A New Gyromagnetic Effect Citation Giamboni, Louis Adams (1950) A New Gyromagnetic Effect. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/avca-0q86. https://resolver.caltech.edu/CaltechTHESIS:06232025-210630695 Abstract A circular cylinder of powdered ferromagnetic substance was magnetized to saturation along its axis by a strong magnetic field. A comparatively weak oscillating field, with a frequency of either 21.75 KC or 30.50 KC, was applied normal to the axis. An intensity of magnetization due to a new gyromagnetic effect appeared in a direction normal to the directions of the two applied magnetic fields. A quantitative theory for this effect was developed. Measurements of the magnitude of this magnetization indicated a value for the gyromagnetic ratio of ρ = (1.04 ± 0.06)m/e for permalloy and ρ = (1.09 ± 0.10)m/e for iron. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics and Mathematics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Minor Option: Mathematics Thesis Availability: Public (worldwide access) Research Advisor(s): Barnett, Samuel J. Thesis Committee: Unknown, Unknown Defense Date: 1 January 1950 Record Number: CaltechTHESIS:06232025-210630695 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:06232025-210630695 DOI: 10.7907/avca-0q86 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17478 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 27 Jun 2025 23:14 Last Modified: 27 Jun 2025 23:17 Thesis Files PDF - Final Version See Usage Policy. 32MB Repository Staff Only: item control page

'.i.'he exl:..1t('nce of this offPct was sun:n-ested b·l' J ...... t:.J i'rofossol' Albert £', int1toin to Profeetw1• 0 . J . Barnett in pi-•i vato conv'-.'1•sntions. ,,oon afterward Professor hnrnett developed the quantltntiv0 theory and hesnn il'lvc.1tigations to tos'c its valintty . Ci:rcumstanco:~, Lo·,11.:-ve:r, r.u,u.h; l t nece;.1:,aP;r to stop Ghe ·.wr•k tci .pcn;nri- ly, b0forc it could be co@pleted . 'l'he autho1• takes groat pleatPn•e tn e:xpres:dng h:l.s dr)e p npn:r•eciation to l'i1ofe1..1sor .bnrnet;t for intPOducinc him to this proll.L0t;1, and for tho riany sum~es• tions and valuable assist~mce whlch he ronde.red . ·1'hls work w11s s11npol'.•tod by th(:) office of Naval Hcuearch, the National Rese::,rch Council, the Carnegie lnstl t,;ition of .,,nshi!·igton, and the Untversi ty of Callf'orn:la . ABS'J.ln.AC'.1' A circular cylinder of powdered f0rromagnetic substance was rm:.-ti~nettzed to saturation along its axis by n stronc magnetic field . A comparatively weak oscil- lating field , with a frequency of either 21 . "15 KC or 30 . 50 KC , was applied nortr!al to tho axis . An intensity of' macnctization due to a new gyromagnetic effect appeared in a u.ireet;ion norutl to the· ctirections of the two applieil..::.ae;netic fields . this effect was dC"veloped . A quantitative tbeory for J,ieasurements of the rno.gnl- tudo of thts um~;nethrn.tion indicated o. vullie for- the t~yrornaenetic ratio of loy and fl=( 1.04- ± 0 .06) ; ; -for por-1,:al- 5> = ( 1.09 ;!:0.10) ~ for iron . 'l'itle PllitF.I l , t.!'.'oc:. .:i.c 1; ion .l ..l 2 4 ~o Ro~onsnce Tffect~ F. ~xperlmcnce witn Rotatin. ~lel~s L:er- i vat.. t or1 o.f 'E.qt:.i.a ti. ens. I I. t) 1.1 2C -. PrlmAry Cl:cult 23 c. C lle anj ~ngnetie ~anples 32 'i:17 ._, I 41 r . '. 'Limensions of 4.3 lo 1,1 -v- v. Conclusions BO A. Iaentificti.tion o.t· the Gyromngnetic hffect 80 B. Calculations 82 c. ~iseusaion of Results 85 Appendix I . Intensity of 1'1agnetizntion of a Body in a Unif Orin Magnetic Field Appendix 88 90 Apoenclix III . Forrnulo. for• Voltage Induced in a ·rest Coil Appendix rv. Formula for Voltage Induced in ~,;econtlo.J•;-r Coil 95 Appendix V. 1Joterm:tnation of the Constant n Au 100 Appendix vr. Saoples of Data 102 Hefcrences l.03 -1- I. ~evlew of ~elateu Research 4.. Introd1lctio!1 In sowe elenentury ctescriptions cf tr0 n-H1 0 net1c o:r-ooer- tles cf matter, it lo assuir.oti t. n t the fundamentnl :nagn :?tic particle consiscs of a macnetic dipole. Thls description h~s been f011nd inadequate to doscribo i::.any ,'agnctic pheno1 e- na, so other Lodals have boen devised. Ampere suggested that paraJ,a.gnetic and fO""l"O,Jagr!et1c properties arlso from intra-lliolecular currents which flow tn closou patmi without resistance. In accordance w1t!1 a tneory of eoer, supportaa now by experimental evidence, electricity nas inertia. or n,ass. r..s a conseq,1ence of these t~·o hyDothe- ses, it can be expected that thare will be properties nnalagous to angular mo~ent~1 assoclatea ~ith these whirling Ampere molec11lar currents. Gyromagnetic e~periments aeruonstrate the existence of t.11s angulu1.. l'.:'lO:.aent Hil b; ::iee.s 11rlng he nurr.crical 1~ntio