»"“S
..
^ A
PHYSICS ABSTRACTS
S E C T I O N A o f
SCIENCE ABSTRACTS
SECTION A, PHYSICS
SECTION B, ELECTRICAL ENGINEERING
POUTECHNlKlj
E dited a n d Issu ed M o n th ly b y
TH E IN ST IT U T IO N O F ELECTRICAL ENG INEERS
In Association with
THE PHYSICAL SOCIETY THE AMERICAN PHYSICAL SOCIETY
THE AMERICAN
INSTITUTE OF ELECTRICAL ENGINEERS
VOLUME 49
ABSTRACTS 1459-1755
JU N E 1946 NUMBER 582
FOR IM M EDIATE DESPATCH
M O D E L 1 — Y C o n n e c t i o n f o r R u b b e r
T u b e 1 5 s . 6 d .
M O D E L 2 — C o n n e c t i o n f o r R u b b e r
T u b e 1 5 s . 6 d .
M O D E L 3 - S c r e w e d J ' B . S . P . T . f o r W a t e r T a p ...£1 Os. (
V A C U U M G A U G E A T T A C H M E N T - F i t t e d t o a n y o f t h e a b o v e P u m p s , e x t r a ... £1 4 s . Od,
c/e/7
$ E N E R A 0 £ © 6 k R E Q U IR IN G
'RESSUSETOF
Gf
EW MILLIMETRESWERCURY M akers o f Apparatus for the Production, Utilisation and Measurement o f H igh VacuumK A N G LEY BR ID G E R O A D , L O W E R SY D EN H A M L O N D O N , S .E .26
‘P h o n e : S Y D en h am 7 0 2 6
’G ra m s : E d c o h lv a c , P h o n e , L o n d o n
PRINCIPAL CONTENTS
P a g e
51 M A T H E M A T I C S 159
5 2 A S T R O N O M Y . G E O D E S Y 161
53 P H Y S I C S 162
530.1 F u n d a m e n ta ls 162
5 3 0 .1 2 R e la tiv ity 162
5 3 0 .1 4 T h e o r y o f p a r tic le s 163 5 3 0 .1 4 5 Q u a n t u m t h e o r y ' 164
531 M e c h a n ic s o f s o lid s 165
53 1 .7 M e c h a n ic a l m e a su re m e n ts 166
532 M e c h a n ic s o f liq u id s 166
5 3 2 .6 C a p i lla r ity 167
533 M e c h a n ic s o f g a se s 167
53 4 A c o u stic s . V ib ra tio n s 168
535 O p tic s . R a d i a tio n . S p e c tr a 169
5 3 5 .2 4 P h o to m e tr y 169
535.31 G e o m e t r ic a l o p tic s 169
5 3 5 J 3 / .3 7 S p e c tr a 170
535 .3 7 L u m in e s c e n c e 172
53 5 .7 P h y s io lo g ic a l o p tic s 174
53 5 .8 O p tic a l s y ste m s 174
536 H e a t . T h e rm o d y n a m ic s 174
5 3 7 /5 3 8 E l e c tric ity . M a g n e tis m . X - r a y s . C h a r g e d p a r tic le s 175 537.1 I E l e c tro n s , p r o to n s , m e s o n s 175
NOTE ON THE ARRANGEMENT OF ABSTRACTS
T h e A b s t r a c t s a r e c la ss ifie d b y s u b je c t a c c o r d i n g t o th e U n iv e r s a l D e c im a l C la s s ific a tio n , a n d a r r a n g e d i n o r d e r o f t h e i r U .D .C . n u m b e rs . ( A n a b r id g e d v e r s io n o f th e U .D .C . a c c o m p a n ie s t h e A n n u a l I n d e x .) A n A b s t r a c t o f in te r e s t u n d e r m o r e t h a n o n e h e a d h a s a d d i t i o n a l U .D .C . n u m b e r s , lin k e d b y th e c o lo n s ig n , “ : ” e .g . “ 536.21 : 5 4 8 .0 C o n d u c t io n o f h e a t in c r y s ta l s .” T h e A b s t r a c t is p r i n t e d o n c e o n ly , u n d e r t h e m a in n u m b e r , e .g . in th e s e c tio n
“ H E A T 5 3 6 ,” b u t C ro s s -re fe r e n c e s a r e in s e r te d u n d e r t h e o t h e r n u m b e r s , e .g . “ 5 4 8 .0 : 536.21 see Abstr. 12 3 4 ” in t h e s e c tio n ‘ ‘ C R Y S T A L L O G R A P H Y 5 4 8 .” T h e s e C ro s s -r e f e r e n c e s s h o u ld b e in v e s tig a te d , th e r e f o r e , w h e n a p a r t i c u l a r s e c tio n is b e in g s e a r c h e d , a s th e y c o n ta in a d d i t i o n a l m a t t e r re le v a n t t o t h a t s e c tio n . A C ro s s -r e f e r e n c e d o e s not re f e r t o th e A b s t r a c t w h ic h a p p e a r s im m e d ia te ly a b o v e it.
A b s t r a c t s s ig n e d w ith th e fo llo w in g in itia ls h a v e b e e n s u p p lie d b y th e c o u rte s y o f th e o r g a n iz a tio n s n a m e d :
“ E . R . A .” = B ritis h E le c tric a l a n d A llie d I n d u s tr ie s R e s e a r c h A s s o c ia tio n . “ M . A . ” = M e ta llu r g ic a l A b s tra c ts .
“ M .-V .” = M e tr o p o lita n - V ic k e r s E l e c tr ic a l C o ., L t d . “ P . O .” = P o s t O ffice E n g in e e r in g R e s e a r c h D e p a r tm e n t.
537.31 E lec . c o n d u c tiv ity P a g e
537.5 D is c h a rg e s 177178
537.591 C o s m ic ra y s 179
538 M a g n e tis m 181
5 3 8 .3 /.5 E le c tro d y n a m ic s 181
539 R a d io a c tiv ity . A to m s . M o le
cu les 181
539.15 A to m ic s tr u c tu re . N u c le u s 181
5 3 9 .1 6 R a d io a c tiv ity 182
539 .1 7 A rtif ic ia l n u c le a r d is in te g r a tio n 183
539.18 N e u tr o n s 183
539 .2 S tr u c t u re o f so lid s 184
5 3 9 .3 /.S E l a s tic ity . S tr e n g t h . R h e o lo g y 184
541 P H Y S I C A L C H E M I S T R Y 185
5 4 1 .1 2 6 /.7 R e a c tio n k in e tic s 185
541.13 E le c tro c h e m is try 186
541.18 C o llo id s . A d so rp tio n 186
5 4 1 .2 /.6 C h e m ic a l s tru c tu re 186
54 3 /5 4 5 C h e m ic a l a n a ly sis 186
548 C R Y S T A L L O G R A P H Y 187
548.73 X - r a y c r y s ta llo g ra p h y 188
55 G E O P H Y S I C S 188
551.5 M e te o ro lo g y 188
77 P H O T O G R A P H Y 190
512.52 J U N E 1946 M ATH EM ATICS 51
518.12
512.52 1459
F orm ulae fo r d irect and inverse interpolation o f a com plex function tabulated alo n g equidistant circular arcs. Sa l z e r, H . E . J. M ath. Phys., 24, 141-3 (N ov., 1945).— F o r m u l a e a r e g iv e n fo r q u a d r a t i c , c u b i c a n d q u a r t i c i n t e r p o l a t i o n . I n v e r s e i n t e r p o l a t i o n is b r ie f l y c o n s i d e r e d . l. s. g.
512.831 : 621.392.52 : 621.318.7 1460
A pplications o f m a trix alg eb ra to filter theory.
Ri c h a r d s, P . I. Proc. Inst. R adio Eitgrs, N . Y. Wav.
Electrons, 34, 145 -5 0 P (M arch, 1946).— [A bstr. 1354 B (1946)].
514.6 : 527 : 518.5 see A bstr. 1470
517.392 : 536.2 1461
O n c ertain in teg rals in the theory o f h e at conduction.
