Science Abstracts. Section A, Physics Abstracts. Vol. 49, No. 581

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PHYSICS ABSTRACTS

S E C T I O N A

° f

SCIENCE ABSTRACTS

SECTION A, PHYSICS

SECTION B, ELECTRICAL ENGINEERING

E dited an d Issued M on th ly b y

T H 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

V O L U M E 49

ABSTRACTS 1191-1458

M A Y 1946 NUMBER 581

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T Y PE IV COMPRESSOR & VACUUM P U M P |

V A C U U M : 2 6 in s . H g . P R E S S U R E : 1 0 lb s . D I S P L A C E M E N T : 3 c u b i t f e e t p e r m i n u t e

This ‘g en eral-p u rp o se’ o u tfit fulfils long-standing re q u ire 

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requirem ents.

B L O W P I P E S • F I L T R A T I O N S S P R A Y I N G

A IR O R G A S C I R C U L A T I N G A S P I R A T I N G , E tc .

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NOTE ON THE ARRANGEMENT OF ABSTRACTS

T h e A b s tra c ts a re classified b y su b je ct a cco rd in g to th e U n iv ersal D ecim al C lassification, a n d arranged in o rd e r o f th e ir U .D .C . n u m b ers. (A n a b rid g e d version o f th e U .D .C . acco m p an ies th e A n n u a l Index.) An A b s tra c t o f in terest u n d e r m o re th a n o n e h ead h as a d d itio n a l U .D .C . n u m b ers, lin k ed by th e co lo n s ig n ,“ : ” e .g .“ 536.21 : 548.0 C o n d u c tio n o f h e a t in c ry stals.” T h e A b stra c t is p rin te d o n ce only, u n d e r th e m ain num ber, e.g. in th e section

“ H E A T 536,” b u t C ross-references a re in serted u n d e r th e o th e r n u m b ers, e.g. “ 548.0 : 536.21 see A b sir. 1234” in th e se ctio n “ C R Y S T A L L O G R A P H Y 548.” T hese C ross-references sh o u ld be investigated, th erefo re, w hen a p a rtic u la r section is being search ed , a s th ey c o n tain a d d itio n a l m a tte r relev an t to th a t section. A Cross-reference does nor refe r to th e A b stra c t w hich a p p e a rs im m ed iately ab o v e it.

A b stra c ts signed w ith th e follow ing initials h av e b een su p p lied by th e co u rtesy o f the o rg an izatio n s n am ed :

" E . R . A .” = British E lectrical a n d A llied In d u strie s R esearch A sso ciatio n . “ M . A .” = M etallurgical A bstracts.

“ M .-V .” = M etro p o litan -V ick ers E lectrical C o., L td. “ P. O .” = P o st Office E ngineering R esearch D e p a rtm e n t.^ ,-.,-

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389.6

M A Y 194 6 ë

389.6 : 535.242 see A bstr. 1277

389.6 : 621.3.011.2 : 537.311.081.6 sec A bstr. 1316 389.6 : 621.383.5 : 535.247.4 see A bstr. 1280

518.5

M A TH EM A TIC S 51

512.831 : 537.314 : 621.392.22 = 4 1191 O n the equations o f propagation on an a rb itra ry line.

Raymond, F . C.R. Acad. Set., Paris, 220, 497-500 (A pril 4, 1945) In French.— A n e w a p p ro ac h to the th eo ry o f tran sm issio n lines is presen ted . T h e lines n eed n o t b e u n ifo rm a n d tra n s ie n t as well as steady sta te p ro b lem s are included. I f P d en o tes th e co lu m n v ecto r ^ ^ • w here V a n d I a re th e L ap lace tran sfo rm s o f th e vo ltag e a n d c u rre n t, th e e q u atio n s o f p ro p a g a tio n a re tak e n in th e fo rm d P /d x = — M P , w here M — o ) ’ a anc^ P’ t ^le *'ne c o n sta n ts> being gener

ally fu n ctio n s o f th e d istan ce x alo n g th e line. T h e value o f P a t th e o u tp u t e n d is expressed in term s o f P 0, th e v alu e a t th e in p u t en d , by m ean s o f th e eq u atio n P = TP0 w here T is a m atrix to b e c a lc u  lated. W rite P = (afl'ji (th e p ro p a g a tio n co n stan t), Z = (a//3)I (the im pedance), C = 2 - i ^ j ^ a n d

( o ' e r ) w here V = Nr

M

Pah-. F u r th e r w rite / v r 'A v v o ,o w here N l = C ~ i dC /dx, a n d let E d e n o te th e u n it m atrix . I t is sh o w n th a t T = CXN 0{ E + S ( - ) ' I/„}C 0- 1, w here

70 = E, In+ \ = M I„(x)dx

•to

a n d Cxa n d C0d e n o te th e values o f Ca t th e po in ts .v a n d x = 0 respectively. T h e first term in Tis

r Z Zq co sh y , — sin h

\ — Zq 1 sin h y , cosh y )

a n d if Z ~ Z q th is gives th e u sual re su lt fo r a u niform

line. l. s. G.

512.831 : 537.314 : 621.392.22 = 4 1192 P ro p ag atio n on a n a rb itrary sym m etric polyphase line. Parodi, M ., and Raymond, F . C.R. Acad.

Sci., Paris, 220, 522-3 (A pril 9, 1945) In French.—

A fu rth e r ap p lic atio n o f th e m atrix calculus to p ro p a g atio n o n tran sm issio n lines. T h e line now co n sid ered consists o f a n y n u m b e r o f c o n d u cto rs a n d it is sh o w n th a t th e usu al q u a d rip o le th eo ry m ay be ex ten d ed to su ch a sym m etric line. l. s. g.

5 1 3 .8 1 3 :5 3 0 .1 2 1193

O n d istan t affine connection. Schrodinger, E.

Proc. R . Irish A cad., 50 A (N o. 9) 143-54 (M arch, 1945).—T h e recen t discovery, b y E in stein a n d Berg- m an n , o f a new fo rm o f geom etrical co n n ectio n o f a c o n tin u u m , th e d is ta n t affine co n n ec tio n , is studied, p articu la r a tte n tio n being p a id to th e reciprocal case.

N ecessary a n d sufficient c o n d itio n s fo r sym m etriza- tio n a n d skew -sym m etrization in a n a rb itra ry fram e

vol. x u x . —a .— 1946. M a y .

are deduced. T h e sym m etric a n d skew -sym m etric cases a re n o t m u tu ally exclusive. T h e m eaning o f the sym m etry p ro p e rty is discussed. l. s. g,

5 1 3 .8 1 3 :5 3 0 .1 2 1194

Infinitesim al affine connections w ith twofold E instcin- B crgm ann sym m etry. Mautner, F ., and Schro dinger, E. Proc. R. Irish A cad., 50 A (No. 13) 223-31 (July, 1945).— A c o n tin u a tio n o f prev io u s w o rk [A bstr. 1193 (1946)]. T w o m eth o d s a rc given fo r tran sferrin g th e E in stein -B erg m an n sym m etry c o n d itio n s fo r a d istan t co n n ectio n to a n infinitesim al co n n ectio n . A general expression is fo u n d fo r a n affinity w hich carries b o th a n o n -sin g u lar sym m etric ten s o r field a n d a skew te n s o r field in to them selves.

T h e c u rv atu re te n s o r o f this affinity is co m p u ted , an d a ten tativ e g en eralizatio n o f th e cosm ological field

e q u atio n s is given. l. s. g

517.512.2 : 612.813 = 393 see A bstr. 1429

517.63 : 621.396.64 : 621.3.01 = 4 1195 T he application o f the L aplace transform ation to electric circuits. Clavier, A . G . Rev. Gen. Elect., 51, 447-55 (O ct., 1942) In French.— [A b str. 1014 B (1946)].

517.942.932 1196

C om putation o f the solution o f M ath ieu ’s equation.

McLachlan, N . W . Phil. M ag., 36, 403-14 (June, 1945).—A m eth o d is given fo r solving th e e q u atio n

d 2y /d z 2 + (a — 2q cos 2z )y = 0

w here a a n d q are real p aram ete rs cap ab le o f an y value. Som e exam ples a re given. l. s. g.

