Science Abstracts. Section A, Physics Abstracts. Vol. 49, No. 584

PHYSICS ABSTRACTS

S ECTI ON A

o f

SCIENCE ABSTRACTS

SECTION A, PHYSICS

SECTION B, ELECTRICAL ENGINEERING

E dited a n d Issu ed M on th ly by

THE INSTITUTION OF ELECTRICAL ENGINEERS

In A ssociation with

THE PHYSICAL SOCIETY THE AMERICAN PHYSICAL SOCIETY

THE AMERICAN

INSTITUTE OF ELECTRICAL ENGINEERS

VOLUME 49

ABSTRACTS 2007-2211

AUGUST 1946 NUMBER 584

PRINCIPAL CONTENTS

Page Page

51 MATHEMATICS 219 538 Magnetism 233

52 ASTRONOMY. GEODESY 220 539 Radioactivity. Atoms. Mole­

53 PHYSICS 221 cules 233

530.1 Fundamentals 221 539.13 Molecular structure 233

531 Mechanics of solids 222 539.15 Atomic structure. Nucleus 234

531.7 Mechanical measurements 223 539.16 Radioactivity 234

532 Mechanics of liquids 224 539.17 Artificial nuclear disintegra­

532.72 Diffusion 224 tion 235

533 Mechanics of gases 225 539.185 Neutrons 235

534 Acoustics. Vibrations 225 539.2 Structure of solids 237

535 Optics. Radiation. Spectra 226 539.3/.8 Elasticity. Strength. Rhcology 237

535.3 Geometrical optics 226 541 PHYSICAL CHEMISTRY 238

S35.33./37 Spectra 226 541.121/. 128 Reaction kinetics 238

535.34 535.37 535.43 535.6 535.8 536 537/538 537.2

Absorption 227

Luminescence 228

Scattering 229

Colour 230

Optical systems 230

H eat. Thermodynamics 230 Electricity. Magnetism. X-rays

Charged particles 231

Electrostatics 231

541.13 541.14 541.18 541.2/.6 542 543/545 54S 548.73

Electrochemistry 238

Photochemistry 238

Colloids. Adsorption 238 Chemical structure 239 Chemical processes. Apparatus 239 Chemical analysis 239

CRYSTALLOGRAPHY 239

X-ray crystallography 239

537.5 Discharges 231 55 GEOPHYSICS 240

537.533 Cathode rays 232 551.5 Meteorology 240

537.542 Counter tubes 232 57/59 BIOLOGY 241

537.56 Ionization 232 . 61 Medical science 241

537.591 Cosmic rays 233 77 PHOTOGRAPHY 242

NOTE ON THE ARRANGEMENT OF ABSTRACTS

The Abstracts are classified by subject according to the Universal Decimal Classification, and arranged in order o f their U.D.C. numbers. (An abridged version o f the U.D .C . accompanies the Annual Index.) An abstract o f interest under more than one head has additional U.D.C. numbers, linked by the colon sign, “ : ” e.g. “ 536.21 : 548.0 Conduction o f heat in crystals.” The Abstract is printed once only, under the main number, e.g. in the section

“ HEAT 536,” but Cross-references are inserted under the other numbers, e.g. “ 548.0 : 536.21 see Abstr. 1234” in the section “ CRYSTALLOGRAPHY 548.” These Cross-references should be investigated, therefore, when a particular section is being searched, as they contain additional matter relevant to that section. A Cross-reference does not refer to the Abstract which appears immediately above it.

Abstracts signed with the following initials have been supplied by the courtesy o f the organizations named:

“ B .A .” = British Abstracts. “ E.R.A .” = British Electrical and Allied Industries Research Association. “ M .A ." = Metallurgical Abstracts. “ M .R .” = Mathematical Reviews. “ M.-V.” = Metropolitan-Vickers Electrical Co., Ltd. “ P.O.” = Post Office Engineering Department.

ABSTRACTORS

W. R. An g u s, M.A., D.Sc., Ph.D., F.R.I.C.

E. H. W. Ba n n e r, M.Sc., M.I.E.E., F.Inst.P.

A. Beer, Ph.D.

N . M. Bu g h, A.R.C.Sc., A.I.C.

C. F. Brockelsby, B.Sc., A.R.C.S.

B. C. Br o w n e, M.A.

E. C. Bu l l a r d. W. W. Ca m p b e l l, B.Sc.

L. J. C. Co n n e l l, B.Sc., A.Inst.P.

N. Co r c o r a n, B.A., M.Sc.

T. G. Cowling, M.A., D.Phil.

E. H. Do c k, M.Sc., A.R.C.S., D.I.C., F.Inst.P.

W. E. Du n c a n s o n, M.Sc., Ph.D.

D. L. Ed w a r d s, A.R.C.S., D.I.C., F.R.A.S.

D. S. Evans, M.A., Ph.D., F.Inst.P.

A. Ev e r e t t, M.A., Ass.Brit.I.R.E.

F . T. Fa r m e r, B.Sc.(Eng.), Ph.D.

V . C. A. Fe r r a r o, B.Sc., Ph.D.

J. C . Fin l a y.

L. B. Fir n b e r g, B.Sc.(Eng-).

G. F . Fr e e m a n, M.Sc.(Eng-), M.I.E.E.

A. G . Ga y d o n, D.Sc., Ph.D.

L. S. Go d d a r d, B.Sc.

R. H. Go l d e, B.Sc., A.M.I.E.E., A.M.A.I.E.E.

C. J. Go l l e d g e, F.R.E.S.

J. Grant, D.Sc.

E. D. Hart, M.A., M.I.R.E.

A. Ha r v e y, Ph.D., B.Sc., F.Inst.P.

H. K. He n is c h, B.Sc.

H. H. Hodgson, Ph.D., M.A., B.Sc., F.R.I.C.

A. Hunter, Ph.D., D.I.C., F.R.A.S.

R. G. Ja k e m a n, D.Sc., M.I.E.E.

G. J. Kynch, D.I.C., Ph.D.

F. Ll e w e l l y n Jo n e s, M.A., D.Phil.

A. La n d m a n, Dipl. Eng.

D. E. Le a, M.A., Ph.D.

B. J. Le g g e t t, M.R.C.S., L.R.C.P., A.M.I.E.E.

G. C. McVit t ie, M.A., Ph.D., F.R.A.S.

E. G. Ma r t in, F.R.A.S.

A. J. Mee, M.A., B.Sc.

H. Mil l e r, M.A., Ph.D.

R. E. Ne a l e, B.Sc., A .C.G.I., A.M.I.E.E.

R. Ne u m a n n, B.Sc.

R. W. Po w e l l, D.Sc., Ph.D., F.Inst.P.

R. S. Re a d, M.A., B.Sc.

T. J. Re h f is c h, B.Sc.(Eng.).

W. A. Ric h a r d s o n, O.B.E., B.A., D.Sc., B.Sc.(Eng), F.G.S.

J. E. Ro b e r t s, Ph.D.

W. Ru s c h in, B.Sc.(Eng.).

H. O. Sm e r d, M.Eng.

H. G. So l o m o n, A.C.G.I., M.I.E.E.

E. O. Ta y l o r, B.Sc., A.M.I.E.E.

J. Th e w l is, D .Sc.

A. M. Th o m a s, B.Sc., F.Inst.P., A.M.I.E.E.

J. S. G. Th o m a s, D .Sc.

J. W. T. Wa l s h, M.A., D.Sc., M.I.E.E.

A. C. Wh i f f i n, B.Sc., M.Sc.(Eng.).

J. A. Wil c k e n, B.Sc., Ph.D.

A. Wil k in s o n, B .Sc.

W. E. Wil l s h a w, M.Sc.Tech., A.M.I.E.E.

A. J. C. Wil s o n, M.Sc., Ph.D., F.Inst.P., A.I.M.

A. B. Wo o d, D.Sc.

512.83 AUGUST 1946 MATHEMATICS 51

O S ,His1Uą% \ rLŚ$Hą g ;)

0k

517.6

512.83 : 531.391.1 2007

F actorization o f a class o f determ inants and applica­

tions to dynam ical chains. Duncan, W . J. Phil.