be- tNeen t.1e o.nt;llur mc!11entm-:1 ar10 the i.nug.netic .r.oment { each ex- pressea in proper units) of macroscopic ac•recates cf ~ipere l.1olecular curr-1:-1ts. ·rhosc st,1cth1s have le sta:1din;; of tn0 o.r·J gin mo nuturE:1 of to ":reatcr ,mder- ,l ) agnetic properties.' B. ,.ax ;;ell's Lxperi1,1ent 'i.':1e f1 rst exuerimt:!lt deair,ned to uetect the an,;ular mo· entmn associ,,t-au .vi th ms.gnetizs.tion was made b.) Clerk _;1ax.ve11< 2 ) aoout 1861. rie predicted that i f s c;;li:1der of iron ··as permunently ~agnetized olo1g lts axis, a~gular t-tmar.icnn dl::,'?!.ce.l ?ociety ~n li;l4 contoi.ned. the first .:--yrc - precess. If the motion continues for an extonded pc1~iod of timo, tho e-lementjary maLnets will experience many interactions wi. th nei~)lboring pa.:rti cles. In th1:., pr•osonca of these interactions tho i.no.gnet1c elemonts will behc.vo oimilo.r,,ly to ma.crose(lpic gyroscop ..,r, wit;h friction. 'fhe elementary mnt,nets will tend to turn so that the ctlreetion of their, spins will bo more closel:f aligned \71 th the axis of 1•otn tion. In genex•al, the olementur•y t:,ucne ts 1n a solid substance ar•o not fx•ee to roto.te, for they r:1.re nctcd upon by forces couplinc; th.om with ne1ghborinc; pe.rticles. '.L'he cur:t•(mt whirls, thercfor•o, will not all nlign com- pletely :i.n the aaol,O uiroction, but will aho·a a tendoney to do so. •~hen tho oler.1ontn.ry maGf1Ct$ in a f error;mr_;netic oub- stunce orient themselves in a 1n .. e.ferred direction o.s do- scribed above, the substance is said to be maenetizod . 'l1he phenm.nan.on of rus.gnotization whict.1 nppears dttring .:"0- ts.tion is I•mown as the Larnett effect; In ,P1-.ofesso1.. Bo.r•nett ' a experiment 11 a ba.l" of f£n•ror,jacnot1c ma~corial was rotu7;ed in a roe;ion of space in \th:1.ch the Lit:t¼th ' a lUflgrrnt1c field wns neutralized, nnd the 1n... tcnsi ty of n,agnct:lzation acquired by rotation was cot:,po.red with thr1t produc0d in the same 1•ou by a known 1:mgnetic :t'iold. -4.,. Proft.: sor Be.1•nett t ef1no<1 'l;b CYI'OH!El[71E.'t1c 1..ntio rnt1o of the angular not.,ont . of th me.! nctic . mont of tho cl ents. mug rntic eh: 1011 o to the :le men.. xaod the ;;1"'0. 1t1!_.rnetic rat1.o f'o1' various substances obtaining va.lu s b tw wh re m 1s the )lectron (hero e is a e 0.8 the 1.00 u/e ")1 a1Ja and e t 1e electron chn1.,ge in F ,U egative number). 'l1J.1001•et· cal consid ro.tions showed that i f th - wa._,net1c ,rope1"'tiea wex•o due to the orbi tnl , otion of the electrons, the ai;not!.c rnti ._,yr wo ld be 2 .oo m/ ; and if the p opt;rti s were due to electron spin, the ratio would ba Pl"'ofos o • Barnett• s l"C ults ·•1e1• er part of ferro1,1n dth the orbital 1ntoz•prote 1.00 ../o. to sho·.; that tho great- etism 1s associated with tl~o n 1nn1n otion co.ntrilmtion at most a f r; electron. pc .. cent, '.1.'h!s experir ent gave the first direct p1~oor c,f t1 e existence of Amp re• o .1ole c,1lo.1" c,u•r nta . It p1•oved that • rnra compooed of negs.ti vo c u.1.rg s and that the, d 'l'he 130.1,nett ffect because 1 t 1•oveale D, so currents 11 ues h t.1 os. s aometi 1 s call d 11 mu(.,n tizat1o ·1 JY rotation" this ne , 1. ct!lo ,1nete1n and ,;i of mn.~·notiz1ng a rod. Ho.as Lffect ~oon after Profes. 01~ 13ar•nott pr 3Cntod his .•osults, unothor expe1,1 iont, closely Pelateu to the L l"nctt eff•3et, ms .1:~cported by Linste1n a.nu do Ho.as. ( ?) '£heir xpa1•1t:.o t r:.ieasur d in effect, the change in an ulnr .aot1on a aociatcd \"11th change 1. Lngnotlzation . ' ..1ey obtained fo1, sign was nogut1ve. •..• ..)o e abo,1t 2 m/o, nnd concluded tl.. e.t the Joon afterwnrd Lorontz(S) e authors use o. q11untity ~ ns t•,(j ,;y1•0U1a{:;notic 1 nt:l.o. 'l'he ratio between e and! is e,:. 2/3"' -5uemc.ms::;.ra.teL! tnat the·r deter ins.tio.1 ot' the s1fn -.i,a cluslve., l;icon- In liHo anotner ueter~!!llnatlon of tne sign f:SB ,uncie b~ ~1nste1n(~) and se nrately by 'e Haas(lO) tL,te cn0:1 6e110nstra.toi.,, tnat trie sign of e , at wnlco. waa ne.:;ativ~. Iroiessor _•srnett hes stuaieu a."1d removea many sources of error taot appear n tnis type of oxperl~ent(ll) , ana ohte. ined results in close agrecmtmt \'\·1 t·t tr1ose or> ta 1ned from tt1e i3arnstt, effect . E. he non a.nee :'..ffec ts In re cont y1~ars number of exper1:nentis usinr- resonance poeno~eno hov~ been dcvlsea to measure ~yromasnetlc ratios of t11 atonlt'.! n clet an.d of tLo electrons . ~!"ie varlet:, of these ex~eri~cnts has greatly 1ncreas~d ~ith the sdvance inen t of' mlcrouave tec~:11 lques . Rabi (l 2 ) anu ot!1ers have developed atomic beam reao - narH,e ru ... tnods to .. ea3urc :; ,e gyromo.~netlc re t io of the nuc .... e i ana. o ttn:.I' ele·neI t :.