518.5 1197

A new type o f differential analyser. Bush, V., and Caldwell, S. H . J. Franklin Inst., 240, 255-326 (O ct., 1945). Errata, 241 (M arch, 1946).— T h e new differential an aly ser is o f g re ater precision, scope a n d flexibility th a n earlier m achines. It c o n ta in s 18 in te g rato rs, b u t p rovision is m ad e fo r e x p an sio n to 30 in te g ra to rs if necessary. A ll in fo rm a tio n is given to th e m achine by m ea n s o f p u n ch ed p a p e r tapes, a n d a sim ila r tap e au to m atically sets the v ario u s g ear ra tio s req u ired , w hile a n o th e r p u ts in th e in itial co n d itio n s. G rap h ical results a re available fro m c u rv e-p lo ttin g o u tp u t u n its, b u t generally th e p rim e d a ta a re n u m erical tab u la tio n s o f th e re q u ire d fu n ctio n s. T h ese ta b u la tio n s are p rep ared o n a u to m a tic typew riters c o n tro lled fro m special c o u n te r u n its. T h e over-all m achiné o p e ratio n accuracy is 1 p a r t in 10 000. T h e m ech an ical an d circu it d etails o f th e new m ach in e a re fu lly discussed

a n d illu strated . l. s. g.

518.5 1198

A slide rule fo r the addition o f squares. Morrell, W . E . Science, 103, 113-14 (Jan. 25, 1946).

131 5

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519.21 523.165

5 1 9 .2 1 :5 1 9 .5 2 1199

T he probable num ber o f a g g reg a te s in random distributions o f points. Silberstein, L. Phil. M ag., 36, 319-36 {M ay, 1945).— A situ a tio n is c o n sid ered in w hich it p o in ts a re placed h a p h az ard ly u p o n a lin ea r segm ent, all p o sitio n s o f a p o in t o n th e segm ent being equally likely. A ¿-ag g reg ate consists o f ¿ p o in ts all c o n ta in ed w ith in a su b in terv al A o f th e segm ent.

T h e p ro b lem o f d eterm in in g th e p ro b a b ility o f any given n u m b er o f aggregates is n o t tra c ta b le fo r large n, b u t th e c alcu la tio n o f th e p ro b a b le n u m b er £?*(«) o f ¿-aggregates a m o n g an y n u m b er n o f p o in ts m ay be carried o u t. T h is is d o n e b o th fo r p o in ts o n a seg

m en t (one dim ension) a n d fo r p o in ts in a p lan e (tw o dim ensions). Q*(n) satisfies th e difference e q u atio n

QkO'

+ 1) = (1 -

Tik)Qk{>!) +

w here th e np. a re c ertain p ro b a b ility coefficients an d th is e q u atio n is solved fo r Qp{n). T h e case o f dense o r congested d istrib u tio n s (A„ ~ 1) is considered sep arately . Som e num erical exam ples a re given.

[Sec A b str. 1202 (1946)]. l. s. g.

519.214 1200

The accum ulation o f chance effects and the G aussian frequency distribution. Goddard, L. S. Phil. M ag., 36, 428-33 {June, 1945).— T h e integral.

w hich ap p ears in a previous p a p e r [A bstr. 75 (1945)], is e v alu ate d by c o n to u r in te g ratio n a n d a n asy m p to tic fo rm u la fo r it, fo r large n, is also o b tain e d . T h is is used to exam ine th e first few term s o f a n o th e r asy m p to tic fo rm u la a p p earin g in th e prev io u s p aper.

l. s. G.

519.283 : 620.113 1201

S ta tistica l m ethods in quality control. VITI. C ontrol charts fo r action on variables. IX . Acceptance sam pling.

Elect. Engng, N .Y ., 65, 23-4 {Jan.); 81-3 (Feb., 1946).

519.52 : 519.21 see A bstr. 1199

519.52 : 772.1 ' 1202

A ggregates in one- and tw o-dim ensional random distributions. (D cvelopability o f silver specks o f known dimensions and the size o f photographic sensitivity specks). Berg, W . F . Phil. M ag., 36, 337-46 {M ay,

1945).— A “ b u rst” o f ¿ ra n d o m events in a tim e series o f events is defined a n d th e frequency o f th e b u rsts a n d th e frequency o f ¿ aggregates [see A b str.

1199 (1946)] a re calculated. T h e fo rm u la e are ap p lied to previous w o rk o n th e develo p ab ility o f sm all specks o f silver. T h e p h o to g rap h ic ap p licatio n is th e m ain p u rp o se o f the p ap er. l. s. g.

A ST R O N O M Y . G EO D ESY 52

521.042 : 539.155.2 see A bstr. 1354

5 2 1 .8 :5 2 3 .8 4 1 .9 1203

A n outline o f the theory o f atm ospheric eclipses.

Kopal, Z. Proc. Am er. Phil. Soc., 89, 590-600 {D ec., 1945).— In close b in ary system s w here o n e co m p o n e n t (o r b o th ) m ay h av e a n a tm o sp h e re, a g ra d u al loss o f lig h t w ill p recede to ta lity d u rin g an atm o sp h eric eclipse, a n d if a re la tio n is established betw een loss o f lig h t a n d geom etrical a n d physical p ro p erties o f th e ob scu rin g a tm o sp h ere, it w o u ld be po ssib le to d ed u ce th e la tte r p ro p e rties fro m ob serv a

tio n s o f lum inosity d u rin g a n eclipse if th e g eom etry o f th e system is k n o w n . A ssum ing spherical sym m etry, e x p o n en tial a tte n u a tio n a n d c o n sta n t extinc

tio n coefficient, th e o p tical d e p th is sh o w n to d e p en d o n m odified Bessel fu n ctio n s o f th e se co n d kin d , fo r w hich a p p ro x im atio n s a re given. A n integral ex

pressin g th e in stan ta n eo u s lum in o sity o f th e secondary is given, b u t th e e v alu atio n is difficult except in special cases; th e ra te o f ch an g e o f lum in o sity w ith distance betw een th e c en tres o f th e sta rs is given by a n in te g ral to w hich close ap p ro x im atio n s a re fo u n d . A ssum ing a d e p th o f th e a tm o sp h eric eclipse n o t exceeding 1 o r 2 ten th s o f a m ag n itu d e, th e lum in o sity integral is ev alu ated ap p ro x im ately . T h e p ro c ed u re o f d eterm ining th e p ro p e rties o f th e ob scu rin g a tm o sp h ere fro m ob serv atio n s o f lum inosity changes d u rin g a n eclipse is described, assum ing th a t th e eclipsed co m p o n en t m ay be considered a s a lum inous p o in t. W h en th is a ssu m p tio n is n o t w a rran te d , a m eth o d o f trial a n d e rro r seem s to b e th e o n ly

feasible one. j. a. w.

522.2 1204

T he W arn er and Sw asey O bservatory o f the C ase School o f Applied Science. Nassau, J. J. Publ. Astr.

Soc. P a c if, 57, 281-6 {D ec., 1945).—A descrip tio n o f a 24 in S chm idt telescope com pleted in 1941. T h e m ain m irro r is 36 in. in d iam eter, focal len g th 7 ft, m ad e o f pyrex, c o ated w ith ch ro m iu m -alu m in iu m . T h e co rrectin g lens h a s a clear a p e rtu re o f 24 in a n d in c o m b in atio n w ith th e m ain m irro r gives a field o f 5° o n a circu lar curved p late in. in d iam eter.

V isual o b serv atio n by th e in se rtio n o f a 7 in flat is also possible. A n objective p rism o f 4° angle an d 24 in. in d iam eter p erm its th e p h o to g rap h y o f sp ectra.

A 10 m in exposure using E astm an high-speed plates gives a lim iting m ag n itu d e o f 18-5, w hile a 20 m in exposure th ro u g h a filter reaches 16*8 fo r re d m ag

nitu d es. F o r sp ectra, a 15 m in e x p o su re w ith w idened im ages reaches a b o u t 12-5. T h e telescope is at p re sen t p h o to g rap h in g te n reg io n s in th e M ilky W ay betw een galactic lon g itu d es 0°-200° in blue a n d red lig h t a n d w ith th e objective p rism , en ab lin g th e a b so rp tio n a n d th e space d ensities o f e ach region to be

d eterm in ed . e. g. m.