M ag., 36, 615-22 (S ept., 1945).— L e t U = (uy) b e a n u m erical sq u a re m atrix , o f o rd e r /;, w hose la te n t ro o ts a re a ll d istin c t a n d le t P a n d C b e sq u a re num erical o r A-matrices o f o rd e r m. T h e sq u a re m atrix con sid ered is

' P + « „ C , « 12C, . . .N

« 21C, P + u21C , .

T h e d e te rm in a n t o f F, o f o rd e r mn, m ay be factorized in to th e p ro d u c t o f n d e te m iin a n ts o f o rd e r m , th u s

\F \ = U \ P + ps C \ s — 1

w here p , . . ., p„ a re th e ro o ts o f U. A p p licatio n s to a dy n am ical c h a in c o n sistin g o f physical elem ents o r lin k s a rra n g e d lin e a rly so th a t e ac h lin k is co u p led o n ly to o n e o r tw o o f its n e are st n e ig h b o u rs a re c o n ­ sidered. A n exam ple co n sid ered in d e ta il is th a t o f a

segm ented w ing. l. s. g.

517.512 2008

Contributions to the problem o f approxim ation o f equidistant d a ta by an aly tic functions. A. O n the problem o f sm oothing o r graduation. A first class o f an aly tic approxim ation form ulae. Schoenberg, I. J.

Quart. Appl. M ath ., 4 , 45-99 (April, 1946).— T he very sm o o th ap p ro x im atio n s d eveloped in th e p re sen t p a p er find p a rtic u la r a p p lic a tio n in ballistic s a n d a c tu a ria l m ath em atics. A stu d y is m a d e o f the L agrange ty p e o f fo rm u la w h ic h com bines th e o p e ra ­ tio n o f sm o o th in g o f d a ta a n d th e o p e ra tio n o f in te rp o la tio n in o n e fo rm u la . T h is fo rm u la is o f th e fo rm

CO

(

)

F(x) = S y nU x - «)

w here y„(n = 0, ± 1 , ± 2 , . . .) a re th e given d a ta a n d L (x) is a n even fu n ctio n . A fte r a d isc u ssio n o f sm o o th in g a n d sm o o th in g fo rm u la e th e in te rp o lato ry p ro p e rties o f fo rm u la (1) a re d escrib ed in term s o f the p ro p e rties o f th e F o u rie r tran sfo rm ,

g(.u) ■■ L (x) cos uxdx

P oly g o n al lin es, th e in d iv id u a l a reas o f w hich are p o ly n o m ials o f degree k — 1, jo in e d to g e th e r w ith k — 2 co n tin u o u s derivatives a re n e x t discussed.

T h ese curves m ay b e sm o o th ed o u t in to w h a t a re called an aly tic sp lin e curves o f o rd e r k a n d th ese m ay be used to ap p ro x im ate given d a ta . T h e m e th o d s fo r accu rately c o m p u tin g th e fu n c tio n s a n d co n stan ts involved a re sta te d a n d necessary tab les fo r ap p ly in g

th e resu lts a re given. L. s. G.

517.516 : 621.396.677 2009

L ag u erre functions in the m athem atical foundations o f the electrom agnetic theory o f the paraboloidal reflector. Pinney, E. J. M ath . P hys., 25, 49-79

vol. xxjx.—a.— 1946. August.

(Feb., 1946).— T h e sc a la r w ave e q u a tio n in p a r a ­ b o lo id a l c o -o rd in ates is sep a ra b le a n d th e so lu tio n o f th e s e p a ra ted e q u a tio n is expressible in term s o f th e tw o solu tio n s, iJ’iz) a n d £/{f(z), o f L ag u erre’s e q u atio n . T h e p ro p e rties o f th ese tw o fu n ctio n s a re developed in g reat d e ta il. A n u m b er o f an aly tical expressions fo r th em a re given a n d v a rio u s in teg rals involving th e fu n c tio n s a re ev alu ated . T h e so lu tio n to th e ’ w ave e q u a tio n is expressible d irectly in term s o f

S ?(z) = Z ^ e - ^ C z ) , V ? (z) = Z ^ e - ^ U ^ z ) a n d v ario u s p ro p e rtie s o f th es e tw o fu n ctio n s are deduced. T h e m ath em atics p re sen te d in th is p a p e r p ro v id es a basis fo r th e rig o ro u s th eo ry o f th e p a ra b o lo id a l reflector. l. s. g.

517.564 2010

A n o te on Bessel functions o f purely im aginary argum ent. Montroll, E. W . J. M ath. Phys., 25, 37-48 (Feb., 1946).— A difference-differential e q u atio n w hich o ccurs freq u en tly in physical p roblem s is

ayn + l - (a + b + d/d t)yn + b y „ - l *= 0 (1) w here y n = y n(t) a n d n — 1 , 2 , . . . , N . T h e so lu tio n o f th is eq u atio n m ay be w ritten as a n in fin ite series o f fu n ctio n s I„(x). T h e v alu e o f at is fo u n d w hich m axim izes e ~ axIn(x) a n d asy m p to tic fo rm u la e are fo u n d fo r /„_i(/?/()//„0?«), /„+,(/S/i)//,,(/?«) a n d In(fSn) w hen u is larg e a n d (S > 0. T hese resu lts are used to d iscuss th e so lu tio n o f (1). A n appendix gives a n a sy m p to tic fo rm u la fo r

-b

exp {nf(x)}dx

•Tar

w here f i x ) is a c o n tin u o u s fu n c tio n w ith a single m ax im u m in th e in terv al (a, b). l. s. g.

517.566 2011

O n the com putations o f M ath ieu functions. Blanch, G . J. M ath. Phys., 25, 1-20 (Feb., 1946).— A m e th o d is given fo r c o rrectin g th e ch aracte ristic values o f M a th ie u ’s differential eq u atio n a n d th e c o rresp o n d in g F o u rie r coefficients fo r th e p erio d ic so lu tio n s, b o th o f w hich m ay be o b tain e d by k n o w n m eth o d s. A n expression fo r th e e rro r in th e ra tio o f tw o successive coefficients, in term s o f th e e rro r in th e c h ara cte ris tic value, is also given. T w o exam ples a re studied.

l. s. G.

517.6 : 536.21 2012

Som e applications o f the repeated in teg rals o f the e rro r function. Jaeger, J. C. Quart. Appl. M ath., 4, 100-3 (April, 1946).— T h e in te g ra ls a re I„(n — 0, 1, 2, . . .) w here

& ( x ) = ( « = 1 , 2 , . . . )

a n d th ey a ris e in p ro b lem s o n th e c o n d u ctio n o f h e a t in solids. A re la tio n c o n cern in g th e L ap lac e tra n s ­ fo rm o f a fu n c tio n inv o lv in g /„ is p ro v ed a n d u se d in ded u cin g th e so lu tio n s o f a n u m b e r o f p ro b lem s o f p ra c tic a l in te re s t w h ich in v o lv e h e a t g e n era tio n in th e so lid (e.g. th e h y d ra tin g o f cem ent). l. s. g.

219 8

517.7 523.87

517.7 : 518.2 2013 as functions o f A — lo g 10 (1 — k2) for A uxiliary table o f complete elliptic integrals.

Ka p l a n, E . L. J. M ath. Phys., 25, 26-36 {Feb., 1946).— T ables, co rrect to 10 decim al places, a re given o f th e values o f th e in teg rals

f i n r i n

K-- (1 - ¿ 2 s in 2 0 ) - W 0 E - (1 — k 2 s in 2 6)h/6

A = 1( 005)2( 01)6.