·-y part lcles . ;Jloch en.J ethers {13 ) have measureJ c)rou~cnctlc ratioa o~ the nuclo! anu or 1srAmacne tic sut.s tances b:,r 1.:.pp ... y tr:r osc ills tlnp; f !el.Sa !'.1•.)r~:al to stea y ftel::s. 'rrl1'~lt:.1n and ot1.ers'l4) (lD) 'J.o) :netlwds to .eas· re t·.e ryror-icHrnet:i.c rnt1 os for ,lee trons ir. ferro~a~netlc au0stancas. rn one of tnclr e~rorl:enta, une fi nr.c v a..Ll of a rGsonnnt CJlV it.; W'l:3 con "ltruc tee of the suo- o ta. co to be st•.t.Jiec.. . t111e cavity '.in3 exc.:..tec: ln a. .o.1e of o:,;cUlation ti1e 3Uea that osclllctln.~~ .P.:netj_c flsl:is ,,-re ..... ci t:,i .. ,J --.l:. ---- ........______ _____ ·-~-·-, ..., , 0 J' 0 • n;1 • o~. en .:.fj 9 f:t,l ;:.~l ~ia .~ .... 1 •; ll-•1. l (;6 uy ~. E< ::- :1.rll -'~ f ~wt . , ln c .:31 .... e:r nf tc 0&"' re:..i its, fr•o.tessor F.~ns . . el:--, s,,.•- geste~ trat tno -s.~e ic elerutinJs ~id not ro;ctc ~ltn c.. e int~nslc., cf .a .r.ei:L..:a 10.1 vcctoP, bs...:t tia~. coor-L.ntt~ O%H~ .1~oa al.u.. f ro .. avi..•, tue a.x G '10.-ncnts i;.1e.1.:"' vf tr:.o c;;-.'i. 'n.:.:er . a.,. otlc fi .... la 1~ as:.s.!mt1a slr,a. s to lie tlon, a! u. r,.J:.o in t~.e 2 1..:,lr-t:ctl that tr.vse lo ;e,1 ta:ry •i, , net;;; 1. }urtran·, 0.1£i :L"'l CJ:Jn rno .. 1e 33su.110 c JO.n,.,e tneir -.,. irec t ton cf or €-n.,ac.1on only ty a:;rupt j .... a.. s of l.,~f'. u.er~· ly j;..m.:) ln s·...:ch :1u:nL-ers tnat t'te intensity ..:. f •'iB TI~t:i - ~st lon, whi.ch ·.. t ·.e V'""C co-r• BV.;"t of all t rn :nacrnetlc ,i:o men ts :Jer t~ni:: \"o:.ur.c, ~.1::J. i-otot f:i.e_c.,. . ~~~l~ e.r1,, foll•~\'. t.rn ,a.netic :__rH. . o:." these con._ltl:,··s, n::) -:-Yl'~:.1:-;.f,nGtlc effect Ls ~x.ect:a o s .. ' 1.le classics...1. :q.. lru.10.tion ior t . . L nul:. ef"f€ct . 9.S t e y, ..,._• \.J.\. ..... -. ..L " - .1 t on sly1 .1..r l~ (•..-:;.,,) inclosir...r, as mar.y as 10 '"'atc:.,s . '-'-' VCJ. V - -11- It is well known thnt 1n tho region ot near saturation after tho completion of most of the Barkhausen Jumps, changes 1n the direction or magnitude of the intensity of' magnetization oc-eul' e.s a result of rotation of tbo elome11.... tary magnets out of the direction ot easiest magnetization (along the 100 planes of the crystal) of the applied magnetic field. (23) towa1-d the direction It was suggested that a cylinder be magnetized to near saturation along its ax1s 1 so ths.t practically allot the magnetic elements point in the same direction. '!'hen a small oscillating magnetic f1eld, applied normal to the axis of the ~yllnde:r, would cause the 1n tensity of mognet1zat1on to rotate through a small angle about the axis of the cylinder. Since the rod was magnet1zed to near saturation in qne direction, one oan assume that all of the change 1n the direction of the intensity of magnetization would be due to rotations or the 1nd1• v1dual elern&bta, and would not be due to quantized jumps. It these elements could be made to rotabe, then they would pttecess, and give rise to gyromagnetic effects. 'l'h1e experiment employs procedures designed to detect this pre• cession. Xn this work 1t is assumed that the results obtained with the ba:rnett effect (4) and the E1nste1n de Haas effect demonstrate the validity ot the concept or the gyromagnetic ratio, and verify equation(~) page 13. This equation is used aa a basis to develope the relations needed for this C. experiment. X A long circular cylinder ot th substance to be studied is plod with its ax1s in the Z direction, 1n a homogeneous time independent magnetic field R1 • 17 strong to pro uce th t1zat1on J 25 which 1a clos This field is suf'f1 e1ent• axis along an intensity of m gne. t o the satur tion value , so that one can assume that all of the magnetic elements point es ential• ly in the~ direction. In a di tteetion X, normal to ~ , os cillating magnetic field 1s applied . comparatively \10 k nhen the rod is ab- sent , · the magnetic 1ntens1ty in t1e space tho rod 1s to occupy 1~ uniform and can be described by the formula HX ':' H '5 IN (JJi., (l) O'l Thia ·oso1llating magnetic field causes the totnl intensity of agnet1zat1on of the rod always practically par 1- lel to and equal to Jz to oscillate through the small angle e 1n the XZ plane , thus producing L'\. s mall intensl ty or magnetization Jx, synchronous with Rx, and proportional to it . The angle e is given by the relation-r.-* e= J: • il-* J2 Here, W:: 2. -,rf when t 1s th frequency. Eddy cu~rents are neglected 1n t his derivation . (2) tbe :rotation of' these elo1:1on·to c1 v•:.