide; the

excess salt is then washed out with water, and a

plastic allowed to diffuse in. The cell can then be

sliced with a glass knife into slices of 0.03-0.05

microns thickness. One of the organisms illus-

trated by use of this technique was an interesting

protozoon known as Euglena gracilis. This organ-

ism contains both chlorophyll and a purely animal

pigment, hence can be considered as either ani-

mal or vegetable, or both. The fact that the

chloroplasts can grow within the Euglena cell is

shown by the fact that under suitable growth con-

ditions, the amount of chlorophyll per cell in-

creases with time. On the other hand, treating

the cells with streptomycin or holding them at

40° Celsius will knock out the chloroplasts, but

the cells will grow and divide at their normal rate.

JANUARY 1956

There are about five chloroplasts per cell, on

the average, and these plastids have a layer struc-

ture, about 20 ‘dark’ layers separated by

“light” layers. The light layers are mainly water

and protein, the dark layers contain fat protein,

and pigment, the pigment beimg chlorophyll in

this particular case. There are about 10° chloro-

phyll molecules per plastid. These molecules are

assumed to “‘sit’’ on the surface of a layer.

In a purely animal structure, the eye of the

perch, the cones and rods show a similar layered

or banded structure. The thickness of the bands

is about the same as those found in Euglena and

also in higher plants. The rod cells and cone cells

also show about the same number of pigment

molecules as did the plastids, even though these

animal structures are much larger than those of

Euglena. The apparent paradox is resolved by

the observation that the visual pigments, of less

molecular weight than chlorophyll, are attached

to very large protein molecules in about a one-to-

one ratio, whereas the chlorophyll molecules are

attached to small protein molecules, still in about

a one-to-one ratio. The larger animal proteins

lead to the larger banded structures. Thus it is

found that the dark bands in a wide range of cell

types contain approximately the same number of

proteim molecules, or rather, of protein-pigment

complexes. There is chemical evidence for the

existence of a protein-pigment macromolecule;

the pigments in isolated form exhibit different

chemical properties than do those in cells. (Secre-

tary’s abstract.)

1388TH MEBTING, FEBRUARY 12, 1954

The Society was addressed by Herman

Branson, of Howard University, on the topic

Information theory and the structure of protein

molecules. Shannon’s definition of imformation

was reviewed, with attention to its additive

properties. A table was displayed, giving the

channel capacities, in bits per second, of various

sensory organs, and the much slower information

accepting capacity of the human brain. Informa-

tion theory can be formally applied to the struc-

ture of proteins, considering the 20-odd amino

acid residues as alphabetic characters, and the

protein chains as words. Each possible orienta-

tion or other “complexion” of an amino residue

is considered to be a different letter. The amount

of information “stored”? in the molecule can be

taken as the difference in the Shannon entropy,

or uncertainty, of the particular amino chain in

PROCEEDINGS: PHILOSOPHICAL SOCIETY 27

question, and the maximum uncertainty that a

chain of the same number of residues could have.

The uncertainty is the logarithm of the number

of possible “complexions”. In natural proteins,

the uncertainty is greater than 85 percent of its

maximum possible value, in most cases. This im-

plies little information storage. As the total num-

ber of residues, N, in the chain increases, the ratio

of the uncertainty to its mimimum possible value

appears to be a linear, increasing function of N.

(Secretary’s abstract.)

1389TH MEETING, FEBRUARY 26, 1954

The Society was addressed by E. O. Hutgurt,

of the Naval Research Laboratory, on the topic

Magnetic storms, aurora, ionosphere and zodiacal

light. Magnetic measurements have indicated

that the earth’s magnetic field behaves as if there

were a magnetic dipole at its center and a ring

current of about 10° amperes encircling the earth

in an east-west direction near the Equator. Dis-

turbances in the earth’s magnetic field may be

local or world wide, the latter being referred to as

magnetic storms. During a magnetic storm, the

earth’s field first increases, then it decreases below

its normal value, and finally after a recovery

period returns to its initial value. These disturb-

ances arise from outside the earth’s atmosphere

and are usually associated with sun spots.

A so-called “ultraviolet light theory” has been

proposed by Hulburt for explaining these mag-

netic storms. The theory suggests that the sun

bathes the earth in a sudden flare of ultraviolet

light. This ight increases the ionization in the

ionosphere with the result that the current in the

east-west direction increases also increasing the

earth’s magnetic field. The ionosphere however

is also heated so that an outward expansion fol-

lows. Because of the earth’s magnetic field at the

equator, these ions are forced into a west-east

current which brings about a decrease in the

earth’s magnetic field. This theory has had con-

siderable success in explaining many of these

phenomena.