518.2 : 517.7 see A bstr. 2013

L. S. G.

5 1 9 .2 8 3 :6 2 0 .1 1 3 2014

S tatistical m ethods in quality control. X. C lassifica­

tion o f defects and quality ratin g . Elect. Enghg, N. Y., 65, 117-19 {M arch, 1946).

ASTRONOMY . GEODESY 52

521.03 : 621.396.9 2015

P ro je ct D ian a. A rm y ra d a r contacts the moon.

We b b, H . D . S k y and Telescope^ 5, 3-6 {April, 1946).— [A bstr. 1938 B (1946)].

5 2 3 .1 1 :5 3 1 .5 1 :5 3 0 . 1 2 = 3 2016 T he one-body problem in the E instcin-de S itter expanding universe. Ja r n e f e l t, G . Ann. Acad. Sci.

Fenit. A {No. 12) 38 p p. (1942) In German.—T h e first p a r t o f th e p a p e r d eals w ith th e re d u ctio n o f c ertain differential form s:

ds2 _ e v(r, DdP _ e>.(r, »{dr1 + r 2d 0 2 + /•2 s in 2 0d<f>2) to th e s ta n d a rd co -o rd in a te s, p, r in w hich

d s1 = H (p, r ) d r 2 - G{p, r )d p 2 - p 2d 0 2 - p 2 s in 2 0 < # 2 T h e tw o cases con sid ered a re (1) th e E in s te in -d e S itter universe in w hich v = 0, A = g = log (1 + j k 0t) (k 0 = c o n stan t) a n d (2) M cV ittie’s fo rm fo r a p article o f m ass m a t th e o rig in o f co -o rd in ates in th is universe fo r w hich

1 1 — rn/2re$8 \

V = 2 l0g \ l+ m l2 r e i * ) ’ A“ 4 ' 0g 0 + " ' / > e i(0 + i ' T h e fu n ctio n s H a n d G a re fo u n d in M cV ittie’s case as pow er-series in th e tw o v ariables x = p ~ ' , y = k l p 2l{ 1 + |7c0t ) : . T h ese series are then g eneralized a n d a m o re general field th a n M cV ittie’s is o b tain e d , still w ith a p a rtic le o f m ass m at the o rigin. I n th is m o re general field, th e o rb its o f p lan ets tra c e d o u t ro u n d th e p a rticle a re show n to be unaffected by th e ex p an sio n o f th e universe as a

w hole. g. c. M cv.

523.165 : 621.396.821 2017

In terstellar origin o f cosmic radiation a t rad io ­ frequencies. Gr e e n s t e in, J. L., He n y e y, L. G ., a n d Ke e n a n, P . C . Nature, Lond., 157, 805-6 {June 15, 1946).— T h e m easu red ra d ia tio n fro m in terste llar sp ace [A bstr. 1205 (1946), 2112 (1945)] agrees closely w ith th e v alu e calcu lated fo r free-free tran sitio n s by electro n s in th e field o f p ro to n s in in te rste llar space [Astrophys. J., 91, 625 (1940)]. T h e suggestion [A bstr. 897 B (1946)] th a t th e o rig in o f th is ra d ia tio n is to be fo u n d in “ b u rsts” fro m sta rs is sh o w n to be u n ten ab le.

5 2 3 .8 2 3 :5 2 3 .8 5 1 .1 = 4 2018

T he m asses o f a non-rcsolvable system o f stars.

Du r a n d, G . C.R. Acad. Sci., Paris, 222, 275-7 {Jan. 28, 1946) In French.— T h e a p p lic a tio n o f th e m ass-lu m in o sity law to a system o f sta rs w h ich are s o close to g eth e r th a t th ey c a n n o t b e observ ed in d i­

vidu ally is considered. T h e m ass-lu m in o sity law is a lin ear, o r a n app ro x im ately lin ea r, re la tio n betw een th e lo g arith m o f th e m ass o f a s ta r a n d its ab so lu te b o lo m etric m agn itu d e. T h e p rin cip al resu lt o f the

in v estigation is the value o f th e relative e rro r in th e m ass o f th e system w hich resu lts by a p plying the m ass-lum inosity law to th e system as a w hole in stead o f to each in d iv id u al sta r. g. c. mcv.

523.83 2019

T he space m otions o f the cluster variables. McLeod, N . W . Astrophys. J., 103, 134-8 {M arch, 1946).—

T h e available ra d ia l velocities (67 stars) for. sta rs o f th is type gave a so la r m o tio n o f 157 k m /sec to w ard s th e apex a = 20h50m, S = + 5 9 ° , w h ilst th e available tan g en tial m o tio n s (58 stars) gave 142 k m /sec to w ard s a — 21h24m, <5 = + 38°. F o u r different so lu tio n s w ere com pleted o f th e velocity ellipsoid b u t th ese w ere in disagreem ent. T h e velocity d isp ersio n a lo n g . th e axis in th e d irectio n o f th e g alactic c en tre w as 170 k m /sec w h ilst it w as 50 k m /sec in th a t o f th e g alactic poles. SW B o o tis, R Z C ephei a n d U C o m ae are possibly in re tro g ra d e m o tio n a b o u t th e g alactic

c en tre. g. c. mcv.

523.841.1 2020

T he relatio n between light curves and lum inosities o f novae. McLaughlin, D . B. Publ. A str. Soc.

Pacif., 57, 69-80 {April, 1945).— N o v a lum in o sities are determ in ed fro m expansions o f n e b u la r shells, in te rste llar lin e in ten sities, galactic ro ta tio n an d occurrence in th e A n d ro m e d a n eb u la, g reater M agellanic clo u d a n d S ag itta riu s cloud. T h e ra te o f decline (defined as th e tim e tak e n to fall 3 m ag n itu d es fro m m axim um ) show s stro n g co rre latio n w ith lu m in o sity , th e slow er n o v ae being fain ter. T he re la tio n h o ld s betw een th e lim its M = — 9 to

— 3 -6 ; som e su p e m o v ae , “ p e rm a n en t” a n d “ d w a rf”

n o v ae d o n o t fit th e re la tio n . d. l . e.

523.841.372.4.035.92 2021

S ix-colour photom etry o f sta rs. IV . V ariation o f a U rsae M inoris a t different wavelengths. Stebbins, J . Astrophys. J., 103, 108-12 {M arch, 1946).— G ives th e am p litu d e o f th e lig h t v a ria tio n o f P o la ris [see A b str. 2708 (1945)]. T h e v a ria tio n m ea su re d is o f th e c o rre sp o n d in g v a ria tio n fo r <5 C ephei. T h e p e rio d o f th e v a ria tio n h as increased o v er th at p red icted by an y o f th e o ld form ulae. e. g. m.

523.841.9 2022

O rb ital elem ents o f the Algol variable S S Bootis.

Sa nfo rd, R . F . A strophys. J., 103, 114-16 {March, 1946).

523.841.9 : 523.877 see A bstr. 2028 523.851.1 : 523.823 = 4 see A bstr. 2018

523.87 2023

S pectra o f BD sta rs within five degrees o f the N o r th "

P ole. Nassau, J. J., and Seyfert, C. K . Astrophys.

J., 103, 117-32 {M arch, 1946).—A tab le o f a b o u t 220

523.87 530.145

1 150 sta rs is given, show ing sp e ctral types estim ated fro m objective p rism sp ectra, w ith lum in o sity g ro u p s (g ian t o r d w arf) fo r a ll th o se o f type G 2 o r later.

T h e percentages o f dw arfs a re in agreem ent w ith th o se fo u n d b y o th e r w o rk ers, a n d sh o w a strik in g d ecrease fro m types G 2 to G 8 — in d ica tin g tire necessity fo r acc u rate classification. T h e selective a b so rp tio n in th is region is fo u n d to increase linearly to 0 -3 0 m at 450 parsecs, a n d to re m ain c o n stan t

th ereafter. d. l. e.

523.87 2024

T he spectrum o f P rocyon: a typical sta r o f class F.