-s :r1so to a gyromagnet;ie intensity or wne;notization 1n the Y d1l;'t'ect1on ( normal to X and Z) cqu1. vnlent to that whi oh wo,1ld be prodtJccd by a real magnetic intensity liy of' s t1•~.mgth (4 ) (ID) de H == e d-t t In this equation :UY 1:3 the m.acnt)tie intensity t.1eo.s11red in dS gausses , 1s the gyromac,netic ratio., and d t;. is the angular e velocity of t~he mo.gr1etic elements . ~ubstitttting in equnt1on ( S) the vo.luo for e frorJ 0~1ut1on (2) , one obto1ns d J~ ( 4) cl t An exact Cl'.leulntion of the intenstty of t:me;netization in a cylindi:r of :finite lenf;tb is d1ff'1cul t . llOt'tever , a close npproxin.ation f'o1• a long , nar•row rod can bo obtained by assuming thnt tho ·i ,. m:d. 'i;y of rna.:;netizo.t1.on is unifo1"ln inside tho roti alon: • lo.tions . A well ln1own for ..11110. for the intensity of mao10t.1zation page BB) . rs - I - 4-lT+l - 1----------- ( 5) wr.H:n·e J 3 ls tn.e in ten el ty of magnetization, /-'- .s tne per·11es - bll l ty , D8 tne cemat~etlsn factor ~epcnding upon the reometr::.cal shape of t11e mec...lum , and H5 tne opplied ma 0netic .intensity ,. icto oquo.tior_:i ( 4) Hl j) one obtglnn ('x 't 1t + ( t" •- I ) ' d e .::D]f HJ( ~ dt Co) Sutstit:rtln_:; the expression for Hx fron equation (1) , one obtair:s rl1-== {fx-1) ew H c.os wt ··n Ft 1( t ( D)c] J"z. 0 ~ f) _,) 41( f (fi-l )D-1 <e > Substit·1tin~r for ny f'rom eq·.1a.tlon (7) irto eq:rn. ., ton (8) , one obtains~ tion due to the gyrovna,~netlc oi'fect . uere we assume y--,."'ft ''1.C. Dx = Dy • l·rou t:1is polnt on t.t;.e subscri:pts ere el L1lna tee o It ls of interest at tGis potr.t to ct~viat runin ,;:,en· o the L: r ·.ratlon, to . agn'tu e cf tr.1.e ei.'i'ecu o stimscc; tie fro~ tne or ... er of ~ram eq1ati.on (i:.i), after sct - tir r !J equal to its a 1-'r xl ..ate val 'G ~1r ~, one obtain ... (10) J =- intensity o.: .:nacrnetlzation , in tr.o case cf a cylln ... er of 1nflnit length , :y ~1e form~la B "' pr xln ate values for t J.\. obt0lne (ll} .0 qu. n tit tes concerne .... , as ln the expe"i~e t , were f -= e... ... tr.. -:.he;:;e n -- ... j_Q 0xl 4 L , ga.Mss 5xl.G l:J;::, 1er-ical values for the g ant1tte"1 in equation ( O), one obtalns for By fro~ quatlcns (1) a.lu ( 11} :au ses Ib.e pro Jle1.• of d.etectlr,g e.n o cillatL -~ m,·netlc ausu 1n tne Y ct~ ec~ion, ,'Jit, nn osci_.s.atin magnetic .t iel-.. ot a stre.~r,th o _ ________________ 10 ~auss in the X 'rec~ion prove~ to bo Jlff c ~t . . •• See pa e ( ~1) for an xpcri!';e,itally 'eter'. :n.,: •1nl 1e f r:;. flclli o ~ tho ( 14) b is the radius ot the rod . N 1s the nwnb ~ of turna in the secondary eo1l. ll is the mpl1tude or the applied oscillating magnetic field . l.J is related to the frequenc7 of the oscillating field "3 ..-z.-.-f e is th Jz is the int~na1ty of msgn~t1zat1on (near saturation) gyromagnetic rat1o . along the axis ot the rod. l 1a the length of the rod . -A is a experimentally determined conatan~ of the secondary coil. ~ is equnl to c-b, D is the transverse demagnetizing factor. to 2TT for an lntin1tely long cylind r . For It 1 equal long, narrow rod it dll differ from 2.n by a small a.mount as indicated by tho relation D==27T"( J-S) where 5 ie a small number. ( 16) This quantity S was measured ex• per1mont lly, as was described on page (41), and found to be Upon substituting th (1s) into equat1on . (l4), on expression for J obtains 01 from equation ( 17) ( 18) was based upon rnaorosoopic arguments. A derivation based upon m1eroacop1c arguments would produce similar re• sults. lf the elementary maenets are aligned 1n the Z direction, by the application of a strong extemal macnet1c f1eld 1 and if a small d1stUl'b1ng magnetic field is suddenly applied 1n the X d1:reetion. the elementary magnets at first respond d1a.magnet1cally to tb1s change and start to precess. In the solid stat~, this precession 1s dampened out 01 interactions between particles, leaving the magnetie elements in a new or1en• tation such that the direction or th.air magnetic moments 1a more closely aligned with the applied field. If, instead or a single, abrupt change• one applies o.n osc1lle.t1ng field with a frequency small compared w1th the relaxation time, and small oompared with the preceas1onal frequency, then the magn~tic elements will continually readjust theh• posi t1ons so as to follow the uppl1ed f'1eld. In thla way the magnetic elem nts will rot-ate fie.Ls ., Apnarst,J;i A. uenoral [iiactrnsion of li..xperlmen~ 1. 