Horenstein, W . Quart. Appl. M ath ., 3, 183-4
(July, 1945).—T h e in teg rals
x ~ n exp (— a2/x — b2x )d x
w h e r e n — a n d ¿ » a r e e x p r e s s e d in t e r m s o f t a b u l a t e d f u n c t i o n s , o n e o f w h i c h is t h e e r r o r f u n c t i o n , l. s. g.
5 1 7 .4 3 3 :6 2 1 .3 .0 1 1 1462
T he stead y -state operational calculus. Wa i d e l i c h, D . L. Proc. Inst. R adio Eitgrs, N .Y ., 34, 7 8 -8 3 P (Feb., 1946).— T h e d ire c t a n d inverse tra n s fo rm s o f th e stead y -state o p e ra tio n a l c alculus a re p resen te d , to g eth e r w ith tw o m eth o d s o f ev alu atin g th e inverse tra n s fo rm , th e first resu ltin g in a F o u rie r series a n d th e se co n d giving a su m fu n c tio n . A p r o o f o f th e in v ersio n th eo re m co n n ectin g th e tw o tran sfo rm s is ou tlin ed . T w o exam ples a re p re sen te d illu stra tin g th e ap p lic atio n o f th is o p e ra tio n a l calculus to circuit p ro b lem s, a n d a co m p a riso n is m ad e betw een th e o rd in ary a n d th e stead y -state o p e ra tio n a l calculi.
517.51 1463
Theorem s concerning functions subharm onic in a strip . Ha r d y, G . H . , a n d Ro g o s in s k i, W . W . Proc. R oy. Soc. A , 1 8 5 ,1 -1 4 (Jan. 10, 1946).— A sub- h a rm o n ic fu n c tio n is defined, a n d th e p rin cip al th eo rem is th a t if f ( x , y ) is su b h arm o n ic a n d b o u n d e d above in th e h alf-strip , a < x < f t y > y , th e n eith e r (
1
) if>(x) — l i m f(x , y ) = — oo f o r a < x < (3, o r— y —
(
2
) <f>(x) is c o n tin u o u s a n d convex fo r a < x < f t I t is also sh o w n th a t th e in teg ral o f / ( x , y ) o v e r all values o f y is a co n tin u o u s convex fu n ctio n o f x . V ario u s ap p licatio n s a re m ad e. O n e relates to in teg rals ta k e n alo n g a line o n w hich x is c o n stan t;a n o th e r to th e th eo ry o f co n fo rm al re p resen tatio n .
l. s. G.
517.522.2 = 4 1464
Form ulae fo r the coefficients o f inverse pow er series.
Ka m b e r, F . A cta M ath.- Uppsala, 78 (P ts I -I I ) 193-
204 (1946) In French.— G iven th e p o w er series x m = y m(
1
+ m T ), w hereT = q y + C2>'2 + • • •
th e p ro b lem is to revert th e series to give y " = x " (l + ttSn), w here
S n — ftr, 1 X+ b„t 2 X2 + . . .
H e re m a n d n n e ed n o t b e integral. T h e fo rm u la o f L ag ran g e is u sed to find th e coefficients bni (i — 1, 2, 3, . . .) a n d i t is sh o w n th a t each bni m ay be w ritten as a d e te rm in a n t, e.g. bnl — — q a n d
b,a — '■
1 (2
+ n ) q 2(2 + n)c2 2 !(2
+ n)1 (2
+7
i -f- m )c j A s a n exam ple th e series f = y p ]4
- y272
+ • • • is rev erted to give jj = f t f — f t f2
+ . . ., th e f t being d e te rm in a n ts involving th e yj. In a n o th e r exam ple th e derivative Tf = d nx!dyn is expressed in term s o f th e d erivatives o f v w ith resp ect to x , th u s 7)1
= (y ') 1,7
i2
= y " ( y ') ~ K: 3 y "/2 y "
y
2
y7)3 = 0 - 0 - 5
L. S. G.
517.564 1465
O n som e in teg rals involving Bessel functions. Bo se, B . N . Bull. Calc. M ath. Soc., 37, 77-80 (Sept., 1945).— T h e L ap lace tra n s fo rm s o f certain expressions involving B essel fu n ctio n s, e.g. p U 0(api),
p i l2n(P*)> a re fo u n d a n d u se d to ev alu ate so m e in teg rals in c losed fo rm . A m o n g th ese a re
-*0
a n d
*e ~ y in(y)yn ,
( a + y ) " + f y (a >
0
),I
exp (—a2
s i n 2 6)1,q(o2 s i n 2 6) s i n 0 dd r i ItI„(a sin
2
0) exp ( — a sin2 0
) (sin 0 ) ~ i d0l. s . G.
517.564 1466
T able o f Bessel f u n c tio n s / „ ( I 000). Co r r i n g t o n, M . S. J. M ath. Phys., 24, 144-7 (N ov., 1945).— T h e tab le covers th e ra n g e n — 935(1)1 035. E n trie s a re given to eig h t decim al places. T h e tab le w as c o m p u te d fo r use in th e sp e c tru m analysis o f a frequency- m o d u la te d ra d io w ave. l . s. g.
518.12 1467
A convergent iterativ e process. Sa m u e l s o n, P . A . J. M ath . Phys., 24, 131-4 (N ov., 1945).— A n e q u a tio n x = g (x ) is o ften solved by a n ite ra tio n o f th e fo rm x „ + j = g(xn). W h e n th e convergence is slow it m ay b e m ad e m o re ra p id by u sin g y „+1 = h(y„) w here
K a =, [g{g
<»}]2
~ gM glg fe M }]! y
2
g{g(y)} - g (y ) - g[g{g(y)}]T h is p ro cess is generalized in th ree d ifferent d irectio n s.
L. S. O .
VOL. XLIX.— A.— 1946. JUNBt. 159
518.3 519.4
518.3 : 536.2 : 532.542.4' 1468
L ogographs. To u r, R . S . Trans. Airier. Soc. M ech.
Engrs,
68
, 143-9 (Feb., 1946).— A new ty p e o f c h a rt is p resen ted fo r g raphical so lu tio n o f e q u atio n s o f the fo rm T P W V r Ws = K, dep en d in g basically o n the ad d itio n o f lo garithm s. T h ey develop fro m th e fact th a t a stra ig h t line d ra w n o n sem ilog p a p e r represents a fu n ctio n o f th e fo rm : log y — oc + bx, o r x = c + it log y . T h eir c o n stru ctio n is e xplained a n d exem plified in th e d evelopm ent o f a c h a rt fo r th e calcu latio n o f h e at-tra n sfe r coefficients in tu rb u le n t flow. C h a rts a re also given fo r th e tu rb u le n t flow o f fluids in pipes a n d fo r th e flow o f fluids th ro u g h sh a rp -ed g e d orifices.
T h e eq u atio n s und erly in g th e la s t tw o c h a rts rep rese n t new fo rm s o f th e sta n d a rd expressions a n d a re briefly discussed a n d th e ir lim itatio n s indicated.
518.5 • 1469
A com puter for solving linear sim ultaneous equations.
Be r r y, C. E ., Wi l c o x, D . E ., Ro c k, S. M ., a n d Wa s h b u r n, H . W . J. Appl. Phys., 17, 262-72 (April,
1946).— T h e m ath em atical p rinciples o f th e classical ite ra tiv e m eth o d o f solving lin e a r sim u ltan eo u s e q u a tio n s a rc discussed. B asic electrical c ircu its fo r setting u p a n an alo g u e o f th e m ath e m a tical re la tio n s are given c o m p risin g p o te n tio m e te r n etw o rk s fo r m ultiplying a n d ad d in g voltages, a n d a com m ercial m o d el o f a 12-equation c o m p u te r is briefly described. T h e results o f solving a n u m b er o f p ro b lem s o n th e c o m p u te r a re given to illu stra te its accu racy a n d speed o f o p eratio n . I t is fo u n d th a t solving sets o f 12 e q u atio n s req u ires on ly i to \ th e tim e req u ired b y c o n v en tio n al m ethods.
518.5 : 527 : 514.6 1470
A new instrum ent fo r solving spherical triangles.