Swensson, J . W . A strophys. / . , 103, 207-48 (M arch, 1946).— A n extensive tab le (a b o u t 3 600 lin es) is given o f w avelengths, estim a te d in ten sities a n d iden tificatio n s o f a b so rp tio n lin es betw een 3 800 an d 6 768 A fro m high d isp ersio n sp ectra. A b o u t 8% o f th e lines a re unidentified, m o st o f them being also found in th e s u n a n d so m e late ty p e stars. M any m etals sh o w stro n g lines fro m b o th n eu tral an d singly ionized ato m s, an d m o st o f th e ra re earth s are present. B ands o f C N a n d C H m olecules are also

fain tly recognizable. d. i.. e.

523.872 : 535.343 2025

O n the continuous absorption coefficient o f the negative hydrogen ion. Chandrasekhar, S. A stro­

phys. J., 102, 223-31 (Sept., 1945).— D ifficulties arisin g fro m th e fa ct [A bstr. 825 (1945)] th a t th e ab so rp tio n coefficient o f H ~ dep en d s o n th e wave fu n ctio n o f th e g ro u n d sta te in regions fa r from the hyd ro g en ic c o re a re avoided by deriving th e a b so rp ­ tio n cro ss-sectio n fro m th e m atrix elem ent o f th e m o m en tu m o p e rato r. T h e new a b so rp tio n curve so determ in ed gives a m ax. a t 8 500 A, w here th e ab so rp tio n coefficient is 4 - 3 7x 1 0 ~ 17 cm 2. a. hu.

523.877 2026

O n the radiative equilibrium o f a stellar a tm o ­ sphere. V I. Cesco, C. U., Chandrasekhar, S., and

Sahade, J. Astrophys. J., 101, 320-7 (M ay); Erratum, 102, l'37 (July, 1945).—T h ird -a p p ro x im a tio n so lu tio n s to th e p ro b lem o f lin e fo rm atio n in a ste lla r a tm o ­ sp h ere a re tab u la te d [see A b str.. 2137 (1945)], an d num erical fo rm s o f th e so lu tio n fo r th e ra d ia tiv e equilibrium o f a p lan etary n eb u la a re ob tain ed .

A. HU.

523.877 ' 2027

O n the radiative equilibrium o f a ste llar a tm o ­ sphere. V II. Chandrasekhar, S. Astrophys. J., 101, 328-47 (M ay, 1945).— T h e so lu tio n to th e e q u atio n o f rad iativ e tran sfer w hen th e co n tin u o u s ab so rp tio n coefficient varies w ith w avelength is con sid ered beyond th e first ap p ro x im atio n provided b y th e grey-body assu m p tio n . T h e c o rre ctio n to be m ad e to th e tem p eratu re d istrib u tio n to allow fo r m aterial w h ich d e p arts fro m greyness are e valuated to a seco n d ap p ro x im atio n in w hich th e m ean a b so rp ­ tio n coefficient is n o t R o sselan d ’s m ean b ut is a stra ig h t average o f values w eighted acco rd in g to the n et m o n o ch ro m atic flux in a grey a tm o sp h e re at the w avelength concerned. T h e m o n o ch ro m atic fluxes an d th e ir derivatives a rc ev alu ated fo r a range o f

o p tical dep th s. a. hu.

5 2 3 .8 7 7 :5 2 3 .8 4 1 .9 2028

O n the radiative equilibrium o f a stellar a tm o ­ sphere. V III. Chandrasekhar, S. Astrophys. J., 101, 348-55 (M ay, 1945).— M eth o d s previously developed [see A b str. 829 (1945)] are ap p lie d to the p ro b lem o f th e reflection effect in eclipsing b inaries.

G e n era l so lu tio n s a re fo u n d fo r th e eq u atio n o f tran s fer rep resen tin g th e ra d iativ e e q u ilib riu m o f an atm o sp h ere exposed to a n o b liq u e beam o f p arallel ra d ia tio n . A re la tio n is developed betw een th e a n g u la r d istrib u tio n o f th e reflected ra d ia tio n a n d th e law o f d ark en in g in a n atm o sp h e re characterized by a c o n stan t n e t flux an d w ith n o in cid en t ra d ia tio n .

A. HU.

523.877 : 537.562 : 533.75 see A bstr. 2062

PHYSICS 53

53.081.3 = 3 2029

Q u a n tity o f m atter as a fundam ental quantity.

Pohl, R . W ., and Stockmann, F . Z . P hys., 122, 534-8 (1944) In German.— In ste ad o f w riting “ m ol.

vol. => 2 2 -4 1 ” it is suggested th a t th e co rre ct expres­

sio n is “ m ol. vol. = 2 2 -4 1 p e r M O L ” (w here M O L is th e q u a n tity o f m a tte r in 1 gm m olecule). T h is q u a n tity o f m a tte r is to b e reg ard ed as a fu n d am en tal u n it, to g eth e r w ith th e usual u n its o f length, tim e,

m ass, tem p, a n d ch arg e. b. a.

53 .0 8 1 .5 :6 2 1 .3 .0 1 1 = 4 2030

Sim plification o f electric and m agnetic dimensions.

Tarbouriech, M . Rev. Gen. Elect., 55, 151-5 (April, 1946) In French.— R eferrin g to B ry lin sk i’s p ro p o sal [see A b str. 1791 (1946)], tri-b asic system s in c u rre n t, len g th , tim e; a n d c u rre n t, velocity, tim e a re c o n sid ered as altern ativ es; e ach show s som e saving in to ta l n u m b er o f sym bols, b u t ele ctro sta tic a n d electro m ag n etic system s still differ. By th e a d o p tio n o f a q u a d ri-b a sic system th is difference m ay be m ad e to vanish; perm eab ility asso ciated w ith e ith e r L, M , T (classical) o r Q, L, T (B rylinski)

exem plify th is. A lternatives a re L, / , T associated w ith eith e r p e rm eability o r voltage, e ac h show ing a saving in sym bols, b u t the p referred suggestion is a system b ased on R, I, T a n d L (ohm , am p ere, second a n d m etre), w hich requires o n ly J o f th e le tters an d e x p o n en ts necessary fo r the classical L, M , T, per­

m eab ility system . T h e a b b rev iatio n “ O .A .S .M .” is suggested to d e n o te th is new system . o . f. f.

F U N D A M E N T A L S 530.1 530.12 : 531.18 see A bstr. 2039-2041 530.12 : 531.51 : 523.11 = 3 see A bstr. 2016

530.145 2031

Elim ination o f divergencies in quantum electro­

dynam ics and in meson theory. Gustafson, T.

Nature, Lond., 157, 734 (June 1, 1946).

530.145 = 3 2032

O bservations on the energy-im pulse tensor o f the field theories o f m atter. Iskraut, R . Z . Phys., 119 (Nos. 11-12) 659-76 (1942) In German.— B elin fan te’s

530.145 531.19

m eth o d [A bstr. 4465 (1939)] o f d e te rm in in g th e sym m etrical energy-im pulse te n s o r is d iscussed a n d sim plified. T h e a n g u la r m o m en tu m a n d its reso lu tio n in to o rb ita l a n g u la r m o m e n tu m a n d sp in a n g u la r m o m en tu m a re d e a lt w ith in c o n ju n c tio n w ith th e lo calizatio n o f th e energy a n d im pulse. A sum m ary o f im p o rta n t m ag n itu d es o f th e scalar, M axw ell, Y ukaw a a n d D ira c th eo ries is in cluded fo r c o m p ariso n .

h. G. s.

530.145 : 535.14 = 4 2033

O n th e theory o f the photon in a R iem annian space.