'fhe first group inclucted all of the elec troni o equ1pr.1ent t:,o.t aided in pr•oduclng strong oscillating 2., 1rh0 second grO'lP included the p:rimary coils which nided in the production of the magnetic field Jx; a large 300 lbo coil, -.vhich produc-eu the · steeay maz;netic field llz; the second,qr•s coil, which was used to detect tire ~;rro:nagnetic. induction By; trie su.bst11nce to bo tested; find ther- , incr·ease t.te strene;tt: of the e.YrO.Lagnt"tic slg,_•·u::l .t1p:rnar- In solectlnG the proper frequencl~a, it wne desirabl e of the col::p.resned powdera would he ,tiod1f1ect only .slirl:,tly by 1?ddy currents. I t was i:ilso deatred to u.se f'req~l-:'nc1 es such that the ti~e of oscillation was long, collip~red ,1th t.:e rele.xa.tion tLne of tl}f" :m1.tori a.l. w1th \;he squt1r':" of th0 f .req110nc:,r, On the otl1er c;r.. nd 9 ( See e<p1a.tton ( 17)), s: l> :0 G) l> 0 "' 0 0 r CD rn C ;:o Ci) ,, I SUPP LY PO WE li 200 V <.:L1 ~ A '-ff'L I F I E h 6SN7 OSC I l. '. .A roRS 6SN7 .:UH· _Y FILAMENT -- :a- M. PLI F lt.h 6L6 >- ·> - SU P PLY I000 vo LT l SUPP:..Y PO 'ER 2 70 vou p,----- -- - ,__ _j ' .AMPLI F I ER 803 -- METEfl QJ A MPLIFIE R C.u NDEt·b rR T UNIN G s 0SGI L LOSC0 P E VA tdOM ETE R -p~p ~ I I I\.') SOO K 6 L 6 AMPLI F ! E R 6 ~- N7 OSCILLATOR .002 P.f" 300 V S OKA .002 µ/ F I GURE 2- C I RCUIT DIAGRAM OF PRIMARY CIRCUIT 350 V 803 50 P/" CSN7 AMPLIFIER TO ~ ~l I- /':.'. w e ;;f ~ I.I.I a: ~ ('-= ~ ~ SWEF..P OSCILLOSCO P E COIL PRIMARY I I N N l~rre voltages. }re~ th~se considerstions, fr3~uencies push-pu.ll circ11ita ·Nere u.sed 'N.oere practic8ble. 'l1he ci:rc11i t adopted proli1.1ces n. st~ady outp1,1.t vol ta.ge at a constant fre~1ency, and provlJes an easy means to change t~1e frecp1enc,y if dos ired (F'iguro 2). 'I'bis oscillat- or consisted essentially of a 6SN? vacuulli tube in a multivibrator circuit, with an attached ~ank coil. Specially selectea culca condensers and a. high 11 (.i.11 "1.nnut .~a.nee iivare used in tne tank circuit to insure favorable resonance ulnced on the tank circ11it. The oscillator wAs follow,"'d by a G3N17 buffer a.,Gpllf le.c. 1J,1.sb - pt1ll, 'i'he coupl i.n.c- between the ose i J. lRtor nnc tne amplifier was made swall 1n accord8nce· w!th accepted practices. ragulateu power supply, using 5U4, 684, and e:;J'/ tubes in stanaa.rd o1rcui ts, furnishing a plate vol taco of abo11t 200 vol ts. A com,c,1011 60 cycle f 1 la,rient voltage ~.rnpply was provided for these and otLer tubes. rrvri.e oscillator an<l bt1ffer amplifier ·voi--e inclo::rnd to- ~ethe-r in a grounded iron box that provided ;nagnetic shieJ.ding. The tank circuit was incloeed in o. separate r.he r,ri.d and screen crld circ11.i. ts to prov11:1c G. chol ce of ors w·':lr0 t.1sed to bnlance tlie ga.:n of !:.he two channels. ;..n iron box inclosf:Hi tnc- Ui..C 's ~mn t.ne acco~.pan:llng circ1li t e-lewenta. tic.~ oxceile!tlJ at tnese ~ :aclve~y hi L fr.quenc~esa ed ·:r on bos .. ,.. J. t.. .... • oscil.Lating maene tic i lal.:., anu. t .. e capac 1 ty cons is ting of tv.c va1•iatle cordense:-s. i'ne two coru.ie. ser-s ere so placed as to prov taa s~d .1e try tr _m,r:er conC.en- a"1-· La lance. ,"\ S'.Ilal.1. ser was 1,laceo fr. parallel ~1th one of the large varlR'ble co:.\...et s~::•s for a f !.nc t a.n ing control. 1nesc condensers v:cre inc~cseG in anotner iron box. I'ho se~on.:.:.. gro..i;., cf apparatus coi:s ts~e~ ot sev :r~u coils, tna e~nple t0 be test~J, anL t1e therxnl control devlces o Sone of r;r1ese co.nponents sho1aac1 rnicro;ihon~LC behavior ana wer•e plnee...:. o., specle.l tE\blos, separate fr0-r1 tr.e rest ct -~~H: ut_.;ut or' t ..le 303 a .y..1.lfie.r .·as Liseu to excite tne -"'ri, ary co:l.1.. P-P ir. }lE?;u.re (5)) an.: provL:e ttie oscillat- 1n~ 1 agnetic fiel~ tlx• TI1a prima~y coils flnslly o~o,teu ~ere cor.s true ted on a rec tanr..:ul ':.lr l incn baBo bskel i to fraae, 16~ inctes leap a~ct 3 scd 0/10 inches ~lde, a~. 0th, inch t.r-dct!o ·i.v,o sot-s o.f 1'."roove2 (l•ig!.lre (3)), b:,, 8/10 inc~1 \!Cre ~i.1.1.e ... 1.n t.1e out;slue ec...-;e• ', inch t 10 Ja ...:Gl i te, 6/1-..J :nc ..'l from In .Jacr, r!roov2 3vCJ t .1rns ci 1 ena!el cavore~ co~1er olr~ ,are uo~c~ 1. 29 sil:.:., n 13 layers of 20 t ....rns p ~' layer. EarJh tur·n wos se_;arated fro·1 the next by a a!n ··le layer of c,.plro clot.:..i 9 an::.. vm9 liborlllly cove~:'e1.: \" 1 t.a Ge:rn.;:,al ~·J.::,c t:· le lee tr tc al va:-n.'i.sn, to ir.cres se t' e mecnan1cal str- -:.;th an .. electrics_ lrs....iletlon .. ·r.r.e ends of the i~.tre ... '!'◊.•, eact1 cotl v,er.. ·:•l:"oug'. t to sc para te ter t1ine .i.s on t113 s tc.e of t 1 f'!'e.r.:t:. -27I E .1-=-- - - -~_:_ ~ j- ~ ✓.1- - ·- A p / ~ -I p' / p /~ I ,.,/ r 1.- A ll lf I ( 111'1 l I l(ll/( ..- I - .. ., ~ I (Ill I I( •~HJ ~ I I I ( t HJ ..... I s I I i I I X ! '' I' I I ' i I I II I ; I I ~~ Ji ~ ~ I I/ ,o, ~ p' II .,___ _ _ _ _ _ _ll FIGU RE 3- ,JI pI PRIMARY AND SE CO NDARY COIL E -28- FIGURE 4- CROSS SECTION OF 300LB COIL M,COOLINGCOILW, R D C, AND SECONDARY COIL , -29- F I GURE 5- CROSS SECTION OF PRIMARY COILS PP, ~p~ ROD C, SECONDARY COIL S, ADJUSTING SCREWS B AND COOLING JACKET W 'l'ho ratio of the vJictth m of o, ch coil to the distanco n separating the coils •.10s ( Seo f'igure 5) chosen so as to SP- proximate the conditions f'or mc.ximum uniformity of thl;} magnetic 1ntcnslty at tho center of the coils . 