Abnormal ionospheric activity is also closely

associated with magnetic storms, but due to a

lack of sufficient data and a complete evaluation

of existing data on a world wide basis, ionospheric

activity has not led to a better understanding of

magnetic storms. Statistical studies have been

started, but the work is unfinished.

Several corpuscular theories have also been

advocated for explaining magnetic storms. These

28 JOURNAL OF THE WASHINGTON ACADEMY

theories assume that the sun projects streams of

particles of like or unlike signs toward the earth,

some of which enter the polar regions and produce

aurora while others are trapped by the earth’s

magnetic field and give rise to an increased east-

west current at the Equator and hence an increase

in the magnetic field. These theories then make

plausible the first increase in magnetic field dur-

ing a magnetic storm, but the explanations of the

other phases are admitted as purely speculative.

The zodiacal light and the ‘‘Gegenschein”’ were

also discussed briefly. According to the older

theories, both were explained in terms of the dust

theory. Recently, however, the zodiacal light has

been found to vary in brightness during a mag-

netic storm and this cannot be understood in

terms of the dust theory. To explain these mag-

netic variations of the zodiacal light, Hulburt

has extended his ultraviolet light theory by as-

suming that the atoms which reach the outer

regions of the ionosphere accumulate in an oblong

ring in the plane of the ecliptic which absorbs the

ultraviolet light and reemits part as visible light.

This light is the zodiacal light. The portion of the

ring away from the sun streams away due to light

pressure and when viewed on end becomes the

“Gegenschein.”’ Experiments to check these ideas

are not in agreement.

1390TH MEETING, MARCH 12, 1954

The Society was addressed by Herpert

FRIEDMAN, of the Naval Research Laboratory,

on Solar X-rays, extreme ultraviolet radiation, and

the ionosphere.

Experimental data on the penetration of solar

radiation into the atmosphere have been obtained

primarily from rocket-borne equipment. Rocket

flights reach the D, E, and F layers of the iono-

sphere. In the ultraviolet range, 1300 to 1700 A,

the main absorber is molecular oxygen, which is

dissociated by the radiation. The atmospheric

absorption possesses a deep window which passes

the Lyman alpha line of hydrogen at 1216 A. The

2000 to 2800 A range penetrates to about 30 kil-

ometer altitude, where it is strongly absorbed by

ozone. The Lyman alpha radiation penetrates to

about 70 kilometers, which is the deepest pene-

tration of any radiation below 1800 A.

Between 1000 and 2000 A, the spectrum is too

weak for diffraction grating observations in the

time available in a rocket flight. Intensity meas-

urements in this range are therefore made at spot

wavelengths with suitable photon counters.

OF SCIENCES VoL. 46, No. 1

These are essentially Geiger counters with photo-

sensitive cathodes, and special windows for fil-

ters. Such an ultraviolet counter was demon-

strated. A flashlight produced absolutely no

response, but the flame of a match yielded a

strong signal. It was also demonstrated that glass

is opaque to the ultraviolet to which this counter

responded. Various photoelectron thresholds

down to 1900 A are obtainable by the use of a

suitable cathode. Filling the counter with the

proper gas will suppress emission from the cath-

ode, and require photoionization of the gas for

response. Appropriate combinations of cathode,

gas, and window material make possible counters

responding to only a relatively narrow band of

wavelengths. A counter was demonstrated,

having a 1300 A threshold. Sapphire and lithium

fluoride windows were used. Sapphire gives a pass

band from 1050 to 1300 A, and allows measure-

ment of the Lyman alpha line intensity. Ninety

percent of the solar radiation in this wavelength

range, below 100 kilometers altitude, is Lyman

alpha. The D layer of the ionosphere is explain-

able by Lyman alpha absorptioe producing

ionization of Nitric Oxide.

For measurement of X-rays of approximately

10 to 20 Angstroms, beryllium and aluminium

windows are suitable. The major absorption of

10 to 100 A radiation is found to be in the region

from 100 to 120 kilometers altitude. The resultant

ionization is a reasonable source for the E layer.

Measured X-ray intensities fit the known ioniza-

tion density of the E layer.

The sun’s corona contains highly ionized

atoms, with as many as fourteen electrons re-

moved. Recombination of these atoms with free

electrons yields a continuous spectrum that is

characteristic of a temperature of 1,000,000°

Celsius. This supplies the 20 to 50 Angstrom

energy for producing the E layer. Helium II radia-

tion is strong at about 200 A and may contribute

to the F layer. The coronal green line is attributed

to Fe XIV, and is apparently a good indicator of

the solar X-ray output. (Secretary’s abstract.)