522.21 : 535.313 see A bstr. 1282

523.165 : 621.396.821 1205

C osm ic rad iatio n s a t 5 m etres w avelength. Hey, J. S., Phillips, J. W ., and Parsons, S. J . Nature, Lond., 157, 296-7 {M arch 9, 1946).— P erio d ic o b serv a

tio n s w ere m ad e o v er 9 days w ith a receiving aerial h aving a b eam w id th o f ± 6 ° in elev atio n a n d ± 1 5 ° in bearing. T h e in ten sity betw een d eclinations —30“

a n d + 6 0 ° is sh o w n o n a c o n to u r c h a rt; th e m ain source ap p ears to be clo se to th e d irectio n o f the galactic c en tre w ith a seco n d ary source in Cygnus.

T h e in ten sity in th e reg io n o f th e p e a k w as deduced to b e 13-2 x 1 0 -2 lA rA co H 7 m 2 (A v = b an d width in c/s, A tu = solid an g le su b ten d ed in steradians).

132

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523.38 523.852.3

523.38 1206

Eclipse predictions. Campbell, J. W ., andJ o h n s , H . E. J.R . A str. Soc. Can., 39, 347-54 (N ov., 1945).—

T his p a p e r explains a g raphical m eth o d o f finding the circu m stan ces o f a n eclipse fo r an y locality, devised by P ro f. D u p u is n early 60 y ears ago. T h e lo n g B essellian m eth o d is necessary fo r h ig h accuracy, b u t this m eth o d is sufficient if th e g re atest accuracy is n o t req u ired . T h e fo rm h a s been m ad e m o re c o n v en ien t fo r use on p resen t-d ay sta n d ard s. T h e e rro rs o f th e m eth o d are c alcu lated a n d a co m p a riso n w ith the co rrect values

is m ade. e. o. m.

523.5 : 551.594.6 see A bstr. 1417

523.7 = 4 1207

R esearches on so lar problem s. Grenat, H . Bull.

A str., Paris, 12 (N o. 3) 99-145 (1940) In French.—

A m o dification in e lectro static law s a t larg e d istances is p ro p o sed . A n e lectro static th eo ry o f th e co ro n a, p ro m in en ces, cosm ic ray s, a u ro ra e , ste lla r heat, n e b u la r red -sh ift, etc., is th e n developed. S tars are su p p o sed h e ated fro m w ith o u t, n o t fro m w ithin.

t. a. c.

523.746 : 550.384 see A bstr. 1400

523.755 = 3 1208

The behaviour o f hydrogen in the corona o f the sun.

W a ld m e ie r, M . Experientia, 1, 118-19 (July 15, 1945) In German.

523.82 1209

The absolute m agnitudes o f the sta rs o f type K0.

Martin, E. G . O bservatory, 66, 82-7 (June, 1945).—

T h is a rticle co llects o b serv atio n al evidence o f the frequency d istrib u tio n o f sta rs o f ty p e K 0, show ing th e lim it to w h ich th e w o rk is co m p lete. T h e p ro b a b le e rro rs in th e d ed u ctio n o f th e ab so lu te m ag n itu d es by tw o m eth o d s a re q u o te d a n d th e difficulties d u e to selectio n effect a re stressed. A t p re sen t m aterial to d eterm in e th e frequency d istrib u tio n is insufficient especially in th e cen tre o f th e curve w here, in theory, a m inim um exists betw een g ian t a n d d w a rf stars.

A list o f 35 sta rs w ith w ell-determ ined a b so lu te m ag nitu d es is given to d e m o n stra te th a t sta rs can be fo u n d in th e re g io n o f th e m inim um . A n ap p eal is m ad e fo r th e o b serv atio n o f su itab le stars. e. g. m.

523.821.3 1210

R ed m agnitudes o f the north polar sequence stars.

Nassau, J . J., and Burger, V. Astrophys. J., 103, 25-34 (Jan., 1946).—T o establish s ta n d a rd sequences o f red m ag n itu d es th e values fo r 51 N P S sta rs have b een d eterm in ed o n p h o to g rap h s ta k e n w ith the B u rrell S chm idt telescope [see A b str. 1204 (1946)].

A co m b in a tio n o f n e u tra l filter a n d c o lo u r filter w ith a n effective w avelength o f A6200 w as used. T he average p ro b a b le e rro r ± - 0 3 to ± ’07 m ag. varies acco rd in g to th e brig h tn ess o f th e stars. A co m p a ris o n w ith H a rv a rd show s n o over-all scale differences w hile the z ero -p o in t difference is -06 m ag.

T h e m ag n itu d e range is fro m m ag n itu d e 6 to 15.

523.841.1 1211

A recurrent nova. Stratton, F . J . M ., and Butler, H . E. Nature, Lond., 157, 270 (M arch 2, 1946)..

523.841.2 : 523.87 see A bstr. 1218, 1219

523.841.9 1212

T he spectroscopic orbit o f the eclipsing variable B D + 55 “ 616. Deutsch, A . J . A strophys. J., 102, 496-9 (N ov., 1945).— R a d ia l velocities fo r H , H e I a n d C a II(K ) fro m 49 sp ectro g ram s ta k e n a t M c D o n a ld a n d Y erkes o b servatories a re listed. A system atic difference, ap p aren tly real, is fo u n d betw een velocity curves fro m H a n d H e I, except n e a r th e ascending n o d e, a n d ro ta tio n a l d istu rb an ce is in d icated d u rin g th e p rin cip al eclipse. O rb ital elem ents are given fo r b o th curves, th e p e rio d in eac h case being 2 -7278 days.

T h e K lin e ap p ears to be o f in terstellar origin, d. l. e. 523.841.9 : 521.8 see A bstr. 1203

523.841.9 : 523.87 1213

G aseous rin g s in close binary system s. Struve, O.

Observatory, 66, 208-15 (Feb., 1946).—T h e existence o f ten u o u s gaseous rin g s su rro u n d in g th e sm aller, h o tte r c o m p o n en ts o f som e eclipsing b in aries is show n by th e a p p earan ce a n d changes o f b rig h t h y d ro g e n lines n e a r tim e o f eclipse. T h e sizes o f th e rings a rc sim ilar to th o se o f th e larg er (eclipsing) sta rs, a n d th eir ro ta tio n a l velocities a re high. E leven k n o w n system s o f th is k in d are discussed a n d c o m p a red w ith B e sta rs w hich, th o u g h sim ilarly su rro u n d e d , sh o w co n sid erab le differences in th e ir sp ectra. T h eo retical difficulties o f in te rp re ta tio n a re briefly discussed.

D . l. E.

523.842.3 1214

T he W o lf-R ay et spectroscopic binary H D 168206.

Hiltner, W . A . A strophys. J., 102, 492-5 (N ov., 1945).—T h is s ta r is o f im p o rta n ce since its b in ary n a tu re offers a n o p p o rtu n ity fo r a c o m p lete in vestiga

tio n o f a W o lf-R ay et s ta r. T h e W o lf-R a y et co m p o n e n t is o f class W C 7 + ; th e p e rio d , 29-675 days.

T h ree em issio n b an d s, H e I I 4 686, C I I I - I V 4 652, C I V 44 4 1 a n d H g in a b so rp tio n w ere m easured fo r ra d ia l velocity. T h e em ission gives a sem i

am p litu d e o f 165 k m /sec. H y d ro g e n a b so rp tio n varies oppo sitely w ith a sem i-am plitude o f 55 km /sec, suggesting a ttrib u tio n to th e early ty p e co m p an io n . M in im u m m asses a re M \y n sin2 i = 8 - 2 0 a n d

A /g s in 2 i —2 4 - 8 0 - d . s. e.

523.851 1215

R egression lines and the functional relation. I I . C h a r- lic r’s form ulae for a moving cluster. Seares, F . H . Astrophys. J., 102, 366-76 (N ov., 1945).—A c o n tin u a  tio n o f a previous p ap er. T h e fo rm u lae fo r th e fu n ctio n al coefficient o f a lin e a r re la tio n d eriv ed in th e fo rm er p a p e r a re ex ten d ed to th e so lu tio n o f C h a rlie r’s e q u a tio n fo r th e convergence o f th e m o tio n o f a m oving s ta r cluster. A p p lica tio n to th e T au ru s c lu ster show s th a t neglect o f th e reg ressio n e rro r lead s to a d istan ce a b o u t 7% to o sm all. T h e so lu tio n given by M e rrim an a n d by H e rtzsp ru n g fo r a lin e a r e q u atio n involving c o n stan t w eights a re sh o w n to be a special case o f th e general so lu tio n . [See A b s tr. 2107 (1945)].

v. c. A. F.