Tonnelat, M . A. Ann. Phys., Paris, 15, 144-224 {Jan.-M arch, 1941) In French.—T h e th eo ry is in tro ­ d u ced by a p re sen ta tio n o f th e e q u atio n s o f th e p h o to n in a E u clid ean space. T h e fo rm alism o f D ira c ’s e q u atio n a n d th e w ave fu n ctio n s w ith 4 a n d w ith 16 co m p o n en ts a re discussed a n d th ese lea d to the M axw ellian a n d no n -M ax w ellian e q u atio n s in th e th eo ry o f th e p h o to n . T h e n th e p h o to n eq u atio n s in a n o n -E u clid ean sp ace a re fo rm u lated . T h e space is, in general, su p p o sed to have b o th c u rv atu re and to rsio n , a n d th e p h o to n e q u atio n s involve tw o o p e ra to rs in tim ately re la te d to th e g eom etry o f the space. T h e c o m p atib ility o f th e e q u atio n s is d is ­ cussed. T h e electro m ag n etic e q u atio n s in th e p h o to n th eo ry a re stu d ied an d th e second o rd e r eq u atio n s o f p ro p a g a tio n a re given. T h e final discussion co m p ares th e w ave a n d c o rp u scu lar th eo ries o f light o n th e basis o f th e resu lts o b ta in e d in th e paper.

L. S. G.

530.145.1 2034

Q uantum equations and nuclear field theories.

Fl i n t, H . T . Phil. M ag., 36, 635-43 (Sept., 1945).—

D ira c ’s e q u atio n fo r a ch arg ed p a rtic le in a g rav ita ­ tio n a l a n d electro m ag n etic field is m odified to include th e influence o f a n u c le a r field. T h e fo rm o f th e e q u atio n is given explicitly in 4 cases. In th ese the field is characterized respectively by (1) a vector (K ^), (2) an tisy m m etric ten so rs o f th e se co n d ra n k , ( a n d (Tjiv), (3) ten so rs o f th e th ird ra n k , (Fxnv) an d (7>,|i.v) an tisy m m etric in (A, /<) a n d (//, v) a n d (4) ten ­ so rs (F?,|ivp) a n d (7>,nvp) an tisy m m etric in neig h ­ b o u rin g suffixes. T h e in te ra c tio n term s, a risin g from th e in te ra c tio n betw een th e field a n d th e sources, suggest th e in te ra c tio n w hich o ccurs betw een th e field a n d p o lariza tio n in th e ele ctro m ag n etic th eo ry o f p o larizab le m edia. T h is an alo g y is stu d ied a n d an expression fo r th e energy ten s o r is derived. T h e field c o m p o n en ts a re determ in ed by th e p o la riz a tio n te n ­

so rs a n d vectors. l. s. g.

530.145.1 2035

D erivation o f D ira c ’s equation fo r a free particle.

C h e n g , K . C . Proc. Camb. Phil. Soc., 42, 185-7 {June, 1946).— It is sh o w n th a t th e e q u a tio n m ay be o b tain ed fro m q u a n tu m m echanics alo n e i f th e relativistic energy o f th e p a rticle is trea te d as an

energy o p erato r. L. S. G.

530.145.1 : 531.314.3 2036

A note on the H am iltonian equations o f motion.

Ch a n g, T. S. Proc. Camb. Phil. Soc., 42, 132-8 {June, 1946).— I f th e L ag ran g ian , L , co n ta in s only th e field observables a n d th e ir first derivatives, th e field e q u atio n s, o b tain e d by v ary in g th e L agrangian, m ay b e b ro u g h t in to can o n ica l form an d th u s q u a n ­ tized by in tro d u cin g su itab le c o m m u tatio n relations.

A stu d y is now m ad e o f th e case w here L c o n tain s derivatives h ig h er th a n th e first. W ith p ro p e r d efinitions o f th e c o n ju g ate variab les an d o f the H a m ilto n ia n th e field eq u atio n s can in m o st cases be b ro u g h t in to c an o n ica l form . A m odified fo rm is given w hen th e c o n ju g ate v ariab les are in d ep en d en t.

A special case, suggested by th e L ag ran g ian fo r a D ira c e le ctro n , is discussed. L. s. G.

530.145.6 = 4 2037

O n the wave m echanics o f elem entary particles.

Kwal, B. C .R. Acad. Sci., Paris, 218, 613-15 {April 12, 1944) In French.— A c o n tin u a tio n o f a prev io u s n o te [A bstr. 1506 (1946)]. T h e seco n d ary e q u atio n s are n o w stu d ied . T h o se fo r a sp in j = 1 a n d j = ■§ a re given explicitly an d th e fo rm fo r g eneral values o f j is in d icated . l. s. g.

530.145.6 : 537.12 = 4 2038

T he specific ciiarge and the spin o f the classical electron. Stueckelberg, E. C. G . H elv. Phys. A cta., 18 {No. 1) 21-44 (1945) In French.—T h e lin e a r e lectro ­ dy n am ical th eo ry o f th e ele ctro n , given in tw o previous p ap ers [A bstr. 1342 (1944)], is n o w replaced by a th eo ry in w hich th e field eq u atio n s m ay be n o n ­ linear. I t is th e n p o ssib le to in tro d u c e th e th eo ry o f g rav itatio n . T h e resu lts are: (1) th e g rav itatio n al ch arg e o f th e com p lete system is th e sam e as its in e rtial m ass, (2) th e fu n ctio n al e q u a tio n fo r th e w o rld lin e o f th e electro n possesses, fo r c e rtain n o n -lin ear th eo ries o f a highly sin g u lar form , p e rio d ic solu tio n s, even in th e absence o f a n in cid en t field o f ra d ia tio n . I n th is th eo ry a n acceleration o f ch arg ed p a rticles w ith o u t ra d ia tio n is possible. l . s. o .

M E C H A N IC S O F S O L ID S 531

531.18 : 530.12 2039

A note on the relativistic problem o f uniform rotation.

Hill, E. L. Phys. Rev., 69, 488-91 {M a y 1 and 15, 1946).— A stu d y o f u n ifo rm ro ta tio n a l m o tio n a b o u t a n axis is m ad e o n th e basis o f a definition o f h y d ro - k in etic ch aracter. A so lu tio n is fo u n d in w hich th e p a rticle speed is lin e a r w ith d istan ce fro m th e axis o f ro tatio n to term s in (R c o jc ) 2, b u t a p p ro ac h es the speed o f lig h t a t g reat d istances. T h is re su lt is un ch an g ed by th e in tro d u c tio n o f relativistic ac­

celera te d E u clid ean axes. R easo n s a re given fo r co n clu d in g th a t E h ren fe st’s p a ra d o x in th e p ro b lem o f th e ro ta tin g disc a n d th e q u e stio n o f th e “ geo m etry ” o f th e m o tio n , in th e sense o f general relativity theory, c an be answ ered only o n th e basis o f a th eo ry o f the g en era tio n o f th e ro tatio n .

531.18 : 530.12 2040

R elativistic dynamics o f spin-fluids and spin-particles.

Weyssenhoff, J. W . Nature, Lond., 157, 766-7 {June 8, 1946).

5 3 1 .1 8 :5 3 0 .1 2 2041

Spin-particles m oving w ith the velocity o f light.

Weyssenhoff, J. W . Nature, Lond., 157, 767 {June 8, 1946).

531.19 = 4 _ 2042

D istribution law for sum m ation functions in sta tistical m echanics. Khintchine, A . C .R . Acad. S ci., U R S S 34 {N o. 2) 55-7 (1942) In French.— It w as p reviously sh o w n th a t th e classical lim it th eo re m s o f the calculus o f p ro b a b ilities m ay be used to derive 222

531.19 531.788.7

asy m p to tic fo rm u lae for th e m ean values an d d is­

persio n s o f su m m atio n fu n ctio n s, w hich a rc the m o st im p o rta n t fu nctions o f statistical m echanics. T h e law o f d istrib u tio n fo r su ch fu n ctio n s is n o w deduced.

I t is o f th e G au ssian form . T h e disp ersio n is also

fo u n d . l. s. G.