1391sT MEETING, MARCH 26, 1954

The twenty-third Joseph Henry Lecture was

delivered by Henry Marcenav, of Yale Uni-

versity. His paper Advantages and disadvantages

of a causal interpretation of quantum mechanics

was published in full in this JourNaL 44: 265-276.

1954.

JANUARY 1956 PROCEEDINGS:

1392p MEETING, APRIL 9, 1954

The Society was addressed by A. MrcHE.s, of

the University of Maryland and the University

of Amsterdam, on the subject Some aspects of

high-pressure molecular physics.

The classical Van der Waals picture of molecu-

lar interaction was reviewed, and its quantum

mechanical explanation in terms of the inter-

actions of electric charges. According to this

model, the electronic orbits must be distorted as

a substance is compressed, i.e., as the molecules

are forced to be closer together. For example, if

pv is strongly increased in an isothermal com-

pression, both the total energy and the kinetic

energy increase. Since the temperature is un-

changed, the additional kinetic energy must be

in the electronic orbits.

An interesting rough theory of high pressure

effects has been worked out assuming close packed

hydrogen atoms. Each electron is assumed to be

confined to a geometrical cell centered on its

proton. A computation of the electron kinetic

energy increase of 5000 cal/mole for a pressure

of 3000 atmospheres. This result is in approxi-

mate agreement with experimental values for a

number of gases. For sufficiently high pressure,

several hundred thousand atmospheres, the

electron energy would exceed the ionization po-

tential. Does this imply that hydrogen would

then behave like a metal?

A similar orbit distortion verification was per-

formed on germanium. A pressure of 3000 atmos.,

increases the gap between the full energy bands

and the conduction bands by 3 percent, as indi-

cated by conductivity measurements. These re-

sults are also shown by the shift in the edge of the

infrared absorption spectrum.

Electron orbit distortion also shows up directly

in polarizability. Measurements on carbon dioxide

show a peak at about the same density for which

the isothermal kinetic energy is a minimum.

Another interesting property is shown by the

behavior of the vibrational absorption of mole-

cules as the pressure is increased. The nitrogen

molecule, for example, has no polar moment and

its vibration is not optically active. Under 100

atmospheres pressure, the distortion produces a

polar moment, and a wavelength of 4.2 microns

is absorbed. In the case of hydrogen, the absorp-

tion coefficient varies as the square of the density.

If, however, the compression is produced by add-

ing argon instead of more hydrogen, the variation

is linear. These results are interpreted as a linear

PHILOSOPHICAL

SOCIETY 29

increase due to pressure distortion, and an addi-

tional density factor arising from the increased

collision rate when hydrogen alone is_ used.

(Secretary’s abstract.)

13938D MEETING, APRIL 23, 1954

The program was entitled “An Evening of

Crystal Growth” and consisted of a set of three

related lectures. Pau Eat, of the Naval Re-

search Laboratory, acted as organizer and chair-

man.

The first topic was The role of impurities in

crystal growth, discussed by SAMUEL ZERFOSS, of

NRL. Large single crystals are grown from solu-

tion, from a melt, or by a flame melting process.

Samples of these types were demonstrated. A

particularly large solution grown crystal of ADP

(ammonium dihydrophosphate) was exhibited

and discussed. A flat seed plate was used to start

the growth of a square bar, by extension of the

faces, but not the edges, of the seed. The first

step is to grow end-caps on the plate. This yields

foggy material, but develops the equilibrium end

shape, by growth along preferred planes, starting

from the corners of the seed. After the endcap is

developed, growth of clear crystal proceeds.

The addition of impurities to the solution

modifies the growth habit of crystals, changing

the preferred faces. Sometimes the modification

is beneficial, as in the case of sodium chloride.

This substance, in pure solution, grows too vigor-

ously, and makes a large cubical assembly of

many relatively small crystals having approxi-

mately the same orientation. The addition of

lead chloride inhibits the growth on certain

regions of the crystal’s surface, with the end re-

sult of a large, perfect, single crystal. The lead

chloride action is transient, for the resulting crys-

tal is free of lead chloride.

The flame fusion process, familiar as the source

of synthetic rubies ete., requires very pure raw

materials. The residual impurities gather on the

surface of the boule as a scum. This technique

has been modified at NRL to allow processing in

vacuo. The flame is replaced by a section of

carbon pipe, heated as an induction furnace.

The second topic was The role of dislocations in

crystal growth, presented by F. Hussarp Horn,

of the General Electric Co.