1 Lb.e coil was placed in an electrical ovo11 and bc.ked at 75° (.; . for 18 hOUJ:'S , and at 100° C . fo1• Oicht h0t;,11 s . proccos dried the varnish . 'l'his *I'he resistance of tho two l1alvos of the coi l in sories, meo.our•ed wi th liiroct cu1.. ronts , vms 52 ohms . At each on-d of the coll fratne , a. hole , one inch in diameter, was drilled oo as to·be cantered accurately between the two coils . 'l'h.1s hole was used to emplace nnd ren,ove the srunple to be tested , and to provi de an opening tbrouf:h which tho sar.1ple anc1 sccondax1 y coil could be 1•ota.ted . 1 1 l h1'ce rods of compres:J(•d powdered fE-rrorungnot1c material ..;;- wore used in the ex.periuient . .Po1.'1dcrod mat01•1nls , ru t;he1• than solid r:1aterials , v1c1·e choson to .1:•educe the effects of eddy curronts . '1.'hese rodu v1e1.. e cyli"ltirica.1 in shape~ about 25 cm . in length, and averaged 1 . 411 ± o.oos cm . in tlio.mot0l'. The rods wore formed from small disks of compressou iron nnd permalloy dust . J.Jisks l . 411 cm. in diameter, cut f1 om riings of 1 the cot:1prossed material, and pucked closel;r, w1 th cm11ent bo- tween then, in ba.kcli tc tubes 5/8 inch 011tside dinmoter and l/32 inch th1ck . -:~ '1'he u1sks were squoezec togethe~ in a vise . 'Ehese some rods , from the naterinl s1,.pplied by tho Bell Telephone leborntories , were used by Profoosor n. J . 1.:.nmett in expt?r.ir,ents w1 th rotating magnetic fiolds . (~ce Reference (21)) . -31- while tho eew.ent: dried. 'i'ho length of each rod 1s listed ;;il Permalloy 1'l2 Iron 24.40 cm //-3 Per:na.lloy 24.00 cm '!'ho secondary coll used in the final experiment {Figure 3) was constructed upon a linen baae bakel1te tube 12 inches long, 1} inches outst~e dia~eter, and l inch inside diameter. Narrow groov~u ( s-s in Fig11ra 3) were milled in t.:e tube, and 100 t,1rna of 1140 silk wire wound in the grooves. Two groups of four holes were drilled in the bakelite tube, the groups being about 9 incbea a.part . In each group, the four ~:oles we:re accurately spaced at 90o intervals around the cylinder, antl threaded . 'l'ile cylin- dri-eal sample of the substance to be tested was placed inside the tube. Since the dia.rneter oJ: the t11be • was greater than the die.meter of the rod, a Si!iall space remained between the sample and the-walls of the tubeo Eight bakelite screws { B-B , Figure 5) penetrated the cylinder through the holes, and clampod the rod in the center of the tub6 . \id th these screws, the rod could be aligned and centered with respect to the tube. The secondary coil, 1th the sample inside, was placed 1n the center of the primary Helmholtz coil. (Figure 5), in such a position that the mutual ind11otance between prima~y and secondary was close to ze1"0. A bakelite bearing (D, F1gu~e (3)) taotened the bottom or the seconda1t7 coil to the bottom or the frame or the p~1mary coil. At the top of the secondary coil, a p1oee or one inch nutsida dia• meter bakolit~ tube (A.A, Figure (3)) was fastened to the a econda.tty coil w1 th bakel 1 te eorews • Th1 a t;ube extended th~ough a. hole in the primary coil. frame, and sevGral inches beyond. A 'brasa ba:r ( E • !, 1''1gure ( S}) was fastened to the top of the tube, $0 as to provide a lever to rotate the tube and secondary coil.. &or-aw elawps, mounted on :fixed supporta, provided. means of rigidly holding the bar, and henee, the secondary eo1l, at any selected angular position. D1 Seeongarz 0Jrs~1~s In order to detect the sma.ll gyromagnetic signal 1t was important to reduce to a small value all extraneous voltages in the secondary coil that might mask the effect. S!nee the secondai-y coil was placed in the oscillating field of the primary coil, precaution& were taken to reduce the induced vottages in the secondary coil. To do this, t1r$t the secondary eo1l was mechan1call1 rotated 1n azimuth into a. position of approximately minimum mutual inductance and clumped in this pos1t1on. To reduce the eoupl1ns between tho two eo1ls further, a variable mutt1al inductance, oou:pling the primary and secondary c1~cu1ts was used. (Figure (2)). 'l1he stationary coil of the vartomcter was placed in series with the primary coil. 