523.852.3 : 530.12 1216

T he spiral form o f e x tra -g ala ctic nebulae. Walker, A . G . Observatory, 66, 215-17 (Feb., 1946).— Since len g th scales in k in em a tical relativ ity a re defined in term s o f tim e-scales, th e m ath em atic al e q u a tio n o f a n o rb it m ay be a spiral if o n e tim e-scale is u sed a n d a closed curve i f a n o th e r is em ployed. O bserved o rb its a re closed a cco rd in g to M iln e’s th eo ry o f g rav itatio n .

vol. XLix.—a.—1946. May. 133

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523.854.12 530.12

A n e b u la r a rm is a stream o f pa rticles m oving in closed o rb its (on th e dynam ical tim e-scale). B ut s tre a m lines d o n o t tran s fo rm in to stre am lines w hen th e tim e-scale is changed, so th a t it is n o t possible to assum e th a t, usin g th e cosm ical tim e-scale, th e spiral is b o th th e fo rm tak e n by a stream o f particles and the o rb it o f each ind iv id u al particle. g. c. mcv.

523.854.12 1217

N atu re o f absorbing m aterial w ithin the galaxy and its influence on estim ates o f g alactic dimensions.

Beals, C . S. J.R . Astr. Soc. Can., 39, 329-74 {N ov., 1945).— U sing a b so lu te m ag n itu d es derived fro m line sp ectra a n d C ep h eid variability, a n d stellar distances derived fro m studies o f op en cluster d iam eters and galactic ro ta tio n , a n average coefficient o f a b so rp tio n o f 0 -8 m ag. p e r lOOOps is ob tain ed . C o u n ts o f extra-galactic n eb u lae give a sm aller value o f 0 • 65 m ag.

T h e a b so rb in g lay er is a b o u t 1 000 ps th ick a n d the co rrected lin e a r m a jo r d iam eter o f th e G a lax y is a b o u t 33 000 ps. T h e ab so rb in g m ateria l is irregularly d istrib u te d a n d its a b so rp tio n m u st fo r th e m o st p a rt be d u e to solid p articles o f d iam eter 10- 5 cm . In te r

ste lla r gases also occur, th e ato m s o f N a , K , C a, Ti, F e, H , O , N h aving been identified in v arious stales o f io n izatio n . M olecules o f C H , C N a n d C H + h av e a ls o been discovered. U nidentified diffuse lines a re possibly d u e to th e solid pa rticle s. T h e density o f the m aterial is p ro b a b ly o f th e o rd e r o f 6 x 10- 2 4 g r/cm 3 a n d th e m ain co n trib u tio n is d u e to th e gases ra th e r th a n to th e solid p articles. T h e to ta l m ass o f th e ab so rb in g m aterial m ay well be e q u al to o r greater th a n th a t o f th e c o m b in ed m asses o f th e stars.

G . C. McV.

523.87 : 523.841.2 1218

M easurem ents in the spectrum o f R bydrae. Merrill, P . W . Astrophys. J., 103, 6-12 {Jan., 1946).

523.87 : 523.841.2 1219

T he period o f the spectrum variable i Cassiopeiae.

Deutsch, A . J. Astrophys. J., 103, 99-101 {Jan., 1946).

523.87 : 523.841.9 see A bstr. 1213

523.87 : 539.153 1220

T he m otion o f an electron in the H a rtre e field o f a hydrogen atom. Chandrasekhar, S., and Breen. F . H . Astrophys. J., 103, 41-70 {Jan., 1946).—T h e ra d ia l w ave fu n ctio n s Xq a n d Yi (o f u n it a m p litu d e at infinity) o f a n electro n m o v in g in th e static field o f a gro u n d -state h y d ro g en a to m w ith a n g u la r m o m e n ta o f 0 a n d 1 B o h r u n its respectively a re ta b u la te d fo r k in etic energies o f astro p h y sica l interest. A uxiliary qu an tities su ch as p h a se shifts a re also tab u lated .

D . l . E.

523.877 1221

Curve o f grow th fo r 5 C anis M ajoris. Steel, H . R . Astrophys. J., 102, 429-32 {N ov., 1945).— Inten sities o f 62 F e I lines m easu red by O ’K eefe a t Y erkes, w ith M enzel a n d G o ld b e rg ’s so la r v alues o f log Xq, a re used. T h e ex citatio n tem p e ra tu re (4 400°) agrees w ith o th e r F -ty p e su p erg ian ts, b u t th e tu rb u le n t velocity (5 • 1 km /sec) is hig h . V isual in te n sity estim ates o f lines o rig in atin g in n o rm a l a n d m cta stab le levels, co m p ared w ith values in sta rs w ith n o a p p reciab le d ilu tio n , suggest th e p ro b ab ility th a t n o d ilu tio n effects a rc

presen t. d. l. e.

523.877 : 539.172.3 see A bstr. 1362

PH Y SIC S 53

53(43) 1222

W ar physics in G erm any. G o u d s m i t , S. A . Rev.

Sci. Instruin., 17, 4 9-52 {Jan., 1946).

53.081.5 : 537 : 538 = 4 1223

Sim plification o f the dimensional form ulae for electric and m agnetic quantities. Tarbouriech, M . C.R.

Acad. Sci., Paris, 221, 745-7 {Dec. 12, 1945) In French.

—T h e usu al f o u r basic sym bols a re L , M , T an d P, th e p erm eability. In term s o f these th e fo rm u lae fo r electric a n d m agnetic q u an titie s h av e fra c tio n a l ex

p o n en ts. A n im p ro v ed system is o b tain e d b y taking as th e fo u r basic sym bols, R , /, T a n d L, w here R is resistance a n d I is c u rre n t in tensity. T h e n a ll q u a n  tities, in cluding p u rely m ech an ical q u a n titie s, have form ulae w hich possess in te g ral indices, e.g. m ass is R I2T ^ L ~ 2 a n d p erm eability is R T L ~ l . T h e fu n d a  m en tal u n its in this system a re th e o h m , th e am père, th e second a n d th e m etre a n d it is referred to as th e O .A .S .M . system . A list o f a d v an tag e s o f the O .A .S .M . system o v er o th e r system s is given, l. s. g.

F U N D A M E N T A L S 530.1 530.12 : 513.813 see Abstr. 1193, 1194 530.12 : 523.852.3 see A bstr. 1216

5 3 0 .1 2 : 531.18 1224

A generalization o f the relativistic theory o f g rav ita

tion. Einstein, A . Arm. M ath., Princeton, 46, 578-84 {O ct., 1945).— A n a tte m p t is m ad e to establish a

unified field th eo ry , sta rtin g w ith the g ro u p o f real co n tin u o u s co -o rd in ate tran sfo rm a tio n s. T h e th eo ry is unified in th e sense th a t n e ith e r th e field e q u atio n s n o r th e H a m ilto n ia n fu n c tio n can b e expressed as th e sum o f several in v arian t p a rts , b u t a re form ally unified entities. A n infinitesim al p arallel tran s la tio n is in tro d uced a n d a n expression is fo u n d fo r th e c u rv atu re ten so r. T h e H a m ilto n ia n den sity fu n ctio n is c o n stru c te d a n d used to derive th e field e q u atio n s. T h e physical significance o f th ese e q u atio n s will d ep en d u p o n th e c o n stru ctio n o f exact solu tio n s. l. s. G.

530.12 : 531.18 : 535.13 1225

D erivation o f th e L orentz transform ations. Iv e s , H . E. Phil. M ag., 36, 392-403 {June, 1945).— It is sh o w n th a t th e tran s fo rm a tio n s m ay b e derived by im posing th e law s o f c o n serv atio n o f energy a n d m o m en tu m o n ra d ia tio n processes as developed by M axw ell’s m eth o d s. A stu d y is m a d e o f th e im p act o f ra d ia tio n u p o n a reflecting p article initially a t rest.

T h e energy a n d m o m en tu m o f th e ra d ia tio n a re o b tain ed from th e wave th eo ry , a n d th ese qu an tities fo r th e p article are o b tain e d by th e c o n d itio n o f c o n serv atio n . A n a p p a re n t discrepancy arises a n d this necessitates th e in tro d u c tio n o f a m ass varying w ith the velocity. T h e sam e im p ac t is considered w ith the system in u n ifo rm m o tio n a n d th is dem ands th a t the in terv als o fle n g th a n d tim e a lso v ary w ith th e velocity.