5 3 1 .1 9 :5 3 2 .7 :5 3 3 .7 2043

T he statistical mechanical- theory o f tran sp o rt processes. I. G eneral theory. Kirkwood, J. G . J. Chem. Phys., 14, 180-201 (M arch , 1946).—O utlin es a re sk etch ed fo r a general statistical m echanical th eo ry o f tra n s p o rt processes; e.g. diffusion, h eat tran sfer, fluid flow a n d resp o n se to tim e-d ep en d en t ex tern al fo rce fields. In th e case o f gases th e th eo ry leads to th e M ax w ell-B o ltzm an n integ ro -d ilferen tial eq u atio n o f tran s p o rt. In th e case o f liq u id s a n d so lu tio n s, it lead s to a generalized th eo ry o f B row nian m o tio n , in w hich th e frictio n c o n sta n t is explicitly re la te d to th e in te rm o le cu la r forces actin g in the system .

531.261 = 4 2044

Solution o f a n inverse problem in the theory o f potential. Zamoreff, A . A. C.R. Acad. Sci., U P SS , 32 (No. 8) 546-7 (1941) In French.— A continuation of previous work [C.R. A cad. Sci., U R SS, 31 (N o. 9) (1941)]. It is now shown that if, on a certain line, the derivative of the potential due to a heavy body be known, the shape and density of the body may be

determined. l . s. g.

531.314.3 : 530.145.1 see A bstr. 2036 531.391.1 : 512.83 see'A bstr. 2007

531.51 : 530.12 : 523.11 = 3 see A bstr. 2016

M E C H A N IC A L M E A S U R E M E N T S 531.7

531.711 = 4 2045

T he new g raduated prototype o f the In ternational B ureau o f W eights and M easu res for the subdivisions o f the m etre. Moreau, H ., a n d Cabrera, N . Rev.

Opt. (Theor. Instrum.) 23, 255-60 (O ct.-D ec.., 1944) In French.— T h e difficulties originally en co u n tered in w o rk in g w ith P t - I r (p o o r p olish, difficulty in m ark in g , etc.) m ean t th a t som e o f th e o ld er p ro to ty p e s w ere n o t en tirely satisfacto ry . O ne o f th ese (T 4) h a s n o w been ren o v ated , m ark in g s rem oved, su rfa ce p lan ed a n d repolished, an d re g ra d u a te d . T w o independent e x am in atio n s h av e n o w been m ad e o f th is new p ro to ty p e a n d it is fo u n d th a t th e e rro r fo r any g ra d u a tio n ra re ly exceeds a m icro n . T h e len g th is given as 1 m — 1 • 14 /< at 0°c. a. h.

5 3 1 .7 1 7 .8 6 :5 3 5 .4 2 3 2046

A m ethod for precision alignm ents, van Heel, A . C. S. J. Opt. Soc. Am er., 36, 242-3 (April, 1946).—- In aligning th ree p o in ts , o n e p o in t bein g m idw ay betw een tw o e n d p o in ts se p a ra ted by 30 to 50 m , an a tte m p t w as m ad e to u se th e diffrac tio n m ax. an d m in. on th e o u tsid e o f th e geom etrical sh a d o w o f a stra ig h t edge. A precision o f th e o rd e r o f 0 • 1 m m w as th u s o b tain ed . A second a tte m p t su b stitu te d a d o u b le slit fo r th e stra ig h t edge a n d in this case a p recision o f th e o rd e r o f 0-01 m m w as o b tain ed . T h e suggestion is m ad e th a t th e m eth o d co u ld be used fo r th e d e te rm in a tio n o f th e dev iatio n s o f m achine

p a rts , lath e beds, etc. a. h.

vol. xlix.—a.— 1946. August.

531.776 2047

M easurem ent o f high ro tational speed. Majum dar, S. D . Indian J. Phys., 28, 153-8 (Aug., 1945).—

T h e m eth o d is a n ap p licatio n o f th e stro b o sc o p ic principle. In te rm itte n t lig h t fro m a m irro r o n a n electrically m ain tain ed tu n in g fo rk passes th ro u g h a n a rro w slit an d is reflected fro n t a slightly tilted m irro r fixed to th e centrifuge; a circle o f b rig h t d o ts ap p ears o n a screen. T h e n u m b er o f th ese d o ts is eq u al to th e d e n o m in a to r o f th e ra tio o f th e frequency o f ro ta tio n to th a t o f v ib ratio n . T o o b tain th e n u m e ra to r th e slit is m oved a litt.lc, a n d each d o t splits up in to tw o w hich ag ain coincide. T h e d is­

placem ent o f th e slit fro m th e zero p o sitio n necessary to get th is co incidence is m easu red , a n d fro m th is th e n u m e ra to r is calcu lated . T h e m eth o d is cap ab le o f a very high degree o f accuracy.

531.788.12 = 4 2048

M cL eod gauge improvem ents. Tarbes, P. L e Vide, 1, 9-11 (Jan., 1946) In French.— R elates to gauges w ith fixed com pression ra tio s. T h e D u n o y e r m odification, w ith fo u r ra tio s , necessitates fo u r read in g tu b es o f different diam eters to elim inate th e effects o f cap illarity in d eterm in in g th e p ressu re differences. T h e im p ro v em en t described consists o f using o n ly o n e tu b e a n d c o rrectin g fo r cap illarity by m oving th e zero o f th e scale on w hich th e m agnified p ressu re difference is read . T h e a m o u n t o f this co rre c tio n is d eterm in ed by a se p a ra te c alib ra tio n w h ich req u ires freq u en t rep etitio n , as it dep en d s o n th e sta te o f th e glass w alls o f th e tube. N. c .

531.788.6 2049

Therm ocouple vacuum gage. Robinson, H ., and Flan ag a n, M . C . Gen. Elect. R ev., 49, 42-4 (M ay, 1946).— U tilizes v a ria tio n o f th erm al con d u ctiv ity o f gas w ith pressu re a t low tem p eratu res. A s ta n d a rd h e atin g cu rre n t is p assed th ro u g h a w ire in th e gas, a n d th e eq u ilib riu m tem p e ra tu re o f th e w ire m easured by a th erm o co u p le, connected m echanically b u t n o t electrically to th e w ire. T h e h ig h er th e pressure, th e h ig h er th e con d u ctiv ity o f th e gas an d th e low er th e th erm o co u p le reading. T h e in stru m e n t covers the ra n g e 0-200 m icro n s, is d irect-read in g a n d m a y be u sed to give rem o te in d ic atio n s. By c o m p a riso n o f readings w ith th o se o f a M cL eo d gauge, th e p a rtia l pressu re o f condensible gases m ay be estim ated.

N. C.

531.788.7 2050

A n ionization gauge o f sim ple construction. Fogel, C. M . Proc. Inst. Radio Engrs, N . Y. Wav. Electrons, 34, 302-5 (M ay, 1946).— A new g auge is d escribed fo r m easu rin g p ressu res fro m 10- 4 to < 1 0 “ 8 m m o f Hg. E xcept fo r a m ultiplying fa c to r o f 10, it gives a d irect read in g o f resid u al a ir p ressure. T h e gauge em ploys tw o p lates, as th e e le ctro n a n d io n collector, respectively. T hey a re lo cated o n o p p o site sides o f th e filam ent, b u t e q u id ista n t fro m it. T h is allow s easy outg assin g o f p a rts , e ith e r by ele ctro n b o m ­ b a rd m e n t o r by r.f. heatin g . A p ro tectiv e shield in fro n t o f th e io n c o lle cto r aid s in red u cin g th e electrical lea k ag e to th a t elem ent.

531.788.7 : 621.316.71 2051

A reliable high vacuum gauge and control system . Pic a r d, R . G ., Sm ith, P. C ., a nd Zollers, S. M . Rev. Sci. Instrum., 17, 125-9 (April, 1946).—T w o

223 8*

532.526 532.72.08

gauges a re em ployed, o n e a th erm o co u p le a n d the o th e r a discharge gauge. T h e in stru m en t is extrem ely satisfacto ry for th e m easurem ent o f p ressures in the range, atm ospheric to < 1 0 ~ 4 m m H g. B o th gauges are o f a type w hich w ill n o t be dam ag ed if gases are su ddenly ad m itte d to th e system . T h e gauges an d pow er su pply a re described in de ta il. A circu it is given w hereby th e c u rre n t fro m the gauges m ay be u sed to co n tro l eq uipm ent so th a t th e pressu re in th e vacuum system m ay be used to o p e rate o th e r devices.