'l'wo rotating coils, one wit~ a large effective area for coarse adjustment, and the other with a .small o.rea for fine adjustments, were placed in series wi ti-:. tb~ secondary clrcu1 t. By adjust- ing t:1e two rotating coils, the coupling between the pri~:1ary a.nu secondary ci rc11i ts, and, hence the induced voltages, could be reduced to a small quantityo The large 0011,{~4) used to produce the steady .11agnetic .field, llz , was constructed of about 300 pounds of copper wire, wound in 3900 turns, giving a D.c. resist- ance of l0.4 ohms at room temperature., (Figure 4) ..It pro- duced a magnetic field of approximately 90.2 gauss per a~npere, averaged over the region in which the sainple was placed. The circular opening in the center of the coil, into which the apparatus was placed, was about 6 3/16 inches in diai.:1eter and 20 inches lone. ·rne current for this coil, fro:n zero to 30 amperes, was f1.1.rnished at first b:,· storage batteries, and later by a generator. Large variable re- sistors and a reversing aw-itch were placed in series with this coil' to control the rcngn1 tr.10.e· and direction of the current. On top of tt1e large r::iagnet two screw aujustn,ents were bolted. ~1ese adjustments encaged the brass bar (E E,Fig- ure 4) and rotated tt10 sample and secondary coil tr.ro11gh small angles as described above. .I, '\._ _.,_ filI 9~~ I l o., 1 --,-I .,P/ I I WVVVWVv---n .o,n 700 t / 6SJ7 i: ~ ,aov i-•- .... 300K..l'L I 2.5 fnli I ,.,,, E .001_..µf T .01 e FIGURE 6 - CIRCUIT DIAGRAM OF SECONDARY CIRCUIT l ,"r iL ___o.,t (FINE) VARIOMETER VARIOMETER COIL SEC ONDARY T - o, T fa-/ OUTPUT t I (),I - 35- brass tu:rns o '•· i th '.tnc cool:tnr. untc assembly fltt.:ea tir.;htly in the clrcular n.olc or t.1e 30J lt, co 11. Connect ions to tne ?,a ter .oelna were provl~~~ so taat tnp water could oe forced by :nsc'1ined b,,h:ell te discs bol teJ to tho primary coll , ruiC fJttl.:1.cr closely to tho brass tub~ . -::'he reJrnln:::;er of f:)r;,1.er oil o insi•.Je t .c cyl lnlltH' coula be ,{cpt to less t~an e. tentb of a degree during all expor:xe □ ts . TI1€ th.ire group of apparatus include{~ an e.,1!:;lifier (Figure (G)J , ~sed to increase tho etrcngth 01 t0e gyr~aeg- neti~ sigr-.al of o few tenthn ot a .Jillivolt , to a mn~·ni t~~o moot convenient to ~aes~ra by standard instr~~ents . l'!1e clrcul t finally adopt3~ e np10ye:.1 n uSJ'I va.cu..im tube 'l'he ar.1plifier ns provided rri th its own filmnent trans- former and with a bank of batteries for its plate supply. ~pecial shielded loads wore used for• input and ontput connections for all power lenus. 'fhe ar,,pl1f ler was inc losed in n grounded box. ll1gh " li," no.rnllcl r.•osonant circu:! ts vrn1"e used• in the grid and plate circuits to peak tho amplifier and allow only a no.rrO\, band of frequencies to be ampl'lfied . In this way , ba.clq;roi.md nolse, always troubleso ie , was grontl:r reduced . An oscilloscope and an electron volt t1eter wore attached to tho output of the o.mplifie1" (Fir;uro ( 1)) to the phase und r.i1f:nl tudc of the signa.l . 1cc..s11r•e The oscilloscope was oper•nt;cd on ext~rnal sweep., with a sy-nchr•oniz1n 0 signal tapped froL the output of the 803 amplifier . In all, foul" different n0tero \'J 1;re 11sod in tho course of' the experirnont . 'l' ..10 v:e1--e u.o.nufacturcd by tho Ballantine Corpo1•ation, and two by the lle\1lott l"'n ckn:rd Company . One of the liewlett Packard 00tcrs ~ns calibrated by co1par1son with a thori•onu. 1eter . '.L'he tv.:o Ballantine r1 etors were also sepa- rately calibrated by another laboratory . 'l1he metors were then cot ipo.red alllone thews cl ves for all scale reaoi ~1Gs . In the fiDnl calculations, data takon with each of the four meters vJOre usou , p.rorJorly weighted, to cnlculo.te the gyromcnetic ratio . h. Ja.eral .isc~sston re~ e ~11stioi (l·, , tne rw~ate~ to ot,cr ex~orl~~n~ully ·et~r1i c~ ~an~it: ·s ~ Ll o::>uer tv ce.lc . . .1 t.., t, .e value of e , ... econ ... ::,.,o .er ~ o fur .J.lo. { l 1 ) ; anu A:-.i: car!:l 01 eaci1 quf n. 1 ty c 1 tly in t.1c t,.e otLsr ot~o.nt!ti...:s . ~ o, :'..t wu ueslro l.;. tc, ueter•rr.ine ti,· .frequency to en accuracy of ry precision lr. U ,..; ':'inal ve.lle for e. wae i i ! ct. ca.J.illrst..e ... cy :n * ~~. • equation 'lle$l.., re-nerd, of sever·s e , i.s yrc,·•a_"·etic ra •io ,ls of t. e vi...;:>s.tir.~ "T"la f,;."ea..1. ,ncy ~ ,.s re:nte...: t<J ,:•:,•..,c; c ;c C1, • t' ,.,' W eq..:etlon (1 ) ~y : 1e rel~• ion W = 27T .f of fur- o;;;clllaco.r ai~..-:2.icc'. to tll.e v~)rticel sweep cf an oscilloscope . figures ~era ob~alnea o :1:;:x t 8 tae et:ip.i.lfhn.. leac.s were disconrocted fro:;;. t.1e nor 12,on tal swoop , and a ·!ewlet t f'aclrnrl.. oscllle tor , ~;,1 ich uac. t-,er: 1 -reviou.sl:y t,.1rne.i on for a sufficiently lonr tLne to reach a s ~ea..;i.y s ts. te , 'io as cor., .. ected to tbe osc 1llosc ope " \e'v', :..tssa,jou' a f'J.;:ures wore obta!.nec. ..,.hen the He,t;lett Pac!,,._ era os~illeLor was ajjuste~ to exactly 1/5 of the oriplnal .freq 1...1ency Q : e.x:'t., the \.es tarn r loctrlc osc1.llator wes r~a,.::j'.J.s te , '-'. t 11 l ts :. :::.