M a t th e w s , B. H . C . Proc. R oy. Soc. A , 185, 241-9 (M arch 14, 1946).— T h e in stru m e n t w as designed fo r u se in celestial n a v ig a tio n by a m a te u r yachtsm en.
I t is m u ch m o re ra p id to u se th a n th e tab les u sually em ployed, a n d c a n b e m ad e to be a ccu rate to ± i ' o f a rc in calcu latin g zen ith distance. A W h e a tsto n e b rid g e a rra n g e m e n t is used to effect th e c o m p u ta tio n s.
T w in p o ten tio m e ters, e ac h h av in g tw o m oving c o n tac ts, a re se t by d ials m a rk e d in an g le to m ak e resistances re p re se n t th e a p p ro p ria te d e riv a tio n s o f latitu d e, d eclin atio n , h o u r an g le a n d zen ith distance.
W h en o n e o f these is u n k n o w n , i f th e p o ten tio m e ters a re b alan ced th e fo u rth resistance gives th e so lu tio n . T h e in stru m e n t m ay be u sed to solve an y sp h e rical tria n g le fo r a b o d y above th e o b serv er’s h o rizo n fo r decim atio n s a n d latitu d es u p to a b o u t 80°. l. s. o .
518.5 : 53 1471
Sim ple differential equations arisin g in physics;
rap id solution by using h atch et planim eters. Ca l l e n d e r, A . J. Sci. lustrum ., 23, 77—81 (April, 1946).—
T h e p rinciple o f th e h a tc h et p la n im eter is explained a n d th e th eo ry is given o f th e m eth o d s in w hich th is p lan im eter is u sed to solve a p p ro x im ate ly p ractical physical p ro b lem s governed by e q u atio n s o f th e type
CdOldt = k(<j> — 6) C^dO^dt = &
2
(®t — O2)o r C ^ iO Jdt -f- C^dO^dt — ky((j> — 0j)
S u ch e q u atio n s arise in a larg e n u m b e r o f an alo g o u s pro b lem s, e.g. th erm o d y n am ic, electrical, h ydraulic,
m echanical, etc. T w o exam ples, ta k e n fro m th e th e o ry o f h e a t flow, a re given. l. s . g. 518.5 : 535.317.1 = 4 see A bstr. 1566
518.5 : 621-531 1472
An a p p ara tu s fo r investigating the behaviour o f reg u latin g devices, v o n Fr e u d e n r e i c h, J . Brown Boveri R ev., 31, 228-32 (July, 1944).— [A bstr. 1246 B (1946)].
518.5 : 621.389 1473
T he E N IA C , a n electronic calculating m achine.
Ha r t r e e, D . R . Nature, Lond., 157, 527 (A pril 20, 1946).— T h e m ach in e is desig n ed fo r th e step-by-step in te g ra tio n o f e q u atio n s, a n d o p e rates by th e c o u n tin g o f electrical p u lses p ro d u c ed a t
100 000
p e r sec.T h ese a re fe d to th e scale-of-10 c o u n tin g circu its by electro n ic sw itches acco rd in g to th e o p e ra tio n (ad d i
tio n , m u ltip licatio n , etc.) to b e carried o u t. T h ere are 3 fu n ctio n tab les, o n w hich m ay b e se t u p sets o f values req u ire d fo r th e c alcu latio n , a n d th e m ac h in e w ill in te rp o la te betw een values acco rd in g to th e in te rp o la tio n fo rm u la su p p lied to it. T h e a d d itio n u n its p ro v id e a “ m em o ry ” o f cap acity a b o u t
20
n u m b ers, w hich a re im m ediately av ailab le fo r fu rth e r calcu latio n s. T h e final resu lts a re d elivered o n p u n c h ed card s. T h e w hole m ach in e com prises 18 000 valves, 3 000 lam p s a n d 5 000 sw itches, a n d tak e s a b o u t 150 k W in o p eratio n .
518.61 $ 1474
T able o f coefficients fo r double q u ad ratu re w ithout differences, fo r in teg ratin g second o rd er differential equations. Sa l z e r, H . E. J. M ath. Phys., 24, 135—40 (N ov., 1945).— T h e tab le is chiefly o f u se in th e num erical in te g ratio n o f eq u atio n s o f th e fo rm y " + g (x )y = 0 o r y " + <j>(x, y ) = 0. T h e m e th o d fo r th e la tte r is illu strate d . T h e ta b le m ay b e u se d to calcu late a fu n ctio n w henever its seco n d d erivative is k n o w n a t eq u ally spaced p o in ts. I t w as c o n stru cted b y ap p ly in g a d o u b le q u a d ra tu re to th e w ell-know n L ag ra n g ia n in te rp o la tio n fo rm u la. C ases a re covered w here th e seco n d d erivative is ap p ro x im ate d by p o lynom ials ra n g in g fro m th e seco n d to th e te n th
degree. l. s. g.
519.24 1475
Inform ation and accuracy a tta in a b le in th e estim ation o f sta tistica l param eters. Ra o, C . R . Bull. Calcutta M ath. S oc., 37, 81-91 (Sept., 1945).— C e rta in in e q u ality re la tio n s a re derived co n n ec tin g th e elem ents o f th e in fo rm a tio n m atrix , as defined b y F ish e r, a n d th e varian ces a n d covariances o f th e estim atin g fu n ctio n s. A class o f d istrib u tio n fu n ctio n s w hich a d m it e stim a tio n o f p a ram ete rs w ith th e m in im u m v arian ce is discussed. T h e c o n ce p t o f d istan ce betw een p o p u latio n s o f a given type is developed, sta rtin g fro m a q u a d ra tic differential fo rm defining a n
elem en t o f len g th . l. s. g.
519.283 : 621.791.7 : 621.311.i53 = 397 1476 O verlapping o f welding loads. He r l t t z, I. Tekn.
Tidskr., 76, 226 (M arch 2, 1946) In Swedish.— [A bstr.
1271 B (1946)].
519.4 : 548.1 = 4 see A bstr. 1727 160
522.21 523-87
A ST R O N O M Y . G EO DESY 52
. 522.21 1477
Im p o rtan t considerations in m aking reflecting telescopes. Va u g h n, F . J. R . A str. Soc. Can., 39, 53-8 (Feb., 1945).— D e tails re aso n s w hy som e reflectors fail to p e rfo rm w ell d u e to ig n o rin g m an y p ra ctic a l p o in ts. T h e a m a te u r p ro d u c e s h ig h qu a lity m ain m irro rs, tim e co stin g n o th in g , w hich w o u ld b e very expensive i f m ad e b y a pro fessio n al. T h e use o f flats o f o n ly a fa ir degree o f flatness is d ep lo re d , y e t a c e rta in larg e sale p o p u la r b o o k c o n d o n es th is p ractice.
P o o r s u p p o rt system s fo r m ain m irro rs are a freq u e n t cause o f lac k o f definition. T h e b e st m aterials a n d th e design o f th e tu b e f o r a reflecto r a re discussed.
c . G . M.
523.11.: 531.51 : 530.12 see A bstr. 1491
523.37 1478
T h e in fra-red spectrum o f the m oon. Ad e l, A . A strophys. J., 103, 19-24 (Jan., 1946).— G ives p relim in ary re su lts u sin g a p o tas siu m b ro m id e p rism sp e c tro m ete r o n a n im ag e o f th e fu ll m o o n o f d iam e te r £ in , p assed o v er a slit. T h e p o ssibility o f u sin g th e ra d ia tio n s fro m th e e a rth a n d m o o n to stu d y th e n ig h t a tm o sp h e re is d em o n stra ted . T h e only p rio r w o rk o n th e lu n a r sp e c tru m w as by L angley
in 1889. e. G . m.
523.7 1479
S o la r p h y s ic s . Hu n t e r, A . Rep. Rhys. Soc. Progr.