M E C H A N IC S O F L IQ U ID S 532

532.526 : 536.24.01 2052

C alculations concerning theoretical values of boundary-layer thickness and coefficients o f friction and o f heat tran sfer for steady tw o-dimensional lam inar flow in an incompressible boundary layer with m ainstream velocity U oc .x'" or U oc e L%. Old ro yd, J. G . Phil. M ag., 36, 587-600 (Sept., 1945).— T he b o u n d a ry layer thicknesses a n d th e coefficients o f frictio n arc determ in ed by tw o m eth o d s: (1) fro m d a ta given by H a rtre e ’s num erical so lu tio n o f th e b o u n d a ry lay er eq u atio n s [A bstr. 2389 (1937)]; (2) P o h lh a u se n ’s a d a p ta tio n o f th e m o m en tu m e q u atio n . T h e results give an in d icatio n o f th e accuracy o f m e th o d (2).

D iscrepancies a re sm all w hen th e pre ssu re gradient is negative. T h e coefficients o f h e a t tran sfer (C //) a n d sk in -frictio n (C f) a re c o m p a red fo r a range o f values o f the P ra n d tl nu m b er, a. It is fo u n d th a t a law o f th e fo rm C /y /jC / = Aa" m ay b e expected to give good results especially w hen 0 -6 <¡<7 < 7 - 0 . T he values o f A a n d n for different fo rm s o f th e m ain ­

stream velocity a re given. l. s. g.

532.64 : 541.183.02 2053

S atu rated adsorbed films and the stru ctu re o f deeply super-cooled w ater. Ba ngham, D. H. N ature, Loud., 157, 733 (June 1, 1946).— T h e re p o rte d sp re ad ­ ing o f su p er-co o led w a ter d ro p s a t low tem p eratu res [A bstr. 1613 (1946)] does n o t im ply a low ering o f su rface tension, b u t ra th e r th a t th e m o lecu lar p a tte rn o f th e w ater, a n d specially its su rface layer, a p p ro x i­

m ates m ore closely to th a t o f th e a d so rb ed v a p o u r film s on th e m e ta l surface. [See A b str. 1859 (1938)].

532.7 : 533.7 : 531.19 sec A bstr. 2043

532.7 : 539.6 = 4 2054

P rocess o f calculating some m olecular m agnitudes o f the liquid state. Merigoux, R . C.R. A cad. Sci., Paris, 222, 138-9 (Jan. 7, 1946) In French.— O n the assu m p tio n th a t th e force o f m o lecu lar in teractio n is o f th e form f(r ) a(r — ra)/rk, expressions a re fou n d fo r a, ra a n d k in term s o f observ ab le q u an titie s.

a. j. c . w .

532,72 2055

T he diffusion o f electrolytes and m acrom olecules in solution: A historical survey. Lo n g sw o r th, L. G . Ann. N .Y . Acad. Sci., 46, 211-39 (Nov. 30, 1945).—

T his histo rical survey is a n in tro d u c tio n to a m o n o ­ g ra p h o n diffusion w hich co n tain s th e 5 p ap ers w hich follow [A bstr. 2055-60 (1946)]. Its ju stificatio n is to fill in gaps left by the o th e r a u th o rs an d to em phasize experim ental m eth o d s. T h e subjects d ealt w ith are:

F ic k ’s law s o f diffusion; b o u n d a ry con d itio n s in diffusion; in teg ral a n d differential diffusion coeffi­

cients; B o ltzm an n ’s re latio n ; the th eo retical in ter­

p re ta tio n o f the diffusion coefficient; an d experim ental m eth o d s w hich include: layer analysis, th e float m eth o d , optical a n d m icro -m eth o d s, precision o f the o p tical m eth o d s, an d th e stead y sta te m eth o d o f C lack. T h e last na m ed has been discussed a t som e len g th because C lac k 's resu lts w ere fou n d by O nsager an d F u o ss to be m o st nearly in accord w ith th e theory o f th e process, a n d o f p a rticu la r interest to th o se p rim arily in terested in th e op tical m eth o d s. T h e difficulties a tte n d a n t up o n th e developm ent an d m ain ten an ce o f th e stead y sta te have m ad e C la c k ’s w ork an o u tstan d in g c o n trib u tio n to o u r know ledge

o f diffusion. H. H. HO.

532.72 2056

T heories and problem s of liquid diffusion. Onsager, L. Ann. N .Y . Acad. Sci., 46, 241-65 (Nov. 30, 1945).— A fte r a n in tro d u c tio n w hich indicates the relative lack o f developm ent o f th e theory o f liq u id diffusion, th e a u th o r considers system s o f desc rip tio n since n o t o n e o f th e p henom enological schem es w hich a re fit to describe th e general case o f diffusion is w idely know n. T h e treatm en t includes th e g eneraliza­

tio n o f F ic k ’s law, reciprocal relatio n s, th e d issipation- fu n ctio n , a n d diffusion a n d hydro d y n am ics. T he diffusion o f non-electrolytes is next discussed fo r d ilu te an d co n cen trated so lu tio n s, follow ing w hich com es th e c o n sid eratio n o f so lu tio n s o f electrolytes b ased o n a com prehensive analysis o f k inetic an d colligative p ro p e rties su ch as diffusion a n d e lectro ­ lytic co n d u ctio n , a n d the effects, o f C o u lo m b forces.

A b rie f n o te o n c o n ce n tra ted so lu tio n s o f electrolytes

concludes th e paper. h. h. h o.

532.72 : 541.64 2057

T he effects o f concentration and polydispersity on the diffusion coefficients o f high polymers. Beckm ann, C. O ., and Rosenberg, J. L. Ann. N. Y. Acad. Sci., 46, 329-45 (Nov. 30, 1945).— L am m h a s sh o w n th at th ere are m an y a d v an tag es to b e realized by tra n s­

fo rm in g th e experim ental d a ta o b tain e d a t various tim es o f diffusion to a set o f n o rm al c o -o rd in a tes w hich elim in ate tim e, diffusion coefficients, c o n ­ cen tratio n a n d geom etry o f op tical system as v ariables. In su ch co -o rd in ate s, th e experim ental p o in ts o b tain ed a t different tim es w ill a ll fall o n the sam e curve fo r a perfect experim ent. By th is device, a sensitive test is afforded fo r the reliability o f d a ta o b ta in e d a t different tim es o f diffusion, a n d an ideal diffusion curve h a s been derived, w hich is co m p ared w ith curves fro m ex p erim e n tal d a ta afforded by th ree am ylose acetates. T h e effects o f polydispersity o n th e diffusion coefficients o f h igh polym ers are th en discussed, a n d tests fo r polydispersity indicated, e.g. by c o m p arin g the results o f a free diffusion w ith th o se o f a n u ltracen trifu g al experim ent. h. h. h o.

532.72.08 2058

A conductance m ethod for the determ ination o f the diffusion coefficients o f electrolytes. Ha rned, H . S., and Fr en c h, D . M . Ann. N .Y . Acad. Sci., 46, 267-81 (Nov. 30, 1945).— T h e a p p a ra tu s m easures th e differences in c o n d u ctan c e acro ss th e to p an d b o tto m o f a cell o f th e fo rm o f a re ctan g u lar p arallele­

piped, w hile th e electro ly te is diffusing vertically upw ard. T h e th eo ry o f th e cell is developed, a n d - b o th th e th eo retical a n d practical a d v an tag es o f em ­ ploying a difference in co n d u ctan ce ra th e r th an a 224

532.72.08 534.222.1

single co n d u ctan ce m easu rem en t a re show n. In a d d itio n to th e co n d u ctan ce m easu rem en ts a t su itab le tim e intervals, only th e d e p th o f th e cell is req u ired fo r th e a b so lu te d e te rm in a tio n o f th e diffusion coefficient. M easu rem en ts o f th e diffusion coefficient o f KC1 so lu tio n s a t 25°c a n d in th e co n ce n tra tio n ran g e 0 -0 0 2 5 -0 -005m have been m ade. T h ese are c o m p a red w ith th eo retical values derived front the th eo ry o f O n sag er an d F u o ss, a n d th e e rro r ap p ears to be ap p ro x im ately ± 0 - 9 % . h. h. ho.