The growth rate of a crystal depends upon the

degree of supersaturation of the solution. The

relation is essentially linear in the supersaturation

range of 25-40 percent, and in this range seems

30 JOURNAL OF THE WASHINGTON ACADEMY

adequately explained by theory. At lower con-

centrations, crystals still grow well, but the

theory breaks down.

It has been proposed that crystals grow readily

only on edges or other discontinuities, and not on

extensive perfectly flat faces. A screw dislocation

would give rise to a fault line upon which growth

could proceed. Analysis shows that growth on

the face of such a “cliff? would propagate the

cliff in a self-maintaining fashion, quasi-macro-

scopic feature of growth. Such spirals could also

be initiated by impurity specks, or other local

perturbations. Some fascinating color slides of

spiral growth patterns on calcium carbide crys-

tals were shown. (One of these could have been

suitable for a necktie design.) Time lapse motion

pictures, with a speed up factor of 64, convine-

ingly demonstrated this phenomenon in other

substances. It was concluded that the growth of

a single crystal to appreciable size requires the

presence of some type of imperfection.

The final speaker was Mr. Eerr, who used the

remaining few minutes to refute the arguments

of the previous speakers. His title was The role of

theories in crystal growth. Mr. Egli showed slides

of crystals that “obviously” did not grow by

spirals. Their growth was not controlled by im-

purities but by the lattice in keeping with class-

ical theory. The dislocation theory cannot be of

major importance, because these spirals occur on

the slowly growing faces, not on the fast ones.

The spiral growth phenomenon may explain the

existence of growth on faces that really shouldn’t

grow. In the case of ADP, the pyramid faces

grow rapidly, while the prism faces don’t grow.

No theory has yet been proposed that will ex-

plain this basic fact. The state of aggregation of

the molecules in solution may be involved.

(Secretary’s abstract.)

1394TH MEETING, MAY 7, 1954

The program for the meeting was entitled

“History and Traditions of the Philosophical

Society of Washington.” Four Past Presidents

were presented to the Society with a formal bow

both by the speaker and President ForBusH as

was the custom in earlier years.

The first speaker was L. H. Apams, who served

as President of the Society during 1929. Mr.

Adams spoke of the early history of the Society,

quoting quite frequently from W. J. Humphrey’s

paper The Philosophical Society of Washington

through a thousand meetings. The Society was

OF SCIENCES VOL. 46, No. |

founded on March 13, 1871. Joseph Henry was

its first president and continued to serve in this

office until his death in 1878. In the beginning,

the Society included all branches of science. With

the years, various groups split off and formed

independent societies. The first official publica-

tion of the Society was the Bulletin which was

published up to 1911. After that it was discon-

tinued and the present method adopted of pub-

lishing the Proceedings in the Journal of the

Washington Academy of Sciences. Some of the

early papers presented before the Society were:

Anomalies in sound signals, A. B. JOHNSON

Experiments on the photophone, A. G. BELL

Skin friction, A. F. Zaum

Solar radiation, C. G. Abbot

Mr. Adams’s membership in the Society dates

from 1910, at which time he presented a paper

before the Society. Mr. Adams told a few stories

and then gave some personal reminiscences con-

cerning various members whom he had known

over the years.

The second speaker was L. B. TuckERMAN,

who served as President during 1932. At the be-

ginning, Mr. Tuckerman stressed the importance

of the tradition of starting the meetings on time,

stating that the meeting had not started until

8:52 p.m. He also mentioned that over the years

the meetings could be described as reasonably

dignified. Examples of meetings were cited which

were not so dignified and yet which proved to be

equally interesting. Mr. Tuckerman then re-

called in chronological order all the past presi-

dents he had known, giving in each case the par-

ticular things which stood out in his memory

about each one. The first was Lyman Briggs who

was president in 1916. He mentioned what an

inspiration Mr. Briggs had been to all who knew

him. A few stories were also told about W. J.

Humphreys, the most interesting of which

centered about a pig which survived being struck

by a ball of ightning. Mr. Tuckerman also men-

tioned another tradition of the Society which is

falling by the wayside. This was described as the

“pinning back of the ears of the retiring presi-

dent’’, and of course refers to the frolic which is

staged at the expense of the retiring president

during the dinner staged in his honor. An example

of these procedings cited was that of the making

of a LiCl cocktail in honor of the retiring president

in 1940, R. E. Gibson. The making of this cock-

tail was first credited to Mr. Gibson. It was later

JANUARY 1956

learned that this cocktail had somewhat toxic

properties. Mr. Tuckerman stated, however,

that no serious complications developed, for none

of the members who attended that dinner are now

dead.

At the close of Mr. Tuckerman’s remarks, Mr.