E xact expressions fo r th ese v ariatio n s a re given and th ese lead to th e L o ren tz tran sfo rm atio n s. L. s. g.

134

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530.12 530.162

5 3 0 .1 2 :5 3 1 .1 8 = 4 1226

C ovariant definition o f force. C o s ta d e B e a u r e g a r d , O . C.R. Acad. Sci., Paris, 221, 743-5 (Dec. 12, 1945) In F rench— T h e u su al dynam ical equatio n s,

Fdl — d(nw ), Fdr = d W

o f a p o in t m ass m w hose positio n vector is r, are replaced b y th e set

(K x v -f S ) d t — d(nw ), If d r — d W w here K is a n a rb itrary vector d ep en d in g o n r a n d If (th e coforce) is defined by

K x v + j f = F

T h e seco n d se t o f e q u atio n s is relativistically co- v a ria n t b u t th e first se t is n o t. T h e in tro d u c tio n o f th e co fo rce is u seful in v ario u s p ro b lem s o f relativistic dynam ics. A n exam ple is given. i.. s. g.

530.14 = 4 1227

O n the various types o f elem entary particles.

M u r a r d , R . C.R. Acad. Sci., Paris, 221, 607-9 (Nov. 19, 1945) In French.— T h e “ fu n d am e n tal rin g "

o f o p e rato rs o f a- p a rticle is discussed, a n d tw o p o stu lates reg ard in g th ese o p e rato rs a re in tro d u ced in o rd e r to elim in ate th e n o n-physical so lu tio n s o f th e w ave e q u atio n . T h e th eo ry o f th e o p e rato rs involves a stu d y o f v ario u s rep rese n tatio n s o f th e com plete L o rcn tz g ro u p a n d it is concluded th a t all elem entary particles h av e th e sp in i , so th a t particles o f sp in 1 (p h o to n , m eson) o r sp in 2 (graviton) c an n o t b e co n

sidered as elem entary. l. s. g.

530.14 = 4 1228

S pinor and higher representations o f the L orentz group and the theory o f particles o f m ultiple m ass and spin. K w a l , B. C .R. Acad. Sci., Paris, 221, 658-9 (Nov. 26, 1945) In French.— L et D ( i , k ) be th e rep re se n tatio n involving a g ro u p o f k sp in o rs. W hen k — 1 th e rep resen tatio n gives rise to th e wave e q u atio n o f a p article o f sp in a n d zero rest-m ass.

W h en k — 2 (D irac’s case) w ave e q u atio n s are o b tain e d w hich d escribe a p article, o f spin i , w hich ad m its 2 p ro p e r values fo r its m ass. G en erally the re p re se n tatio n D ( \ , k) perm its a definition o f a particle, o f sp in t/ 2, w ith k different m ass values, one o f w hich is zero w h en k is o d d . T h e d irec t p ro d u ct,

£>(}, k ) x £>(}, k ) X . . . x D ( i, k ), w here th ere are 2 / facto rs, describes a p article o f sp in 2 j, w ith 2jk p ro p e r values fo r its m ass; b u t th e irreducible rep re se n tatio n D ( ] ,j, . . .,;') w here th ere a re k factors, h as ju s t k p ro p e r values, e.g. th e v e cto r m eson, defined by 73(1, 1) h as tw o p ro p e r m ass values. T h e w ave eq u atio n s fo r th is p article a re w ritten dow n.

L. S. G.

530.145 _ _ 1229

O n the m ethod o f second quantization. B e c k e r , R ., a n d L e ib frie d , G . Phys. R ev., 69, 34 (Jan. 1 and 15, 1946).

530.145 = 4 1230

P ro p erties o f som e types o f p articles. Application to the nucleon. M u r a r d , R . C.R. Acad. Sci., Paris, 219, 577-9 (Dec. 4, 1944) In French.—T h e follow ing results a re an n o u n ced , th e n u m b ers in b rack ets d en o tin g the p ro p e r values o f th e o p e rato rs.

(I) P articles o f sp in (£, <)) a n d m ass ( —m, m ) satisfy

th e law s o f a D ira c particle; (2) th ere exist n o particles o f sp in ( —i , 0, i ) a n d m ass ( ~ m , m); (3) fo r every p article o f sp in ( —1, 0, 1) a n d m ass ( —m, m) th e o p e rato rs o f th e fu n d am en tal rin g satisfy th e sam e algebraic relatio n s as does a D ira c pa rticle, w ith the exception o f th e spin o p e rato rs; (4) every p article o f spin ( —i , ■}) is a D ira c p article w ith several possible m ass states. A n exam ple o f th e latter is th e nucleon.

T h e fu n d am en tal rin g o f o p e rato rs fo r th is p a rticle is discussed. A base fo r th e rin g consists o f 1, xx , xy , r z w here t is th e iso to p ic spin. F o r a system c o n ta in in g o n ly nu cleo n s th e to ta l iso to p ic spin (o r to ta l m ass) is conserved. U sin g th is principle a n expression is given fo r th e in te rac tio n o p e ra to r o f tw o nucleons.

L. S. G.

530.145 = 4 1231

Behaviour o f particles in an ex terio r field: application to the nucleon. M u r a r d , R . C .R. A cad. Sci., Paris, 221, 547-9 (Nov. 5, 1945) In French.—T h e ham il

to n ia n o f a p article in a n ex terio r field m ay be w ritten H — H 0 + A w here Ho is th e h am ilto n ian o f th e free p article a n d A is a n o p e ra to r satisfying c ertain in  v arian ce co n d itio n s. T h e ex tern al field is defined by given q u a n titie s Uo, U/, Ut J . . . b ehaving lik e the c o m p o n e n ts o f ten so rs o f o rd ers 0, 1, 2, . . . T h en th e o p e ra to r A is expressible in th e fo rm

A — SIqUq + 'EtSijUj + 1jSljjU /j + . . . w here S2q, &t< &ij> • • ■ a re o p e rato rs o f th e fu n d a  m en tal ring. T hese a re tw o o f th e th ree given sufficient co n d itio n s fo r d eterm ining A . T h e results a re ap p lied to th e D ira c p article o f sp in j- a n d to th e n ucleon. In th e la tte r case previous w o rk [A bstr.

1230 (1946)] is co n tin u ed . l . s . o .

530.145.1 ; 537.13 1232

O n the production o f mesons by proton-proton collisions. I I . H e i t l e r , W . Proc. R . Irish Acad., 50 A (No. 10) 155-65 (M ay, 1945).—T h e calculations o f p a p e r I [A bstr. 213 (1944)] w ere c arried o u t o n the basis o f th e q u a n tu m th eo ry o f ra d ia tio n d am ping [A bstr. 2558 (1942)]. T h e results, a n d th e ir ap p lica

tio n s to cosm ic ra d ia tio n [A bstr. 2834 (1943)], a re now m odified by using th e W eizsäcker-W illiam s ap p ro x im ate m eth o d , g re ater accuracy in th e m a th e m atical analysis being o b tain ed . A g ra p h is given o f th e energy sp ectru m o f p seu d o scalar m eso n s p ro d u ced by collisions w ith a nucleon, h aving E = 5M , w here E is th e energy o f th e nucleon a n d M i s its re st energy.

[See also A b str. 809 (1946)]. l . s . g . 530.145.6 : 539.152.1 see A bstr. 1349

530.145.63 : 539.185 = 3 1233

O n spin-path coupling o f tw o nucleons in meson theory. F i e r z , M . Helv. Phys. A cta, 18 (N o. 2) 158-66 (1945) In German.—T h e elem ents o f th e m atrix o f te n s o r fo rces w h ich o c cu r in th e sym m etrical m eson th eo ry w ith s tro n g co u p lin g a re calcu lated by a m e th o d d eveloped in e arlie r p a p ers [A bstr. 983, 985, 986 (1946)]. E xplicit expressions a re given in th e case o f th e d e u te ro n g ro u n d state s a n d th e p o ssibility o f a n ap p ro x im ate trea tm e n t o f th e asso ciated eigenvalue p ro b lem is discussed. T h e m atrix elem ents n ecessary in th e calcu latio n o f th e q u a d ru p o le m o m en t o f th e d e u te ro n are also given. l . s . G.

530.162 : 537.312.62 : 536.48 see A bstr. 1309 135

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531.18 532.517.3

M E C H A N IC S O F S O L ID S 531 531.18 : 530.12 sec A bstr. 1224, 1226 531.18 : 535.13 : 530.12 see A bstr. 1225

531.224.3 ' 1234

T he effective w idth o f cylinders, periodically stiffened by circu lar rings. Biezeno, C. B., and Koch, J. J.