Phys., 9, 101-12 (1942-43).— T h e prev io u s review b y A . D . T h ac k era y (1940) is b ro u g h t u p to d ate. T h e c o ro n al sp ectru m , a n d in p a rtic u la r th e w o rk o f E d ie n (A bstr. 344 (1943)], is discussed, a n d th e b rig h t c h ro m o sp h eric e ru p tio n s a n d th e ir geophysical effects a re review ed. O th e r to p ic s tre a te d a re the m o tio n o f so la r p ro m in en ces a n d convection in the su n . T h e re le v an t lite ra tu re is listed. - l. s. g. 523.746 : 537.591.5 see A bstr. 1667
523.841.1 : 523.87 see A bstr. 1486
523.841.9 1480
S pectrographic observations o f th e eclipsing variables W U rs a e M lnoris, X Z S a g itta rii and K O Aquilae.
Sa h a d e, J. A strophys. J., 102, 470-9 (N ov., 1945).—
T h re e eclipsing b in aries o f s h o rt p erio d w ith m a rk e d differences in th e d e p th s o f th e tw o m inim a. R esu lts fro m 29, 27 a n d 39 sp e c tro g ra m s respectively:
W U . M in .: P rim ary , A 3 ; p erio d , 1 -70116 day s;
y = — 17-9 k m /sec; K =
86-6
k m /sec; e — 0 -0 9 ;<n =
221
° -6
; T = p h a se 0-611//; « s i n / =2
- O x10
« k m ;/( m ) =0
-110
.X Z S gr.: P rim a ry A 3 ; seco n d ary F o r G; K ~ 11 k m /sec; p erio d 3 • 3d. T h e m ass fu n c tio n is very sm all a n d p o ssib ly im plies a very h ig h ra tio fo r th e m asses o f th e tw o co m p o n en ts.
K O A q l.: P rim ary A 0 o r A l ; P — 2-863844 days;
y = — 2 -7 k m /sec; K — 37-8 k m /sec; e — 0 -0 2 ; co = 130°-9; T — p h ase 0 -3 7 2 d ays; a sin / = 1-5 X
10s k m ; f(m ) —0 - 0 1 6 0 . D . s. E.
523.841.9 : 523.87 1481
Spectrographic observations o f the eclipsing variable T T H ydrae. Sa h a d e, J ., a n d Ce s c o, C . U . A stro phys. J., 103, 71-5 (Jan., 1946).—D u rin g a n d n e a r
to ta l eclipse d o u b le em ission lines o f h y d ro g e n ap p e a r a n d und erg o eclipses. T h e p ro b a b le o rig in is a
gaseous ring, sim ilar to th a t suggested b y S tru v e fo r
S X C assiopeiae. d. l. e.
523.841.9 : 523.87 1482
S pectrographic observations o f eleven eclipsing binaries. St r u v e, O . A strophys. J., 103, 76-98 (Jan., 1946).— V elocities an d o rb ita l elem ents a re given fo r all th e sta rs observed. T w o o f th em (V W Cyg., A Q Peg.) show H em ission lines, d u rin g p rin cip al m inim um , w hich u n dergo eclipses. D a ta fo r th ese a n d
6
o th e r eclipsing b in aries w ith gaseous rings are in clu d ed in a d e ta ile d d iscussion o f su ch system s.T hese m ay be co m m o n , b u t co n d itio n s necessary fo r o b serv atio n g reatly restrict th e n u m b e r d etected.
D. L. E.
523.87 1483
P relim in ary rep o rt on a spcctrophotom etric investiga
tion in K ap tey n ’s selected areas. N os. 2 ,
6
, 7 , 15, 16 and 19. El v i u s, T . S tockholm s Obs. Ann., 14 (N o.8
) 1-18 (1945).— T h e p a p e r gives results fo r six selected areas. P h o to g ra p h s w ith th e 40 cm Zeiss a s tro g ra p h a t th e S to ck h o lm O b serv a to ry covering o n e sq u a re degree, give sh o rt sp ectra d o w n to 13 - 5 m w ith a n ex posure o f tw o h o u rs. Special plates have b e en ta k e n a t a n o th e r fo cu s to reach th e H a n d K lines, to classify th e A -type stars. [See A b str. 1898 (1934)]. M o n o c h ro m a tic m ag n itu d es a re derived a n d co rrected to fo rm p h o to g rap h ic m ag n itu d es o n the In te rn a tio n a l System . F o r b o th early a n d late type sta rs th e c riteria u sed to classify th e spectral types a re given, a n d co m p ariso n s w ith H a rv a rd , B erg ed o rf a n d M o u n t W ilson a re m ad e. T h e co rre latio n coefficients f o r86
sta rs co m m o n to B ergedorf, M o u n t W ilson a n d th is p a p e r a re betw een + 0 - 8 5 a n d -f-0-93.A c o m p ariso n o f th e se p a ra tio n o f g ian ts a n d dw arfs b y B e rg ed o rf a n d th e a u th o r show s less agreem ent, th e c o rre latio n coefficient bein g + 0 - 3 3 . T h e relatio n betw een c o lo u r in d ex a n d sp ectral ty p e is exam ined.
E. G . M .
523.87 1484
In terste lla r lines in the spectrum o f [3 L yrac. Me r r i l l, P . W . Pub!. A str. Soc. Pac!/., 57, 306-7 (D ec., 1945).— T a b u la te d disp lacem en ts o f C a l l a n d N a l lines give a w eighted m ea n o f — 1 8 -2 k m /s e c . A s th e velocity o f th e c en tre o f m as s is — 19-0 k m /sec th e lines m ay b e circu m stellar, th o u g h a n in te r
ste lla r orig in is n o t excluded. A d d itio n a l fa in t D lines sh o w velocities co rresp o n d in g to th e e x p an d in g
B5 shell. d. l. e.
523.87 1485
T h e spectrum o f BD + 67° 922. Wilso n, R . E . Publ. A str. Soc. P acif.. 57, 309-10 (D ec., 1945).—
T ab les a re given o f em ission a n d a b so rp tio n lin e displacem ents in 7 s p e c tra 'ta k e n in 1943-45. T h ere is n o evidence o f v ariab ility a n d th e s ta r a p p ea rs to b e a single d w a rf ( M = + 5 -0 ) b u t w ith a co m b in a tio n sp e c tru m in w h ich th e a b so rp tio n a n d em issio n lines h av e different displacem ents. A difference (7 km /sec) betw een th e m ean disp lacem en ts o f H a n d H e I m ay also b e significant. d. l. e.
523.87 : 523.841.1 1486
T he spectrum o f N ova A quilae 1945. Sa n f o r d, R . F . Publ. A str. Soc. P acif., 57, 312-14 (D ec., 161
53 530.12
1945).— P h o to g ra p h s tak e n betw een A ug. 31 an d O ct. 2 4,1945, a re rep ro d u ced . T w o sets o f a b so rp tio n co m p o n en ts displaced to th e v io le t o f em ission lines show ed velocities increasing fro m — 1 980 to —2 610 a n d — 1 1 5 0 to — 1 350 k m /sec respectively. T h e la tte r sp lit u p o n Sept. 12 in to tw o co m p o n en ts, o n e o f a b o u t —
1 200
a n d th e o th e r increasing fro m— 1 460 to — 1 630 km /sec. E m issio n lines o f H , H e II, N II a n d [O III] a re n o te d in th e p h o to g ra p h ic
region, w hile a n in fra-re d p la te o n Sept. 14 show ed lines o f N I, O I a n d th e P asch en scries o f H . d. l. e. 523.87 : 523.841.9 see A bstr. 1481, 1482
5 2 3 .8 7 7 :5 3 1 .1 9 1487
O n the abundance o f nuclei in the universe. Lattes, C ., a n d Wa ta gh in, G . Phys. R ev., 69, 237 (M arch 1 and 15, 1946).— [See A b s tr. 496 (1945), 1739 (1942)].
527 : 514.6 : 518.5 see A bstr. 1470
PH Y SIC S 53
53 : 518.5 see A bstr. 1471
53.08 1488
A sum m ary statem ent o f the principles o f m easure
m ent. Da lze ll, D . P. Phil. M ag., 36, 485-90 (July, 1945).— [See A b str. 2374 (1944)].