MeNish asked permission from the chair to cross

examine the speaker on his statement of the time

of starting on the meeting. After consulting the

acting recording secretary, it was finally agreed

that Mr. Tuckerman had meant 8:22 p.m. instead

of 8:52 p.m.

The third speaker of the evening was H. L.

CurtTIs, who was president of the Society in 1931.

Mr. Curtis appeared in the formal attire of his

period in office, tails and all, and presented a pre-

pared address on The development of a subspecies

of the genus Homo, sapiens scientifica, who no

longer adorn themselves by wearing tails”. This

address has been published in full in this JourNaL

45: 131-132. 1955, and will not be discussed here.

The last speaker of the evening was F. G.

BRICKWEDDE, who served as President during

1939. Mr. Brickwedde discussed the subject The

History and development of the Joseph Henry and

Christmas lecture committees. During the presi-

dency of H. L. Curtis in 1931, the income of the

Society began exceeding the expenses, so a com-

mittee was appointed to determine how the

Society might further serve the interests of its

members. This committee made the recommenda-

tion that a lecture be given each year in some

field of research by scientists outside the Wash-

ington area. These lectures were not started with

the idea of honoring Joseph Henry, but it was

natural that this should follow, for 1931 was the

centenial of the discovery of induction with which

Joseph Henry was so closely associated. The first

Joseph Henry Lecture Committee was composed

of L. H. Adams, C. G. Abbot, and R. E. Gibson.

The first Joseph Henry Lecturer was Joseph

Ames, president of the Johns Hopkins Univer-

sity, and the lecture itself was devoted to the life

work of Joseph Henry. Mr. Brickwedde then re-

viewed for the membership some of the outstand-

ing contributions of Joseph Henry. The names of

several of the following lecturers and their sub-

jects were also mentioned.

Again in 1952, the Society found its income

still increasing in spite of the fact that its dues

per member were still fixed at $3. At this time

Mr. MeNish, the President, appointed another

committee to determine how these funds might

PROCEEDINGS: PHILOSOPHICAL SOCIETY 31

best be placed in the service of the Society. This

committee consisting of A. Stone, L. Marton, and

M. L. Henderson recommended the establishing

of two demonstration lectures to be given for

young people in the age range fourteen to twenty

one. The first Christmas Lecture committee con-

sisted of L. Marton, A. Stone, L. A. Wood, and

A. I. Mahan. The first Christmas Lecturer was

Edwin H. Land, of the Polaroid Corporation,

who gave a demonstration lecture on T'wo- and

three-dimensional color photographs. Last year

these lectures were given by R. M. Sutton, of

Haverford College, who spoke on The world we

see and The world we don’t see.

Several other Past Presidents and members of

the Society made additional remarks. Some of

these were Lyman Briggs, E. C. Crittenden, and

W. G. Brombacher. At the close of the meeting,

15 past presidents assembled in front of the

membership.

1395TH MEETING, MAY 21, 1954

The Society was addressed on Quantum limita-

tion to vision by ALBERT Rose, of the David

Sarnoff Research Center, RCA. The well-known

decrease in spatial and tonal resolution of the

eye with decrease of light intensity is due pri-

marily not to physiological factors but to effects

of quantum physics. At low levels of illumina-

tion, there are just not enough photons reaching

the eye to convey the desired detailed informa-

tion. This quantum effect is not obvious, for there

is no noticeable “granularity” to the perceived

light.

Classical vision theory utilizes the bleaching of

visual purple to generate nerve impulses. Quan-

titative studies have been made using flicker

effect and dark adaptation. Adaptation to the

dark results in an apparent sensitivity imcrease

of about 10,000 to 1. This has been interpreted

to mean that under the conditions of high illumi-

nation, 99.99 percent of the visual purple is

bleached. This would imply that only 0.01 per-

cent (or possibly 0.1 percent) of the incoming

photons can be utilized, but it can be demon-

strated that practically 100 percent must be

utilized for use to see as much as we do!

A slide was shown illustrating a test pattern of

various size gray and black dots photographed in

such a manner that each individual photon re-

corded as a white spot. The smaller the spot, or

the less its contrast with the background, the

more photons are needed to show its presence.

32 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES

In the case of a regular lattice array of spots and

incident photons, a single photon is sufficient to

show a dot (by being absent from the pattern of

reflected photons). If the spot has a reflection co-

efficient of 949, at least 10 photons are needed to

make the minimum detectable difference of one

photon between the dot and the background. For

1 percent contrast, 100 photons are needed, etc.

This illustrates the quantum limitation to tonal

discrimination.