Proc. Ned. A kad. W et., 4 8 ,1 4 7 -6 5 (1945).—N u m erical d a ta are given fo r sim plifying th e c o m p u ta tio n o f the g reatest tan g en tial stress w hich m ay o ccu r in a th in - w alled cylinder stiffened by rin g s placed a t a c o n stan t in terv al alo n g th e axis. T h e lo a d system o f th e cylinder is p erio d ic in th e axial d irec tio n w ith p erio d eq u al to th a t o f th e rings. F o r th e cylinder w ith o u t rings th ere exists a n infinity o f ch aracteristic lo ad system s w hich p ro d u ce only tan g en tial displacem ents. T h e m ath e m atical analysis o f th ese lo ad s is c arried out. T ables o f th e effective w id th are given fo r v ario u s values o f th e p aram eters w hich o ccu r in th e p roblem . L. s. g.

531.259 : 536.41 1235

O n therm al stresses in circular cylinders. Jaeger, J. C. Phil. M ag., 3 6 ,4 1 8 -2 8 (June, 1945).— N um erical so lu tio n s, su itab le fo r p ractical use, a re given o f th e pro b lem o f a solid cylinder, in itially a t co n stan t tem p eratu re, a n d la te r w ith its surface m ain tain ed at zero tem p e ra tu re o r ra d ia tio n a t its surface in to a m ed iu m a t zero tem p eratu re. F o rm u lae fo r th e stresses are given w hich a re o f value w h en th e usual expressions (involving B essel functions) converge very slow ly. T h e pro b lem is also solved w hen th e cylinder is hollow . T h e case o f a periodic surface tem p e ratu re

is exam ined briefly. l. s. g.

531.261 = 4 1236

O n a variational principle o f G auss in potential theory.

M o n n a , A . F. Proc. N ed. A kad. W et., 44 (No. 1) 50- 61 (1941); 49 (N o. 1) 54-62 (1946) In French.— G iven a d istrib u tio n o f positiv e m ass o f p o ten tial V o n an o p en set Q o f b o u n d e d fro n tie r £ , w i t h F = £2 + £ , U th e p o ten tial o f a d istrib u tio n p(e) o f positive m ass o n £ su ch th a t U < V everyw here a n d U = V o n CF, /«(e) th e d istrib u tio n o b tain e d by th e sw eeping o u t process, ]i(e) th a t o b tain e d by th e process o f ex- trem izatio n , th e n Pot/« > t / > P o t¡5. T h e ev alu atio n o f p(e) its e lf in term s o f /«(e) a n d /«(e) by m eans o f Stieltjes’ in teg rals is discussed. T h e d em o n stra tio n ap p ears to b e incom plete. T h e second th eo re m is th a t th e integral J (U — 2 V)dp o f su c h d istrib u tio n s p(e) is a m axim um w hen p(e) is identical w ith /«(e).

A n a p p lic atio n o f th is th eo re m a n d the g eneralization o f these th eo rem s to n o n -N e w to n ian p o ten tials is considered. In th e seco n d p a p e r a sim p ler d e m o n stra tio n o f th e second th eo rem is given. v. c . a . f . 531.36 : 534.015 = 4 see Abstr. 1251

M E C H A N IC A L M E A S U R E M E N T S 531.7 531.717.7 : 535.313.08 see A bstr. 1283

531.787.4 : 532.66 see A bstr. 1245

5 3 1 .7 8 7 .9 :6 2 1 .3 1 6 .5 1237

E lectrom agnetic pressure recorder. B a x t e r , H . H . Electrician, 135, 691-3 (Dec. 21, 1945).— [A bstr.

1095 B (1946)].

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

532.5 1238

T he K arm an-T sien pressure-volum c relation in the two-dimensional supersonic flow o f compressible fluids.

C o b u r n , N . Quart. A ppl. M ath., 3, 106-16 (July, 1945).— K d rm d n a n d T sien treated th e su b so n ic flow by rep lacin g th e pressure-volum e curve b y th e tan g en t line d ra w n a t a n a rb itra ry p o in t o f th e curve. I t is sh o w n th a t th is m eth o d m ay b e used in th e supersonic ra n g e w hen th e flow is fairly unifo rm , a n d th en th e ch aracteristics fo rm a T schebyschcff n et. I f the d iag o n al curves o f th e n e t o f ch aracteristics a re draw n so as to c o rre sp o n d to eq u id ista n t values o f th e a rc len g th p a ram ete r alo n g th e ch aracteristics, th e n these d iag o n al curves w ill b e th e fam ilies o f e q u ip o te n tials a n d stre am lines. T h e general rep re se n tatio n o f the stream lines d ep en d s u p o n tw o real a rb itra ry func

tio n s w hich a re eq u al i f o n e stre am line coincides w ith th e .v-axis. T h e velocity a n d den sity d ep en d only u p o n th e an g le betw een th e ch aracteristics a n d th e M ach n u m b e r o f th e flow. l. s. g.

532.517.3 1239

O n the stability o f two-dim ensional parallel flows.

T. G eneral theory. L in , C. C. Quart. Appl. M ath., 3, 117-42 (July, 1945).—A histo rical survey is m ad e o f th e existing th eo ries o f th e tra n sitio n fro m steady to tu rb u le n t flo w a n d a valu ab le b ib lio g rap h y is given.

T h e p ro b lem o f stab ility is fo rm u la ted m ath em atically a n d th e sta b ility e q u a tio n o f O rr a n d S om m erfeld is solved by m eans o f (1) convergent series, (2) asym p

to tic series. A nalytical p ro p e rties o f th e so lu tio n s are o b tain ed . B o u n d ary v alu e p ro b lem s discussed include (a) flow betw een so lid w alls in relative m o tio n , (b) sym m etrical flow betw een so lid w alls a t rest, an d (c) flow of the boundary-layer type. l. s. g.

532.517.3 1240

O n the stab ility o f tw o-dimensional parallel flows.

II . S tab ility in an inviscid fluid. L in , C . C . Quart.

Appl. M ath., 3, 218-34 (O ct., 1945).— [See A b str. 865 (1945)]. A critical survey o f th e w o rk o f R ayleigh a n d T o llm ien is m ad e a n d th e ir n ecessary a n d sufficient co n d itio n s fo r th e existence o f a d istu rb an ce are sum m arized. T o llm ien ’s re su lt fo r th e existence o f u n stab le m odes o f oscillatio n is p ro v ed rigorously a n d extended. In stab ility in a n inviscid fluid is in te rp rete d physically by considering th e d istrib u tio n o f vorticity. T h e m o tio n is sta b le w h en th e g rad ien t o f th e vo rticity does n o t vanish. A n explicit fo rm u la is derived, in tw o different w ays, fo r th e acceleration o f vortices in a n o n -u n ifo rm field o f v orticity. T h e first is a kinem atical m eth o d , usin g vo rticity theorem s.

In th e second, pressu re forces c o rre late d w ith vorticity flu ctu atio n s are considered. l. s. g.

532.517.3 1241

O n the stab ility o f tw o-dimensional parallel flows.

n i. S tab ility in a viscous fluid. - L in , C. C. Quart.

Appl. M ath., 3, 277-301 (Jan., 1946).—-The w o rk o f th e tw o prev io u s p a rts is e x ten d ed to a viscous fluid.

H eisen b erg ’s criterio n fo r in stab ility is given in a slightly im proved fo rm a n d a stu d y is m ad e o f th e g en eral ch aracteristics o f th e curve o f n eu tral stability.

T h e discussion is th e n restricted to th e tw o types:

(a) th e B lasius case (a b o u n d ary -la y er profile), (

1

b) th e p lan e Poiseuille m o tio n (sym m etrical profile);

T h e sta b ility ch aracteristics a re studied a n d the 136

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532.583.5 534.213.4

n u m erical resu lts o b tain e d are c o m p a red w ith experi

m en tal resu lts. T h e physical significance is discussed a n d a few re m a rk s a re m ad e co n cern in g th e tran sitio n

to tu rb u len ce. l . s. o .

532.583.5 = 3 1242

G liding [on w ater] o f a flat-[sided] keel-shaped slab.

S e d o w , L . I., a n d W ła d im ir ó w , A . N . C .R . Acad.