53.081.6 : 530.14 see A bstr. 1499
53.087.25 : 621.317.351 = 3 1489
T heory of visually observable oscillogram s o f tim e- resolved periodic phenomena. Härtel, W . Z . In- strum kde, 63, 132-40 (April, 1943) In German.—
T h e re la tio n s o f th e vertical d a ta to tim e, as a p p earin g o n th e screen o f th e oscillograph, y = <f>(t), o r to a n o th e r v a ria b le w ith tim e as p a ram ete r, y — ifi(x), a re analysed, a n d th e ap p ea ran c e o f L issajous figures in th e seco n d case explained. T h e m echanical oscillo g rap h u sin g a ro ta tin g m irro r, a n d th e c.r.o.
u sin g a saw to o th deflection fo r tim e reso lu tio n a re con sid ered side b y side. A fte r trea tin g th e statio n ary im age o f a p h en o m e n o n th e p a p e r deals w ith a slow ly m oving im age a n d show s h o w a stro b o sco p ic m eth o d c a n b e a p p lie d to frequency co m p ariso n s, checks a n d
ad ju stm en ts. a. l.
F U N D A M E N T A L S 530.1 530.12 : 530.145.6 ¿ee A bstr. 1504
530.12 : 531.15 = 4 1490
T he Sagnac effect in astronom y and the possibility o f verifying th e kinem atics o f relativity. Pr u n ie r, F . Bull. A str., Paris, 12 (N o. 7) 351-64 (1940) In French.—
B y relativ ity is h e re m ea n t special relativity. T h e S agnac effect gives th e re ta rd a tio n o f o n e lig h t ray relative to a n o th e r m o v in g in a n o p p o site directio n ro u n d a ro ta tin g disc. T h e fo rm u la is ap p lied to m oving particles a n d th e in terv al is c alcu lated betw een successive coincidences o f th e ra d ii to tw o m oving p lan ets fro m th e c en tre o f ro ta tio n . T h e th eo ry dep en d s o n th e ap p lic atio n o f re su lts derived fro m th e use o f th e L o ren tz tra n s fo rm a tio n , w hich im plies th a t m oving p o in ts a re n o t relatively accelerated, to the c ase o f circu lar m o tio n s in w hich th e m o v in g p o in ts necessarily h av e a n acceleration. ' g . c . M cv.
530.12 : 531.18 see A bstr. 1514
530.12 : 5 3 1 .5 1 :5 2 3 .1 1 1491
A theory o f regraduation in general relativity.
Wa lker, A. G . Proc. R . Soc. Edinb. A , 62 (No. 19) 164-74 (1946).— T h e re g ra d u a tio n o f a n o b serv er’s p ro p er-tim e clo ck is discussed, sta rtin g fro m th e local G alilean co -o rd in ate system a t each p o in t o f a R iem a n n ia n space-tim e. I n o rd e r to sh o w th a t n o n triv ial re g ra d u a tio n s exist, a new in te rp re ta tio n o f E in stein ’s g rav itatio n al e q u atio n s is pro p o sed , viz. th a t re g ra d u a tio n s p reserv e th e fo rm o f the
e q u atio n s b u t a lte r th e values o f th e g rav itatio n al c o n sta n t a n d th e c osm ical c o n stan t. N o experim ental evidence is a d d u ced fo r th ese assu m p tio n s. P a rtic u la r cases a re w o rk ed o u t in d etail w ith special reference to L em aitre ex p an d in g universes. I t is sh o w n th a t c ertain re g ra d u a tio n s a re po ssib le w hich tra n s fo rm th e cosm ical c o n sta n t to zero. g. c. mcv.
530.12 : 531.51 = 4 1492
O n a fundam ental result in the relativ ity theo ry o f grav itatio n . L ic h n e r o w ic z , A . C .R . A cad. S ci., P aris, 221, 652-4 (Nov. 26, 1945) In French.— A c o n tin u a tio n o f previous w o rk [ibid., 2 0 6 , 157 a n d 313 (1938)] a n d a discu ssio n o f re la te d w o rk b y E in stein a n d P au li [A bstr. 2997 (1942) a n d Ann. o f M ath ., 44, 131 (1943)]. T h e m ain re su lt is th a t a n e x te rn al field everyw here reg u lar, m u st b e a field w ith o u t g rav itatio n , i.e. it m u s t red u ce to a E u clid ean field. T h e h isto ry o f v ario u s a tte m p ts to p ro v e th is is tra c e d a n d som e consequences o f th e re su lt a re listed . L. s . g.
530.12 : 531.51 : 535.1 = 4 1493
E lectro -o p tics and universal tim e. Dive, P. Bull.
A str., Paris, 12 (N o. 1) 1-71 (1940) In French.—
A n a tte m p t to develop a n a lte rn a tiv e rela tiv istic th eo ry o f electro -o p tics (n o t b ased o n th e L o ren tz tra n s fo rm a tio n ) follow ing u p a n id ea d u e to P o in care, th a t th e velocity o f lig h t signals e m itted fro m a m oving so u rc e is g re ater in a d irectio n p a ralle l t o th e m o tio n o f th e so u rce th a n in a p e rp en d icu la r d irectio n . P o stu la tin g a “ u niversal tim e” t, a n d re ta in in g th e classical (G alilean ) tra n s fo rm a tio n x = ut + x \ y = y ', z = z', betw een tw o system s S (x, y , z , t) a n d S '(x ', y ', z ', t') m o v in g relative to o n e a n o th e r w ith velocity u p a ralle l to th e x-axes, a n d assu m in g th a t th e “ n a tu ra l tim es” t a n d t' in 5 a n d S ' a re c o n n ected by th e re la tio n t' — a t + bx, w here a a n d b d ep en d on ly o n u, it is sh o w n th a t lig h t signals a re p ro p a g a te d as sp h ero id al w aves, o f w hich th ere a re tw o types.
T h e physical consequences o f th is are discussed in d e ta il: to th e seco n d o rd e r in u/c, c bein g th e velocity o f light, th ey a p p e a r to c o n fo rm to th o se o f E in ste in ’s th eo ry . I t is claim ed as a n a d v an tag e th a t an y n e w e x p erim en tal fa c t in volving seco n d o rd e r effects can alw ays b e m ad e to fit in th e new th eo ry ; th e sam e m ay n o t be th e case fo r E in stein ’s th eo ry . v . c . a. f.
530.12 : 531.51 : 538.3 1494
A generalization o f special relativity theory. Co r- ben, H . C. N ature, Lond., 157, 516 (A pril 20, 1946).
530.12 : 531.51 : 538.3 1495
A classical theory o f electrom agnetism and g ra v ita tion. I. S pecial theory. Corben, H . C. Phys. R e f., 69, 225-34 (M arch 1 and 15, 1946).—B y extending th e M a x w e ll-L o ren tz eq u atio n s to five dim ensions, i t- is sh o w n th a t one is le d to a sim ple unified th eo ry o f 162
530.14 530.14
g ra v itatio n al a n d electro m ag n etic p h en o m en a. T h e generalized expressions fo r th e fo rce den sity a n d the w o rk d o n e p e r u n it v o lu m e p e r u n it tim e c o n ta in term s w hich co rresp o n d , respectively, to th e effects o f electric, m agnetic a n d g ra v itatio n al fields. I f it b e assu m ed th a t n o changes o f p hy sical q u a n titie s o ccu r in th e d irec tio n o f th e e x tra d im e n sio n so in tro d u c ed , a special relativ ity th eo ry o f gravito-electrom agnetic fields arises. W ith in th is th eo ry g ra v ita tio n al w aves a re p ro p a g a te d w ith th e velocity o f light, g ra v itatio n a l p o ten tial is in v a ria n t f o r L o ren tz tran s fo rm a tio n s, a n d g ra v itatio n al fo rce acts o n th e re st m ass o f a particle. T h e co n se rv a tio n law s o f charge, m o m e n tu m , a n d energy a re sh o w n to h o ld , b u t th e la s t tw o yield a generalized P o y n tin g vector, a n d a generalized ex
p ressio n fo r th e energy den sity , b o th o f w hich c o n ta in term s w hich d ep en d o n th e g ra v itatio n al field stren g th s.