532.72.08 2059

T he diaphragm cell m ethod o f m easuring diffusion.

Gordon, A . R . Ann. N . Y. A cad. S ci., 46, 285-308 (N ov. 30, 1945).—N o rth ro p a n d A n s o n ’s d iap h rag m c ell is first described w ith v ario u s m o difications o f experim ental tech n iq u e, to g eth e r w ith a deriv atio n o f th e e q u atio n , In

Ac//Ac0

Ao0

s ta n d fo r final a n d initial c o n ce n tra tio n differences, P is th e cell factor, a n d D is th e diffusion coefficient.

It is assum ed im plicitly th at th e cell fa c to r rem ains c o n stan t, i.e. th a t b o th so lu tio n s a re c o n sta n t in volum e. T h e p resen t p a p e r is dev o ted to a c o n ­ sid eratio n o f th e validity o f th e above e q u atio n in in terp retin g cell d a ta . T h e qu e stio n s o f cell volum e, hom ogeneity o f th e in n er a n d o u te r so lu tio n s, th e a ssu m p tio n o f a stead y sta te in th e d iap h ra g m , the m echanism o f tra n s p o rt in th e d iap h rag m , the calib ra tio n o f th e d iap h ra g m cell a n d th e relatio n betw een th e d iap h rag m cell in teg ral coefficient a n d the differential coefficient a re review ed in th is c o nnection.

I t is c o n clu d ed th a t th e cell is still u n su rp assed in its sim plicity an d in th e precision o f th e d a ta it yields.

H. H. HO.

532.72.08 2060

Diffusion constant m easurem ent in theory and practice. Bevilacqua, E. M ., Bevilacqua, E. B., Bender, M . M ., and Williams, J. W . A nn. N .Y . A cad. S ci., 46, 309-27 {Nov. 30, 1945).— A review o f th eo ry indicates th a t th ere is little ju stificatio n fo r m odification o f th e p resen t m eth o d s o f calcu latio n o f diffusion c o n sta n ts in o rd e r to a c co u n t fo r sym ­ m etrical d eviations fro m th e n o rm al (G au ss) curve.

F o r asym m etrical d eviations, th e ty p e o f calcu latio n developed by B eckm ann a n d R o sen b erg m ay be used if a solv en t c a n n o t be fou n d in w hich th e so lu te show s ideal behaviour. A review o f selected diffusion c o n sta n t d a ta is th en given to illu stra te so m e o f the th eo retical p o in ts raised, a n d th is includes results affo rd ed by p ro tein s a n d derived substances, poly­

saccharides, cellulose a n d cellulose derivatives, an d by so d iu m lau ry i su lp h ate. h. h. ho.

M E C H A N IC S O F G A SE S 533 533.15 : 539.155.2 see A bstr. 2147

533.5 : 666.1.037.5 : 669.278 see A bstr. 2211 533.7 : 532.7 : 531.19 see A bstr. 2043

533.72 2061

H e at-cap acity la g in gas dynam ics. Kantrowitz, A . J. Chem . P hys., 14, 150-64 {M arch, 1946).—

T h e existence o f energy dissip atio n s in gas dynam ics, w hich m u st be a ttrib u te d to a lag in th e v ib ratio n a l heat cap acity o f th e gas, has been established b o th

theoretically a n d experim entally. A general th eo ry o f the dissip atio n s in a g en eral flow p ro b lem is developed an d ap p lied to som e special cases. E nergy dissip atio n s d u e to this effect a re to be an tic ip a ted in tu rb in es; they m ight also in tro d u c e e rro rs w hen th e flow o f o n e gas is used to sim u late th e flow o f a n o th e r. U n fo rtu n ate ly , th e rela x atio n tim es o f m o st o f th e gases o f engineering im p o rtan ce have n o t been studied. A new m eth o d o f m easuring th e rela x atio n tim e o f gases is in tro d u ced in w hich th e to ta l-h ead d efects observed w ith a specially sh ap ed im paqt tu b e a re co m p ared w ith th eo retic al c o n sid eratio n s. A p a ra m ete r is th u s ev alu ated in w hich th e only u n k n o w n q u a n tity is th e relax atio n tim e o f th e gas.

T h is m eth o d h as been ap p lied to C O , an d h as given c o n sisten t resu lts fo r tw o im p act tu b es a t a variety o f gas velocities.

533.74 : 548.7 see A bstr. 2183

533.75 : 523.877 : 537.562 2062

O n the equation o f sta te o f ionized hydrogen.

Williamson, R . E. A strophys. J ., 103, 139-44 {M arch, 1946).—T h e e lectro static c o rre ctio n to the eq u atio n o f sta te is calculated from th e virial theorem , using th e D eb y e-H u ck el law o f d istrib u tio n o f ch arg e ro u n d a given charge. T h e fractio n al co rrec­

tio n to th e pressure is — 0 -014[(p/100)/(T /107) 3]l.

T. G. C.

A C O U S T IC S . V IB R A T IO N S 534

5 3 4 .1 3 3 :5 3 7 .2 2 8 .1 = 3 2063

Effect o f a linear inhom ogeneity in the external altern atin g field on the excitation o f a q u artz rod.

Niessen, K . F . Physica, 's Grav., 8, 695-702 {July, 1941) In German.— L au e has show n th a t a h o m o ­ geneous a lte rn a tin g field applied p arallel to a tw o ­ fold axis o f a q u a rtz ro d c u t p a ralle l to th e three-fold axis pro d u ces oscillatio n s fo r w hich th e cen tre o f the ro d is a node, a n d a t reso n an ce th e en d s o f the rods a re a n tin o d e s. T h e re so n an t frequencies a re p ro ­ p o rtio n a l to odd integers. I f th e a m p litu d e o f the field increases linearly alo n g th e ro d the cen tre is n o t necessarily a n ode, a n d re so n a n t m o d es c an be excited fo r w hich the cen tre is an a n tin o d e . T hese re so n an t frequencies a re p ro p o rtio n a l to even integers.

E xpressions are derived fo r th e a m p litu d e o f the oscillatio n s in term s o f th e d im en sio n s o f th e rod, frequency, p iezoelectric a n d elastic m o d u li, an d d am ping. T h e results a re extended qualitativ ely to q u a rtz plates a n d it is suggested th a t o n e p lan e an d o n e cup -sh ap ed electro d e w ould p ro d u ce th e n ecessary in h o m o g en eo u s field. a. j. c. w.

534.222.1 2064

The wave equation in a m edium with variable index o f refraction. Bergmann, P. G . J . A coust. Soc.

A m er., 17, 329-33 {April, 1946).— T h e p a p e r deals th eoretically w ith th e effects o f d ensity g rad ie n ts in the a tm o sp h ere o r in larg e b odies o f w a ter on th e p ro p a g atio n o f so u n d waves. It is fo u n d th a t the g rad ien t o f h y d ro sta tic p ressu re in w a ter is co m ­ p a ra b le in effect w ith a te m p e ra tu re g ra d ie n t o f 0 - l° F /1 0 0 f t. T h is is negligible if th e tem p e ra tu re g radient appreciably exceeds th a t value. S im ilar co n sid eratio n s c a n be ap p lied to the case o f so u n d in air. It is co n clu d ed th a t gravity term s c a n be 225