If the array of incident photons is random,

many more are needed to detect a dot—.e., to

make it obvious that a group is missing in the

reflected illumination. It is found experimentally

that a set of about 25 close neighbors must be

missing from a random pattern to make it ap-

parent that there is a “hole” in the pattern. For

the 10 percent contrast gray dot to be detected,

then, it would require an illumination density

such that some 2500 photons were incident upon

the dot; the 1 percent contrast dot would require

250,000 incident photons. This ‘‘square law”’ in-

crease follows from statistical reasoning.

Under room illumination of 10 foot-candles,

about 4 x 10!® photons are incident on each

square foot each second. Allowing for the area of

the iris, and the tenth-second integrating time of

the eye leaves about 10” photons available to the

entire retina for one observation. This boils down

to 10,000 per receptor, which from above is too

few to detect an image of 1 percent contrast.

Hence for this contrast, the quantum effect would

limit resolution before receptor size would. This

argument is independent of the mechanism of

vision.

For a 10 percent contrast image of 1 to 2

minutes of are extension, there are just enough

photons available if 1 percent of them are used.

For weak light, 145 of the incident photons must

be used to account for what we actually see. That

is, in weak light, the utilization efficiency is about

ten times what it is in good light. This allows only

90 percent of the visual purple to be bleached

under good illumination, leaving a factor of a

thousand in apparent sensitivity still to be ex-

plained.

The speaker suggested that there may be a

built-in amplifying system between the retina

and the nerve fibers. This is needed because the

nerve impulses are more energetic than the re-

ceived light. On this basis, dark adaptation is due

mainly to an Automatic Gain Control in the

VOL. 46, No. 1

amplifying system. The lag in adaptation can be

explained by the time constant of the AGC

system.

The lecture was concluded with some slides

showing the image of a girl under illuminations

ranging from 10~° foot-lamberts to 107? foot

lamberts. The granularity was quite evident at

the lower levels of illumination, and the dis

tinguishability of the image varied with level in

a startling manner. (Secretary’s abstract.)

1396TH MEBTING, JUNE 4, 1954

The Society was addressed by Raymonp J.

SEEGER, of the National Science Foundation.

His subject was On natural Philosophy.

The meaning of ‘natural philosophy” has

changed considerably in recent generations, as

has indeed the meaning of plain “philosophy.”

The speaker traced three eras of relationship

between science and philosophy.

The first period, the age of speculative science,

was typified by Plato and Aristotle. Quoting

liberally from the Greek and Latin classics, Mr.

Seeger illustrated his point that during this

period philosophy and science were intermingled

and indistinguishable.

The second period, the age of national science,

saw the lives of St. Thomas Aquinas and

Immanuel Kant. It was Aquinas who first dis-

tinguished between philosophy and _ science.

Earlier writers had treated science as a part of

their philosophy, not as a study ini itself. Kant

attempted to divorce science completely from

philosophy, rather than to have it as a special

branch of philosophy.

The third period is characterized as the age of

experiential science, with philosophy completely

missing from the picture. Physical principles are

accepted on the basis of logical compatibility and

experimental verification, rather than an appeal

to being understandable. ‘““Meaning”’ is ignored.

Science absorbed metaphysics, whereas Descartes

had science subordinate to metaphysics.

The speaker went on to present scattered

aspects of his own viewpoint, or his philosophy

about philosophy. He commented briefly on

Margenau’s work, and asked rhetorical questions,

about “‘real”’ mass in relativity. He summed up

some of the problems by quoting “The common

sense of today is the uncommon science of

yesterday.” (Secretary’s abstract.)

Officers of the Washington Academy of Sciences

PPEESUACTU ae oxox. dete sis eis sive oes caer Maraaret Pittman, National Institutes of Health

AP OSUETILAELECEam ciara dials: sre ee aiets isieiaisy Sees RaupH E. Gipson, Applied Physics Laboratory

SOPRA Us poate UDO DOG GH GOD ECT Coenen Hetnz Specut, National Institutes of Health

PUT EUSUTEN To. 6 62 5 <6 Howarp S. Rappuirye, U.S. Coast and Geodetic Survey (Retired)

JA RRTATOS 6G aleic a COTES Gee acre crear Joun A. STEVENSON, Plant Industry Station

Custodian and Subscription Manager of Publications

Harrap A. Renper, U.S. National Museum

Vice-Presidents Representing the Affiliated Societies:

Philosophical Society of Washington..:.......-......-+------ Lawrence A. Woop

Anthropological Society of Washington....................... FRANK M. SETzLER

Biolorical) Society, of Washington... .4---.054-76>- 5-05 44- HERBERT G. DIEGNAN

Chemical Society of Washington.................... Pee Nee Wiuui1am W. Watton

Pntomological Society of Washington. .).5.¢-2--ss-++seesss 40650506" F. W. Poos

NationallGeographicisociety-s---n cee eee eee eee ALEXANDER WETMORE

Geological Society of Washington....................-.-005. Epwin T. McKnicur

Medical Society of the District of Columbia................... FREDERICK O. Cor

ColumbiavElistoricaluSocietynnassace anit ieee GILBERT GROSVENOR

Botanical Society of Washington................:-s-0++--s-0:: S. L. EmMswELuer

Washington Section, Society of American Foresters.......... Grorce F. Gravatr

Washington Society of Engineers....................... HERBERT GROVE a Dense,

Washington Section, American Institute of Electrical Engineers...... A. Scorr

Washington Section, American Society of Mechanical Engineers........ i 8. Din

Helminthological Society ofeWashingtonese a3: eee JOHN S. ANDREWS

Washington Branch, Society of American Bacteriologists....... Luoyp A. BURKEY

Washington Post, Society of American Military Engineers...... Fioyp W. Houau

Washington Section, Institute of Radio Engineers................ H. G. Dorsty

District of Columbia Section, American Society of Civil Engineers..D. E. Parsons

District of Columbia Section, Society Experimental Biology and Medicine

W. C. Hzss

Washington Chapter, American Society for Metals............ Tuomas G. DiaeEs

Washington Section, International Association for Dental Research

Rosert M. STEPHAN

Washington Section, Institute of the Aeronautical Sciences.......F. N. FRENKIEL

District of Columbia Branch, American Meteorological Society

Francis W. REICHELDERFER

Elected Members of the Board of Managers:

PROM AIUAT Yel QOGi tel) ike ac ais yee slecere audit 4 scpesnete M. A. Mason, R. J. SEEGER

SRG MUA UAT VL O5 75 ors oe Success sicineedeberre ce eed, lois oe A. T. McPuerson, A. B. GuRNEY

PROM AN UAT Vel OOSie 6 ac. gach as oer e am se ays ets Hee W. W. Rusey, J. R. SWALLEN

SOOT OLOMVMGNAGENSs cach. js ssa4- 42h ase: All the above officers plus the Senior Editor

LECCIRG GY LUCID = mera coxa oe OOO cee ee out Re ENE oo AOE [See front cover]

Harecutiwe Committee... 2... 5...csencnceceeuee: M. Pitrman (chairman), R. E. Gipson,

H. Specut, H. S. Rappierye, J. R. SwALLeN

Committee on Membership.... Roger W. Curtis (chairman), Joon W. ALDRICH, GEORGE

Anastos, Haroun T. Cook, Josep J. Fanny, Francois N, FRENKIEL, PETER KING,

Gorpvon M. Kunz, Louris R. Maxwe.u, Ftorence M. Mrars, Curtis W. SaBRosky,

BENJAMIN SCHWARTZ, Bancrort W. SITTERLY, WILLIE W. SmitH, HarRY WEXLER

Committee on Meetings...... ArNoLp H. Scort (chairman), Harry 8. Berntron, Harry

Bortuwick, Herspert G. Detagnan, Wayne C. Haut, Apert M. STONE

COTE OF. WIGROGPRGHOS..000000669255000000385000000 G. ArtHUR CoopErR (chairman)

FRomanianyelOoOmeee ence eins eee G. ArrHurR Cooprr, James I. HorrmMan

PROM ANU Arye VOD Ta coco ccerties fee hase oe es Haratp A. Reaper, Wiuui1AmM A. DayToN

RoOpanuanyol G58). somes aces eee sees os Dean B. Cowiz, JosepH P. HE. Morrisoyr

Committee on Awards of Scientific Achievement. .. FREDERICK W. Poos (general chairman)

For Biological Sciences..... Sara EK. Branuam (chairman), JoHN 8. ANDREWS,

James M. Hunptey, R. A. St. Grores, Bernice G. Scuusert, W. R. WepEL

For Engineering Sciences...... Horace M. Trent (chairman), JosepH M. CALDWELL,

. Ditu, T. J. Hickey, T. J. Kintran, Gorpon W. McBrips, EH. R. Priore

For Physical Sciences...... Bensamin L. SNAVELY (chairman), Howarp W. Bonn,

Scorr E. Forsusu, Marearet D. Foster, M. E. Freeman, J. K. Taytor

For Teaching of Science....Monroz H. Martin (chairman), Krrta C. JoHNSOoN,

Louse H. MarsHatt, Martin A. Mason, Howarp B. Owrns

Committee on Grants-in-aid for Research.............. FRANCIS O. Rice (chairman),