T h e finite velocity o f p ro p a g a tio n o f g ra v itatio n al w aves lead s a t o n ce to th e resu lt th a t a n accele rated m ass em its energy in th e fo rm o f su c h w aves. O n the classical th eo ry th e ra d ia tio n em itte d by a n electro n th u s h as a sso ciated w ith it a sm all lon g itu d in al g ra v itatio n al c o m p o n e n t. G ra v ita tio n a l forces a re sh o w n to lead to a self-energy fo r a n a cc elerated m ass, a n d th e classical ra d iu s o f a m ass m , c o rre sp o n d in g to th e classical ra d iu s o f a charge, is Gm/c2, w here G is th e g ra v itatio n al c o n stan t.
530.14 1496
T he point singularity in a non-linear m eson theory.
Wa l s h, P . P roc. R . Irish A cad., 50 A (N o. 11) 167-87 (M a y, 1945).— A m eso n field is con sid ered w hose eq u atio n s differ fro m th o se o f M axw ell in possessing: (1) B o rn ’s n o n -lin e a r m odification;
(2) P ro c a ’s self-exciting term c o rre sp o n d in g to a n o n - Vanishing rest-m ass o f th e c o rre sp o n d in g p article.
Since th e m eso n field h as a very c o n sid erab le rest m ass, th ere is a n o v erlap p in g o f th e effects o f (
1
)a n d (2) as e ac h com es in to p lay n e a r th e c en tre. T h e p ro b lem co n sid ered is th u s m o re difficult th a n th e case c o n sid ered recen tly by S ch rö d in g er [A bstr. 1956 (1944)] w here a tte n tio n w as confined to th e e lectro m agnetic field. T h e sp h erically sym m etric static p ro b lem is co n sid ered , a n d p a rtic u la r a tte n tio n is p a id to th e re la tio n betw een th e c h arg e a n d th e to ta l field energy, E. T h e field e q u a tio n is
7 r [ r ~ ^ r2^ 1 ~ = ^
w h e re th e c h arg e is g = {r2>jj(
1
— ip2) ~ i } r=,0 and, a fte r o b tain in g a closed so lu tio n in th e o ne-dim ensional case, ap p ro x im ate so lu tio n s a re o b ta in e d w h en> l\/g <1 1 a n d /I V s 1. T h e results give som e idea o f th e d ep en d en ce o f E o n g . l . s . g .
530.14 1497
O n the fields and equations o f m otion o f point- p articles. Bh a b h a, H . J ., a n d Ha r i s h- Ch a n d r a. Proc. R oy. Soc. A , 185, 250-68 (M arch 14, 1946).—
T h is p a p e r is concerned w ith p o in t particles possessing a charge, d ipole a n d m u ltip o le m o m en ts in te rac tin g w ith fields o f a rb itra ry sp in satisfying th e general w ave eq u atio n ,
(d2ß x ^ x ]i + X 2)U = 0
T h e ra d ia tio n field is d en n ed as th e re ta rd e d m in u s th e advanced field a n d it, to g e th e r w ith all its deriva-
tives, is fo u n d to be alw ays finite a t a ll p o in ts, including th o se o n th e w o rld line o f th e p o in t p articles. T h e sym m etric field (5 ), defined as h a lf th e su m o f the re ta rd e d a n d ad v an ced fields, c o n tain s a p a r t ex
pressible as a n integral I alo n g th e w orld line fro m
— oo to - f co , w hich is c o n tin u o u s a n d everyw here finite. I f X = 0, th e n 1 = 0. T h e m odified sym m etric field (S *) is defined by S * = S — I. T h e actu al field is th e su m o f S * a n d th e m odified m ean field, w hich is h a lf th e sum o f th e ingoing a n d o u tg o in g fields p lu s I I t is show n th a t th e p a rt o f th e stress ten s o r o f th e field q u a d ra tic in S * plays n o p a rt in d eter
m ining th e eq u a tio n s o f m o tio n . B eing conserved by itself, it c a n alw ays be su b tra cte d aw ay, th u s defining a n ew stress ten s o r w hich is free fro m all th e hig h est singularities in th e u sual stress ten so r. T he eq u atio n s o f m o tio n d ep en d on ly o n the “ m ixed term s” in th e inflow w ith th e m odified m ean field su b stitu te d fo r th e in g o in g field. T h e fo rm u latio n fo r several p articles is given. l. s. g.
530.14 1498
O n th e equations o f m otion o f point particles.
Ha r i s h- Ch a n d r a. Proc. R oy. Soc. A, 185, 269-87 (M arch 14, 1946).—T h e results o f th e p receding p a p e r [A bstr. 1497 (1946)] are used to o b tain explicitly the eq u atio n s o f m o tio n , w hich a re in d ep en d en t o f the p a rtic u la r choice o f th e energy-m om entum ten s o r o f th e field fro m a m o n g th e m an y alterh ativ es [A bstr.
983 (1939)]. A c o n v en ien t m e th o d is given fo r calcu latin g th e ra d ia tio n field. T h e sp in a n g u la r m o m en tu m o f a p o in t p article is defined a n d it is p o stu late d th a t th e m ag n itu d e is c o n stan t. A p p lica
tio n o f th e th eo ry is m ad e to a ch arg ed d ip o le in a vector- o r scalar-m eso n field. In th e fo rm er th e co n stan cy o f sp in effects a g re at sim plification in th e e q u atio n s o f m o tio n , w hich a re com pletely d eterm in ed in term s o f tw o a rb itrary co n stan ts. T h ese a re in te rp rete d a s th e m ass a n d th e spin. O n ly those d ipoles fo r w hich th e “ electric” a n d “ m ag n etic”
m o m en ts a re p arallel in .the rest system are co n sisten t w ith th e a ssu m p tio n o f c o n sta n t sp in . T h e eq u atio n s in a scalar-m eso n field also c o n ta in tw o c o n stan ts a n d these are sim ilarly in terp reted . l. s. g.
530.14 ; 53.081.6 1499
A relation between som e n atu ral constants a rii the lesser particles. Dr e w, H . D . K . Phil. M ag., 36, 577-80 (Aug., 1945).—T h e new re la tio n s h ip R = m2c/20M h is ded u ced w here R is R y d b e rg 's general w ave-num ber c o n stan t, tu a n d M a re th e m asses o f th e electro n a n d n e u tro n respectively a n d it is P la n ck ’s c o n stan t. C o m b in in g th is w ith B o h r’s e q u atio n R = 2u2msA\ch'i we o b tain
c h \ i / m \ i 2;t ) \ 10M /
a n d th is yields hje — 1 -375794 x 10—
17
w hich is n e a re r th e o b serv ed v alu e 1-3765 x 10- 1 7 th a n B irge’s estim ate. T h e significance o f th ese re la tio n s is discussed especially w ith reference to th e p o ssibility o f the existence o f a series o f m in u te p articles, l. s. g.530.14 = 4 1500
O n ten relations resulting from D ira c ’s second order equations. Du r a n d, E. C .R . A cad. Sci., Paris, 218, 36-8 (Jan. 4, 1944) In French.— A n o u tlin e is given o f the m eth o d fo r deriving the re la tio n s an d a physical 163
530.14 530.145.6
in te rp re ta tio n is given w here th is exists. Som e o f the ten so rs arising in th e eq u atio n s a re re la te d to th o se previously in tro d u c ed by T e tro d e a n d by Proca.
l. s. G .
530.14 = 4 1501
O n the decom position o f the equations fo r a p a rticle o f a rb itra ry spin, v a n Is a c k e r, J. C.R . A cad. Sci., Paris, 219, 51—3 (July 3, 1944) In French.— T h e e q u atio n o f sta te fo r a p article o f an y sp in , in th e absence o f a n ex tern al field, is resolved in to a system o f eq u atio n s. A su m o f so lu tio n s o f th e la tte r gives a so lu tio n o f th e o rig in al e q u atio n . A special case is discussed in w hich th e eq u atio n is resolved in to
6
g ro u p s o f e q u atio n s:
1
g ro u p c o rre sp o n d in g to p articles o f sp in 2, 3 g ro u p s c o rre sp o n d in g to a sp in 1 a n d2
g ro u p s co rresp o n d in g to a spin0
. l. s. g.530.145 : 538.3 1502
Q uantum electrodynam ics w ith 'bAv]'bxv. = 0.