Sci., U R S S, 33 (N o. 2) 116-19 (1941) In German.—

A b rie f m ath em atical discussion; th e resu lts are illu stra te d by ex p erim en tal d a ta . j. s. G. t .

532.612.4 1243

O n the volumes o f m ercury m enisci and the surface tension o f m ercury deduced from them . K is te m a k e r, J.

Comm. K . Onnes L ab., Leiden (N o. 268c). Physica, 's Grav., 11, 270-6 (D ec., 1945).— By m ea n s o f X -ray sh a d o w g ra p h s d e te rm in a tio n s o f th e volu m es o f m ercu ry w ere m ad e in a tu b e o f ra d iu s 14-738 m m . A fo rm u la fo r th e volum es o f th ese m enisci is given f o r ra d ii o f 3-15 m m . W ith th e a id o f B laisdell’s tables fo r th e volum es o f m ercu ry m enisci [see A b str.

978 (1941)] th e su rface ten sio n is calcu lated to be 430 ± 5 d ynes/cm a t ap p ro x im ately 18°c.

532.63 1244

L iquid rise in a capillary tube. B r i t t i n , W . E.

J. A ppl. Phys., 17, 37-44 (Jan., 1946).— A th e o ry o f th e d ynam ics o f cap illary rise is d eveloped b y m ak in g c ertain a ssu m p tio n s as to th e n a tu re o f th e m o tio n o f th e liq u id in th e tu b e. T h e m o s t im p o rta n t a ssu m p tio n s a re th a t th e sam e fo rces a c t o n th e liq u id w h en it is in a n accelerated sta te o f m o tio n as w h en it is in a ste ad y state, th a t th e su rface ten sio n is c o n stan t, th a t th e a n g le o f c o n ta ct betw een th e m eniscus o f th e liq u id a n d th e tu b e w all is c o n stan t, a n d th a t th e w ettin g o f th e tu b e is n o t a ra te - d eterm in in g fa c to r o f th e m o tio n . T h is th eo ry leads to a se c o n d -o rd e r n o n -lin e ar differential e q u atio n , th e so lu tio n o f w hich re p re se n ts th e m o tio n o f th e 1 ¡quid in th e tube. A fo rm al so lu tio n o f th e differential e q u a tio n is o b tain e d in th e fo rm o f a d o u b le D irich let series. A p p ro x im atio n s to th e series a re c o m p a red w ith experim ental d a ta , a n d it is c o n clu d ed th a t th e ag reem en t betw een th eo ry a n d exp erim en t is satisfactory.

5 3 2 .6 6 : 531.787.4 1245

T he capillary depression o f m ercury and high p re cision m anom etry. K is te m a k e r, J. Comm. K . Onnes L ab., Leiden (No. 268d ). Physica, 's Grav., 11, 2 77-86 (Deer, 1945).— D eterm in a tio n s o f th e capillary d e p ressio n o f m ercu ry in cylindrical tu b es as a fu n c tio n o f th e m eniscus h eight h av e been m ad e by m ean s o f X -ra y sh ad o w g rap h s. T h e resu lts o f tw o series o f m easu rem en ts clearly confirm ed th e view, th a t even w ith th e h ighest p recau tio n s, th e capillary c o n s ta n t a o f m ercu ry in m an o m e te r w o rk , is n o t alw ays th e sam e. I t m ay easily sp re ad o v er values fro m 5 to 10% a p a rt, c o rresp o n d in g w ith a sp re ad in th e d ep ressio n o f 40%. G rap h ical d ete rm in a tio n o f th e c u rv atu re alo n g a m erid ian curve show ed, in the case o f tw o m enisci, th a t a does n o t ch an g e o v er th e surface w ith in th e lim it o f accuracy (5%). A sim ple m eth o d is given fo r d eterm in in g each tim e th e value o f a in a m an o m eter.

533.15

M E C H A N IC S O F G A S E S 534.833 see A bstr. 1266

533

533.275 : 621.317.39 = 3 1246

E lectrical hum idity m eter. Kobel, E . Schweiz.

Arch, angew. Wiss. Tech., 11, 238-41 (Aug., 1945) In German.— [A bstr. 1120B (1946)].

533.5 1247

A m etal packless vacuum valve. Topanelian, E ., J r . , and Coggeshall, N . D . R ev. Sci. Instrum., 17, 38 (Jan., 1946).

533.5 : 542.231.8 1248

A n ap p aratu s for stirrin g under vacuum. Atkins, B. R . J. Sci. Instrum., 23, 84 (April, 1946).

533.56 1249

Device fo r au to m atic protection o f a diffusion vacuum pump. Wang, T . J. Industr. Engng Client.

(A nalyt. E dit.) 17, 670 (O ct., 1945).

533.69 : 629.13.014.7 = 3 1250

P roblem and future o f the variable airscrew . Roth, F . Schweiz. Bauztg, 126, 179-203 (Nov. 3); 209-13 (Nov. 10); 228-30 (Nov. 17, 1945) In German.— [A bstr.

957 B (1946)].

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

5 3 4 .0 1 5 :5 3 1 .3 6 = 4 1251

O n th e dam ping and m aintenance o f oscillations with n degrees o f freedom . Haag, J. C .R . A cad. Sci., Paris, 221, 734-6 (Dec. 12, 1945) In F rench— T he system stu d ied consists o f n + 1 solid bodies subject to a driving force, a n ela stic force a n d a passive re sistan ce w hich a b so rb s th e in stan ta n eo u s pow er.

T h e L ag ran g e e q u atio n s fo r th e system a re w ritten d o w n a n d p erio d ic so lu tio n s a re discussed. T he eq u atio n s a re solved a p p ro x im ately a n d expressions a re o b ta in e d fo r th e p ro p e r frequencies. A th eo ry o f p ercu ssio n is d eveloped in th e case w here one bo d y receives a n in stan ta n eo u s im p a ct each tim e it strikes th e n eig h b o u rin g bod y , a n d th e d am p in g coefficient is calculated. T h e resu lts o b tain ed have a p p licatio n in v a rio u s pro b lem s, e.g. th e d o u b le p en d u lu m o r th e p en d u lu m w ith a n o n -rig id su p p o rt. l. s. g.

534.01 5 :6 2 1 .3 9 6 .6 1 1 .3 _ 1252

System s with gyroscopic coupling term s. Bloch, A . Phil. M ag., 36, 440-1 (June, 1945).—A rep ly to a le tte r [A bstr. 2835 (1945)] relatin g to a n e arlie r p a p e r by th e a u th o r [A bstr. 2399 (1944)]. L. s. g .

534.112 1253

O n the non-linear vibration problem o f the elastic strin g . Carrier, G . F . Quart. Appl. M ath., 3, .157-65 (July, 1945).— A p e rtu rb a tio n m eth o d is u sed in a n analysis o f th e free v ib ratio n s o f a strin g w ith fixed en d s, w h en th e m o tio n is su ch th a t th e relativ e ch an g es in th e ten sio n o f . th e strin g a re n o t sm all.

T h e re su lts are c o m p a red w ith th o se o f th e lin e a r th eo ry . A close ap p ro x im atio n is m a d e to th e perio d ic m o tio n s arisin g fro m a n in itial sin u so id al d efo rm a tio n . T h e m e th o d is ap p lied to m o tio n s n o t restricted to a single p lan e, a n d a n ex act so lu tio n is given fo r th e tran sm issio n o f a localized d e fo rm a tio n

alo n g th e string. L . s. g .

534.213.4 : 534.64 1254

T h e analysis o f plane discontinuities in cylindrical tubes. I and I I . Miles, J . W . J. Acoust. Soc. Anier., 17, 259-84 (Jan., 1946).— [See A b str. 535 (1945)].