HERMAN Branson, CHarues K. TRUBBLOOD

Committee on Policy and Planning.. Ba é _E. C. Ortrrenpen (chairman)

MowanuanyslOSGeae tere een ae: lB, (Ol CRITTENDEN, ALEXANDER WETMORE

PR OVD ANUATY 9D (ects nen evoccd od sme sega aeons JOHN E. Grar, Rayrmonp J. SEEGER

Io) dinar Is, cose vapsoboeouease Francis M. DEFANDORF, Frank M. SErzLer

Committee on Encouragement of Science Talent..ARcHIBALD T. McPuerson (chairman)

Moranuamyal 956i cracsiacertensen.-ra sets che crea a es Harotp EB. Finury, J. H. McMILtLten

Iho) dimen IG disco sonnasoouaenaaane neers L. Epwin Yocum, Wruitram J. YOUDEN

PLOW anu anys Cosy eases ree wate id eriseacieeria ears: A. T. McPuerson, W. T. Reap

Committee on Science Education.... RAYMOND J. SrEGER (chairman), RONALD BAMFORD,

R. Percy Barnes, Wauuace R. Bropn, Leonarp CarmicuagnL, Hueu L. Drypen,

Reaina FLANNERY, Rauew EF. Grsson, Froyp W. Hover, Martin A. Mason,

Grorce D. Rock, Wiiu1am W. Rusey, Wriuram H. Seprety, Watpo L. Scumirr,

. Van Evera, Wiuiram E. WRATHER, Francis E. JoHNsTon

Representative on Council of PAN AWTAL SS seas ain eicas (olay ctcie avers ean SIM os Ry eres Watson Davis

Committee of Auditors...FRaNcts E. Jounsron, (chairman), S. D. Cottins, W. C. Hess

Committee of Tellers.. Ratpn P. Trrrsuer (chairman), E. G. Hamper, J. G. THompson

CONTENTS

Editorials. & e406) 2o6- Pk bee ee ee ee 1

Puysics.—Effect of defects on lattice vibrations, II: Localized vibra-

tion modes in a linear diatomic chain. P. Mazur, E. W. MontTrRo.1,

and Ri. B. Ports «2.4.0.4 25228 be6 ooh ck nee Se eee 2

MatTuematics.—Numerical experiments in potential theory using ortho-

normal functions. P. Davis and P. RABINOWITZ......-..--9emee 12

Zootocy.—The ticks (Acarina: Ixodoidea) of the J. Klapperich Afghan-

istan Expedition, 1952 and 1953. GrorcGE ANASTOS............. 18

BIocHEMISTRY.—FEffect of cortisone acetate on production of liver and

muscle glycogen from C-14 labeled glycine and DL-alanine. W. C.

Huss and I. P. SHAFFRAN ......0..0:..05+ ee 08 oe 20

ProceeEpiNGs: Philosophical Society of Washington................... 23

Notes: and. Newsi.c:...<.#: 25 oaaess sh eee ae a ee eee oe ee Le ae 22

VOLUME 46 February 1956 NUMBER 2

JOURNAL

OF THE

WASHINGTON ACADEMY

OF SCIENCES

Published Monthly by the

meres HiNGTON ACADEMY OF So: GC oL Be N © Bes

MOUNT ROYAL & GUILFORD AVES., BALTIMORE, MD.

Journal of the Washington Academy of Sciences

Editor: Cuester H. Paes, National Bureau of Standards

Associate Editors: RoNaLD BaMForp, University of Maryland

Howarp W. Bonp, National Institutes of Health

IMMANUEL ESTERMANN, Office of Naval Research

This JouRNAL, the official organ of the Washington Academy of Sciences, publishes:

(1) Original papers, written or communicated by members of the Academy; (2) proceed-

ings and programs of meetings of the Academy and affiliated societies; (3) correspond-

ence of interest to Academy members; and (4) notes of events connected with the scien-

‘tific life of Washington. The JouRNAL is issued monthly. Volumes correspond to calendar

years.

Manuscripts should be sent to the Editor. It is urgently requested that contributors

consult the latest numbers of the JouRNAL and conform their manuscripts to the usage

found there as regards arrangement of title, subheads, synonymies, footnotes, tables,

bibliography, legends for illustrations, and other matter. Manuscripts should be type-

_written, double-spaced, on good paper. Footnotes should be numbered serially in pencil

and submitted on a separate sheet. The editors do not assume responsibility for the

ideas expressed by the author, nor can they undertake to correct other than obvious

minor errors.

Proof.—In order to facilitate prompt publication one proof will generally be sent