Ch a n g, T . S. Proc. R oy. Soc. A , 1 8 5 ,192-206 (Feb. 12, 1946).—T h e re su lts o f a n e arlie r p a p e r [A bstr. 1243 (1945)] a re su m m arized a n d th e relativistic invariance o f th e co m m u tatio n re la tio n s is proved. T h e P o isso n b ra ck e ts o f Ap. (th e fo u r-p o ten tial) a t tw o different p o in ts in space a re w o rk e d o u t fo r th e vacuum . A m odified fo rm o f th e eq u atio n s o f D ira c , F o c k a n d P o d o lsk y [Phys. Z . Sow jet., 2, 468 (1932)] is given.
In th is 'iiAv.l'dxv. = 0, b u t th is is n o t tru e in th e original th eo ry . T h e m odified e q u atio n s a lso re su lt in a q u a n tu m electro d y n am ics w here e ach o f th e charges ta k e s a se p a ra te tim e co -o rd in a te a n d bApjlixp. =
0
.F in a lly it is sh o w n h o w th e e q u a tio n h A p/bxp = 0 m ay b e in tro d u c e d in to D ira c ’s n ew electrodynam ics [A bstr. 1742 (1942)], w hich in tro d u ces n egative energy states fo r p h o to n s d u rin g th e seco n d q u a n tiz a tio n , a n d how , as a resu lt, th e lo n g itu d in al p a r t o f th e field c an b e elim in ated . l. s. g. 530.145 : 538.3 : 537.122 see A bstr. 1625
530.145.6 1503
N o te on th e theory o f vector wave fields. Br o e r, L . J . F ., a n d Pa i s, A . P roc. N ed. A kad. W et., 48,
190-7 (1945).— I t is sh o w n th a t F e rm i’s m eth o d o f trea tin g th e electro m ag n etic field c a n b e a p p lie d to th e classical b u t n o t to th e q u a n tu m th e o ry o f th e v e c to r m eson field. T h e ro le o f th e L o re n tz c o n d itio n in this co n n ectio n is exam ined. v . c . a. f.
530.145.6 : 530.12 1504
T he conform al D ira c e q u a tio n .' Ha a n t j e s, J . Proc.
N ed. A kad. W et., 44 (N o. 3) 324-32 (1941).— A co n fo rm al w ave e q u a tio n is o n e w hich is in v arian t u n d e r a co n fo rm al tra n s fo rm a tio n o f th e fu n d a m en tal ten so r: g ik ~ ^ a2Stk' K *s sh o w n th a t th e D ira c eq u atio n s fo r particles w ith o u t m ass a re c o n fo rm al, b u t th e e q u atio n fo r m ass particles is c o n fo rm al o n ly if w e assu m e th a t th e m ass m becom es tran sfo rm e d th u s: m -> m jo. U n d e r th is a ssu m p tio n th e physical dim en sio n [A/L] is in v arian t. T h e physical in te rp reta tio n o f in v arian ce u n d e r c o n fo rm a l tran s fo rm a tio n in special relativ ity is discussed.
C o n fo rm al in v arian ce o f physical law s m eans th e eq uivalence o f observers w hich h av e a c o n stan t acceleratio n w ith respect to eac h o th er. l. s. g.
530.145.6 : 537.122 1505
R elativistic interaction o f electrons on Podolsky’s generalized electrodynam ics. Mo n t g o m e r y, D . J.
Phys. R ev., 69, 117-24 (Feb. 1 and 15, 1946).— T h e w ave e q u atio n fo r a system o f particles is derived o n th e basis o f P o d o lsk y ’s generalized electro d y n am ics [A bstr. 1906 (1945), 206 (1943)]. A n ex ten sio n o f so m e w o rk o f F o c k [A bstr. 602 (1935)] leads to a re p re se n ta tio n in term s o f a series o f fu n ctio n als.
W ith th is fo rm alism th e m a trix elem en t fo r th e relativ istic in te ra c tio n o f tw o e le ctro n s is d eterm in ed , a n d is seen to b e a g en eralizatio n o f M o ller’s fo rm u la [A bstr. 3719 (1931)].
530.145.6 : 537.133 see A bstr. 1632
530.145.6 = 4 1506
O n the wave m echanics o f elem entary particles.
K w a l , B. C .R . A cad. Sci., Paris, 218, 548-50 (M arch 27, 1944) In French.— T w o im p o rta n t p ro p e r
ties o f th e o u te r m u ltip lic atio n o f m atrices a re sta te d a n d u sed to d ed u ce th e p rim a ry eq u atio n s describing p a rticles o f sp in ■£, 1 a n d 4 . F o r th e p a rticle o f sp in j th e re a re
2
2J ~ l system s o f p rim a ry e q u atio n s, e ac h c o n sistin g o f 2 ] g ro u p s o f2
V eq u atio n s (ifi, th e w àve fu n c tio n , h a s 22J c o m p o n en ts). T h e seco n d ary e q u atio n s fo r a p a rticle o f sp in £ are discussed. T h ese involve the use o f sp in o rs. l . s. g.530.145.6 = 4 1507
T he principle o f correspondence fo r a n asym ptotic classical m echanics. St u e c k e l b e r g, E . C. G . C.R.
Soc. Phys. H ist. N a t., Genève, 61, 155-8 (A pril-July, 1944) In French.— T h e e q u atio n o f m o tio n in D ira c ’s th eo ry o f th e e le ctro n [A bstr. 3660 (1938)] is d is
cu ssed a n d it is n o te d th a t, becau se o f th e possib ility o f n o n -p h y sical so lu tio n s, final as w ell as initial co n d itio n s m u s t b e im posed. T h is lead s to a dis
cu ssio n o f th e e q u a tio n describing th e v a ria tio n o f physical q u a n titie s a n d to th e in tro d u c tio n o f a
“ ra tio n a l” a n d a n “ asy m p to tic ” m echanics. I n th ese th e final sta te is rep resen ted , in d ifferent w ays, in term s o f th e initial values. T h e co rre sp o n d en ce betw een th e tw o types o f m echanics is explained.
L. s . G .
530.145.6 = 4 1508
T he principle o f correspondence fo r a n asym ptotic quantum m echanics. St u e c k e l b e r g, E . C . G . C.R.
Soc. Phys. H ist. N at., Genève, 61, 159-61 (A pril-J u ly, 1944) In French.— C e rta in re ce n t w o rk o f D ira c [A bstr. 3660 (1938)] is criticized a n d th e m eth o d s o f H eise n b erg [A bstr. 2109 (1944)] a re c o n sid ered to be m u c h b e tte r. I t is sh o w n th a t th ese a re e q u iv alen t to a q u a n tu m a n alo g u e o f th e asy m p to tic classical m echanics in tro d u c e d previously. A n ew p rin cip le o f c o rre sp o n d e n c e betw een th e a sy m p to tic q u a n tu m m echanics a n d th e asy m p to tic m echanics o f S ch rö d in g er is a n n o u n ce d . l. s. ,g.
530.145.6 = 4 1509
T h e ch aracteristics, according to C auchy, o f the equations o f p articles with spin and J a c o b i’s relativistic equation. Ar n o u s, E . C .R . A cad. Sci., Paris, 219, 672-3 (D ec. 27, 1944) In French.— W ave fu n c tio n s in 5-dim ensional space a re considered. T h e eq u atio n s fo r a p h o to n , sim ila r to th e D ira c e q u atio n s fo r an electro n , a re w ritten d o w n , a n d th e ch aracteristic d e te rm in a n t o f th ese eq u atio n s is fo rm ed . A n ev alu atio n o f th is leads to th e Ja c o b i eq u atio n w hich occurs in th e restricted th eo ry o f relativity. l. s. g. 164
530.145.61 531.259.1
530.145.61 1510
A calculus o f finite precision—a correction. Li e- b o w i t z, B . Phys. R ev., 6 9,131 (Feb. 1 and 15,1946).—
[A bstr. 1238 (1945)].