T h e effect o f a p la n e d isco n tin u ity o n a p lan e w ave

v o l . xlix.— a .— 1946. M a y . 137

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534.22 534.24

p ro p a g a te d in a cylindrical tu b e o f a rb itra ry cross section is calculated by consid erin g th e h ig h er o rd e r m odes excited a t the disco n tin u ity . In carry in g o u t th e calculations, a tran sm issio n lin e an alo g y is used a n d th e effect o f th e d isco n tin u ity a t a d istan ce is rep resen ted by a cap acitan ce placed a t th e dis

c o n tin u ity . In I, th e e q u atio n s o f m o tio n fo r the p ro p a g atio n o f a sm all d istu rb a n c e in a cylindrical tu b e a rc assum ed a t th e o u tse t a n d a re sh o w n to yield th e tw o-dim ensional w ave e q u atio n , th e solu tio n s to this eq u atio n c o n stitu tin g a n infinite se t o f m odes, in a d d itio n to th e p lan e w ave usu ally tre a te d in th e lite ratu re. T h e analo g y betw een p ro p a g a tio n o f s o u n d a n d a n electrical tran sm issio n line is established,

■ a n d it is sh o w n th a t e ac h m o d e req u ires a se p arate tran sm issio n line. T h e effect o f th e h ig h er m odes

■excited by a p lan e disco n tin u ity m ay b e rep resen ted b y a lu m p ed capacitance, a n d this cap acitan ce is given by a v a ria tio n a l expression w hich gives a system atic m e th o d o f calcu latio n yielding a n u p p e r lim it to th e tru e answ er. F o r th e case o f a w indow , a v aria

tio n a l p rin cip le is p ro d u c ed w hich gives a lo w er lim it to th e tru e answ er. In n , th is m eth o d is ap p lied to w indow s a n d changes o f cro ss sectio n in circu lar a n d re ctan g u lar tu b es a n d to th e calcu la tio n o f reso n an ce i n c ertain types o f cavities. T h e o rd in a ry reflection a n d tran sm issio n coefficients a re c o rrelated w ith th e th e o r y o f I. F inally, th e experim ental d e te rm in a tio n

o f eq u iv alen t circu it im p ed an ces is discussed.

534.22 : 536.48 1255

Two velocities o f sound in h eliu m -II. L i f s h i t s ,

E. M., and Peshkov, V. P. Vestn. A kad. N auk (N o. 4) 117 (1945). Sum m ary in Nature, Lond., 157, 200 (Feb. 16, 1946).— T h e p h en o m e n o n p red icted by L a n d a u ’s th eo ry [see A b s tr. 2985 (1945)] h as b een d e m o n s tra ted as follow s: A m e th o d o f exciting th e

“ a b n o rm a l” so u n d w aves b y tem p e ra tu re flu ctu atio n s w as a d o p te d , as analysis sh o w ed th a t th e am p litu d e o f pressu re oscillatio n in th ese w aves is low , a n d all th e u su al m eth o d s o f so u n d ex citatio n o n ly p ro d u c e th e n o rm a l so u n d w aves. S ta tio n a ry w aves w ere se t u p in a clo sed tu b e 25 cm lo n g w ith a steel p isto n a t one e n d w hose tem p e ra tu re w as v aried rh y th m ically by h e atin g w ith a lte rn a tin g c u rre n t. F o r d e te cto r, a re sistan ce th erm o m eter o f very fine p h o sp h o r-b ro n z e w ire, w hich co u ld b e m o v ed u p a n d d o w n th e tu b e, w as u se d w ith a lO Sx am plifier. T h e velocity o f the

“ a b n o rm a l” so u n d w aves w as fo u n d to b e 19-5 m m /sec a t 1 -3 5 °k , rising to 2 0 -4 m /sec a t 1-6 5 °k a n d th e n rap id ly falling to zero a t th e A-point (2- 19°k).

N o “ d isp ersio n ” w as fo u n d o v er th e freq u en cy ran g e 100-10 000 c /s. T h e speed o f n o rm a l s o u n d a t these tem p e ra tu res is 250 m /sec.

534.23 1256

A coustic transm ission through a fluid lam ina.

R u d n ic k , I. J. Acoust. Soc. A m er., 17, 245-53 (Jan., 1946).—T h e aco u stic w ave e q u atio n is derived f o r a m oving fluid m ed iu m in w hich all changes follow a n a d ia b atic law , a n d it is sh o w n th a t it m ay be w ritten in a fo rm w hich is very sim ilar to th e u su al w ave eq u atio n . T h e tran sm issio n a n d reflection coefficients fo r a fluid lam in a in u n ifo rm m o tio n a re d eriv ed ; it is only th e c o m p o n e n t o f m o tio n in th e d irectio n o f incidence w hich affects th ese coefficients.

M e a su rem e n ts are re p o rte d o n th e transm ission

coefficients o f a n o n -tu rb u le n t th erm a l lam in a w hose m o tio n h as n o co m p o n e n t in th e p lan e o f incidence, fro m 2 -1 4 k c /s a n d an g le o f incidence 0°-89°. T h ese m easu rem en ts a re c o m p ared w ith th o se calcu lated fo r a th eo retically ap p ro x im ate d lam ina, a n d a re in reaso n ab le agreem ent. I t is sh o w n th a t th ere is c o n sid erab le tran sm issio n fo r angles g re ater th a n th e critical angles a n d th a t fo r very th in lam in a th e tran sm issio n coefficient is a un ifo rm ly decreasing fu n c tio n o f frequency.

534.231 1257

G eneralized plane wave horn theory. S a l m o n , V.

J. Acoust. Soc. A m er., 17, 199-211 (Jan., 1946).—

B y th e u se o f d im ensionless va ria b les a n d sim plifying tran sfo rm a tio n s, W eb ster’s p lan e w ave h o rn e q u atio n [A bstr. 1329 B (1940)] is recast in to a fo rm p er

m ittin g se p a ra tio n o f th e effects o f h o rn c o n to u r a n d frequency. A generalized expression fo r th e a d m ittan ce a lso d isplays th is se p a ra tio n . F u rth e r in terrelatio n s a m o n g th e variab le s a re d eveloped w hich p e rm it th e fo rm al synthesis o f a h o rn fro m a given co n d u ctan ce o r susceptance fu n ctio n . T h e c o n d itio n s f o r realiza b ility o f th e h o rn th u s synthesized a re dis

cussed. Several a p p licatio n s o f th e resu lts a re p resen ted , in cluding a co m p a riso n w ith- F re c h a fe r’s exact th eo ry fo r th e h y p erb o lic h o rn .

534.231 1258

A new fam ily o f horns. S a l m o n , V. J. Acoust. Soc.

A m er., 17, 212-18 (Jan., 1946).— A new fam ily o f h o rn s is syn th esized in w hich th e e x p o n en tial fo rm s a c en tral m em ber. T h is p erm its th e effect o f p er

tu rb a tio n s fro m th e e x p o n en tial c o n to u r to b e estim ated . F ro m o th e r m em bers o f th e fam ily u n iq u e im p ed an ce ch aracteristics a re o b tain e d , a n d a rc discussed w ith po ssib le ap p lic atio n s in m ind.

534.232 1259

A coustic intensity distribution from a “ p iston”

source. I I . T h e concave piston. Williams, A . O ., J r . J. Acoust. Soc. A m er., 17, 219-27 (Jan., 1946).—

A n ap p ro x im ate m eth o d fo r c o m p u tin g th e th eo re tical sup erso n ic aco u stic field fro n t a p la n e p isto n [see A b s tr. 1344, 2205 (1945)] is ex ten d ed to co v er a larg er reg io n a n d is ap p lied to concave p isto n s as w ell.

T h e resulting e q u atio n s a re given fo r a c ertain ra n g e o f frequencies, p isto n sizes, a n d distan ces fro m th e so u rce. T h e excess a coustic p ressu re c an b e e valuated fro m them , alo n g th e b eam axis a n d fo r a n a rro w reg io n a ro u n d it. I t is sh o w n th a t th e assum ed n a tu re o f v ib ratio n o f th e p isto n does n o t m a tte r very m u ch u n less th e so u rce is sh a rp ly curved. T h e locus o f m ax im u m excess p ressu re is n o t, in general, n e a r th e cen tre o f c u rv atu re. L ab a w ’s d a ta o n th e aco u stic fields o f cu rv ed crystals a re a nalysed in th e lig h t o f th e p re sen t e q u atio n s. T h e agreem ent in general is satisfacto ry , b u t it seem s th a t his p la n e c rystal w as fa u lty o r else th a t curved crystals m u st p ro d u c e several tim es th e aco u stic in ten sity o f p la n e o n es w ith th e sam e ap p lied voltage.

5 3 4 .2 4 : 550.834.5 1260

R ayleigh waves and free surface reflections. D ix , C. H ., F u , C . Y ., a n d M c L e m o r e , E . W . Quart.

Appl. M ath., 3, 151-6 (July,

1945

).— N u m eric al an d g rap h ical re su lts a re given relatin g to th e reflection o f a p la n e co m p ressio n al w ave a t a free surface. T h e 138