530.145.65 : 536.71 1511
A verage values o f a group o f m echanical quantities in quantum sta tistics o f m onatom ic gases. De Bo e r, J., a n d M ic h e ls , A . Physica, 's Grav., 7 , 369-80 (M ay, 1940).— T h e e x p an sio n o f th e p a rtitio n fu n ctio n o f a m o n ato m ic g as given by U rsell a n d M a y e r a n d a d a p te d to q u a n tu m m echanics by U h le n b ec k a n d K a h n [A bstr. 2512 (1938)], h a s b e en generalized to o b ta in a scries-expansion in to pow ers o f th e recip ro cal v o lu m e fo r a g ro u p o f q u a n titie s, as fo r in stan c e th e p o ten tial energy a n d th e virial o f th e in term o lecu la r forces o f a m o n ato m ic gas. T h e expressions o b tain e d a re a p p lie d to calcu late th e dev iatio n s fro m th e law o f e q u ip a rtitio n in q u a n tu m m echanics in th e tem p e ra tu re reg io n w here th e dev iatio n s fro m classical sta tistics a re sm all.
530.162 : 533.723 1512
O n the theory o f the Brow nian m otion, II. Wa n g, M . C ., a n d Uh l e n b e c k, G . E . Rev. M od. Phys., 17, 323-42 (A pril-July, 1945).— P a p e r I [A bstr. 352 (1931)] gives a su m m ary o f th e th eo ry up to 1930.
I n th e p re sen t review th e g en eral th e o ry o f ra n d o m processes, a n d , in p a rtic u la r, th e G a u ss ia n ra n d o m p ro cess is u se d as a basis fo r d eveloping th e th eo ry o f th e B ro w n ian m o tio n . G e n era l ra n d o m processes a re described a n d classified a n d som e re m a rk s a re m ad e o n th e th eo ry o f discrete ra n d o m series. T h e G a u ss ia n ra n d o m p ro cess is tre a te d b y m ean s o f th e R ice m e th o d [A bstr. 1385 B (1946)] a n d b y th e d iffu sio n -eq u atio n m e th o d d u e to F o k k e r-P la n c k . T h en th e B ro w n ian m o tio n o f a scries o f co u p led h a rm o n ic o scillato rs is stu d ied . l. s. g.
530.162 : 621.38 1513
M a th em atical analysis o f random noise. I-IV . Ri c e, S. O . B ell S y st. Techn. J., 23, 282-332 (July, 1944); 24, 47-156 (Jan., 1945).— [A bstr. 1385 B (1946)].
M E C H A N IC S O F S O L ID S 531 531.15 : 530.12 = 4 see A bstr. 1490
531.18 : 530.12 1514
A sim ple p ro o f o f the L o ren tz transform ation.
St r a u s s, M . D . H . N ature, Lond., 157, 516 (A pril 20, 1946).
531.19 : 523.877 see A bstr. 1487 531.19 : 532.517.4 see A bstr. 1534
531.224.2 _ 1515
T h e generalised buckling problem o f the circu lar rin g . Bie z e n o, C. B ., a n d Ko c h, J. J . Proc. N ed.
A kad. W et., 48, 447-68 (1945).— In th e general p ro b lem th e rin g is su bjected to ra d ia l a n d tan g e n tial lo ad s, a n d th e co n d itio n s o f e q u ilib riu m o f a ring- elem en t a re w ritten d ow n. I t is sh o w n th a t th e general lo ad system m ay b e d eco m p o sed in to a n /
1
-system ,w here th e b e n d in g m o m e n t a n d th e sh e a rin g fo rce are zero, a n d a B -system w h e re th e n o rm a l fo rce is zero. T h e /
1
-system is stu d ied in detail. A sso ciated w ith th e differential e q u atio n fo r th e b u ck lin g is an in teg ral e q u atio n a n d t! is is solved by a n ite rativ em eth o d . N u m e rical resu lts a re given fo r v ario u s an aly tical types o f com pressive forces. l. s. g.
531.224.4 1516
S tru ts o f variable flexural rigidity. Du r a n t, N , J . Phil. M ag., 36, 572-7 (Aug., 1945).— A n in v estigation is m ad e o f th e elastic stability o f a stru t. T h e e q u atio n o f flexure is
d^yldx2 + k i é ¡x!,( y — ó) =
0
w here k , k \ , I a n d 3 are c o n stan ts. I t is in te g rate d in term s o f B essel fu n ctio n s fo r all values o f k. I t is in teg rab le in term s o f elem entary fu n ctio n s w hen k — 0. T h e c o n d itio n fo r stab ility is determ in ed a n d a tab le o f v alues o f th e critical th ru s t is given fo r v ario u s values o f k . T h e case k -> 0 is investigated, since th is is th e fa m ilia r case o f a u n ifo rm stru t.
l. s. o .
531.23 1517
An application o f the m ethod o f finite difference equations to a problem o f bending moments.— C on
tinuous beam o f N equal spans under transverse loading and a n a x ia l force. Du r a n t, N . J. Phil. M ag., 36, 569-72 (Aug., 1945).— T h e p ro b lem o f a prev io u s p a p e r [A bstr. 1250 (1945)] is generalized so th a t the effects o f clam p in g th e en d s o f th e b eam a n d applying a n axial fo rce m ay b e considered. T h is is a case w here th e p rin cip le o f su p erp o sitio n c a n n o t b e used. A fo rm u la is derived fo r th e b e n d in g m o m e n t a t any su p p o rt a n d som e p a rtic u la r cases a re considered.
l. s . G .
531.23.08 = 69 1518
T he m om ent indicator and its application to models o f 2-d im en sio n al' structures. He n r iq u e s d o s Re is, E . A . Técnica (April, 1944). Publ. Centro Estud.
Engenharia Civ. (N o. 2) 17 p p. (1944) In Portuguese.—
T h e tab le fo r m o u n tin g th e in d ic a to r is d escribed a n d illu stra te d a n d th e th eo ry o f th e a p p a ra tu s is developed [see P roc. A m er. Soc. Civ. Engrs, 64,
8
, 1613-25 (O ct., 1938)]. T h e a p p lic atio n to celluloid m odels o f v ario u s stru c tu re s is explained, in cluding d e te rm in a tio n o f b e n d in g m o m en ts in rig id fram es. J. a. w.531.259 1519
O n p lastic bodies w ith ro tatio n al sym m etry. Se d g e- w i c k, C . H . W . Quart. Appl. M ath., 3 , 178-82 (July, 1945).—A calcu latio n is m a d e o f th e lines o f p rin cip al stress a n d th e lines o f m ax im u m sh earin g stress in som e special cases. N e tw o rk s o f cycloids o r lo g arith m ic sp irals, k n o w n in th e case o f p lan e s tra in >
a re a lso adm issible in th e case o f ro ta tio n a l
sym m etry. l. s. g.
531.259.1 : 532.51 1520
E quations fo r elastic solids in spherical co-ordinates.
Ve n i n g Me ii^e s z, F . A . Proc. N ed. A kad. W et., 48, 469-86 (1945).— W o rk in g in a general o rth o g o n al co -o rd in a te system differential e q u atio n s a re se t u p w hich a re satisfied by th e disp lacem en ts in a n elastic solid. S im ilar eq u a tio n s a re given fo r th e velocity in a viscous fluid. T h e e q u atio n s a re solved u n d e r ce rta in fu n c tio n al re stric tio n s o n th e c o m p o n e n ts o f th e m ass forces a n d elastic d isp lacem en ts, etc. P a r tic u la r a tte n tio n is p a id to a sp h erical c o -o rd in a te schem e; o v er th e a re a stu d ied , th e tem p e ra tu re is v a ria b le b u t g rav ity is assu m ed to b e c o n s ta n t a n d in a ra d ia l d irectio n . V ario u s p ro p e rties o f th e so lu tio n s
a re n o ted . l. s. g.
165