~.:.qJ.ency \"9.0 1/35 t:1c or t.:;inal fr8quoncy , .reHu.ing 0•1 Ln,3 ca.J.lbrato.J. rart of' t'ie scale of t.J.e 't:estern Electric cacil~ator o j. B:· these r)roeeuures the two frequenc ice used in t.ne C. Osclllatin53 _Ma:1;netic : ield T J.8 a,-nplitLlue 01 tne oscillating ..w.gnetlc .r::.eld H0 x was detor~1neG during the experiment fro~ a ktowledge of the cu.rrent 1n t::.e pri.?1ary coll, and an em.pirically J.eterm.ined constant t\ (gsuas per a,:i.pere) of the primary coil. To determine tr::e constant X, a test coil was c ;;ns truc ted on a bakeli!;e fra.,;1_e, shape ..... to tt-10• apI;roximate i:iimensione of t.ne samples of powdere:i iron anG powc..erea permalloy. On ta.is fra.:ne 4G t,1rns of /, 40 si.l.k .::,OV;.,red wlre were wound in a single layer, pressed. close to the fra,ne, enc. va.rnia11ec. L"lto place, I'he c.imensicn s before and after wind.inr:; were measure,.,, ., and averaged to r·tve t!'le mean a.lmeneions o;• the cotl. i::·he test eo11 v;as placed in tr1e rep;1on ordinarily occupieu by tne rna teriel being t(,.s ted, aoa a meter com1cc ted across the terminals . The test coll was then rotated in e.zimutll m1til a ..uaximum voltage appeared across the terminals, a.11.d tnen tt.e coil ~vas locked in place-. Knowing the frequency of' the tnagnetlc field in \'which the coll wes placed , and t!'ie cilrne:islone of t;1e coil, one coulo. calculate the mar - netic field etrenGth from tho lnducae,. volta_;re. wi tl1 t~bo voltat::,O inuuced in the second:.n>,/ coil • In ull , An o.vcpnge vaJ.ue of tht· voltage \JD.:J cnlc11l2.ted fc:t' oach· th'flD ·ate ve.luo of 1 0 . • i1 rm:: this infoP;,1ation it was ( 20 ) ltn0wn . I t wo.s, of COl1r;1c, 11.porrnible to proce<'::;d in tLo -41- p, .l.J~1"'a( nctizhu; 1 'l he Fo.cto:r valne of 6 was dotcr .. •tned b:v dlr,:.>ct experiment. E' X pared to unity , ti.tis etp1ation can ho arrant;ed to the approx1- (22) A number of oxnr-r . ,t. n:~s w •!'(:.' mtHie uo dot; ... r,nlnc the c111antl·cius on the 1~i(_.,ht : a 1t.1 sido of uqn1.1tlon { ~2) . to evnl11a te the f':....ctor /A.-+' ~ r, L,e!l!J,n•C'd in H(•ak 1'icl,.s) \It,s In ordur , tho longi tnd:lnul pot•l.1(mbili ty Has 1ln ex~n•cs3lcn for wH~l. . obtain ·~d f r>Ot, oq,uition ( 46) Appenulx I f~= ~lf J.: Hi! - ])a Jl. +I (24) 'l1o ctetor•r.1ine the q_m 2ti t ·; Pi in e41mtion { 2·1) 1 t wua J; wl th t.,H(• solono1u v1l1en the 1~od v1ri.s plo.ccL in a lc·10un ?;1ac11<:tic field Hi. '.l hc value of Dz , the nocessm•y OU.!./ to rr eGsuro 1 lont:1 tn.d inal dor ,agnetizing 1'11ct;or, and was fo1md t;o lJe O . O'/ . \:US obtainod f POL.1 tho tables 'i'he w1'.'JU~,u1~eu1<.=m t-;s for J z a.nu H~ were n ado with both llirect currents and oscillating c,.:1.pr0nto permalloy wns fou.nu to he 2(:i . co:J.1 was wounu clocely on the ron us 1ncilc1Jtod in the• figul:lo on paec (27) . coil . '.l'b.e I'od o.nd coil \li}re placed inside tlie primary '.rh,e v-olta.:i;fJ indu.cod 1.n this co:t 1 hy the oscilla:ting 1:1ar;- wan ctetcrmln~hl by meucuring tht! c1.1.1'Pcnt tn t1u..~ pri 1,.nr.1 y coil coil . i•-.:ct CU!'l'◊nt 1..:ion::mro ....ents r1ero u::.,cd in oquat1on { 2) inu1.J- r~t;io of lent_;th to Giau:ito:r· of ii1Je rod . cnve a value of' O. OO!., 1n r.:mnonnble agrcc1uont; w:i.th t!"le €iXper•l.:,cmtall ,'." dote1•mi11en vsJ.1rn. value '1'his co.lculntion O . 01 \JUS ttaeu throu.c;hou.t . In tbls xper-:'l.me:1nt the The raoius of the cyllnd:rical sn.mple, b, waB deto:rmined by m,:H:tsu1,tng with a wio:rometer the diameters of a lar"&e number of disks of tho compressed powder, and calculating one-ha.lf t:.he meo.n diameter . Th0 lone;th l oi' each rod was measured wl th ui.croi,eter ct:l.lipera . 'fho dit,JO ..'l.sions fol.. each aamplo are listed on pages (30) and ( 31) . }..(+ I '.1.1l1e qua.nti ty ~ was de1;0rm!ned oxperii;1entally fo:r ench o~..mple . Bine:".l the tro.navonH:> permeability 1s a rune ... 0 tion of the long1t,1dinnl magnetic field etrenct11 nil :t?epeat- eu aeasu:rc:,~ry_ents were mo.de for var1on.s values of H~, nnd a cm."tVe plotted through the menn of a. large nu..'nber of r2adings . (2s) Now, e. woll kno'\.'m equation .t-elating the r.-:a.gnatic in..-. du~tion B! in an infinitely long cylinder with tho apµlied mngnotic fiold fix is (25) Dividing through by lix, and th<)n aubt1..nctine; rm:t t;-r fror.1 each sido, it is foimd thnt (25) reduces to (26) t .,'Q t •1 C.._,..., , ~..,~.u f,.-,,-..,..,, n '"''CU ,__,.._ r.i {'-'.,) u- t4--I ( I+ 2 8) r,-+ I 8 _s re4 te ir'"3ctior.., to s ,.. iscunsea o"l p2gc (1"7) .. In meas rir suov ., 0 psrf:!llo too~ t ·.e f'l"' .. ""L.d" _ c:;;. J tic in :.ic - .., la ·ms f o .... c· ~o ., .., t0 t,c f. i y "• .." ._. ,..., vi.J •on a ra v x 10 -n .; ) ) • • .., { .., -B 2,V W [b+ ~] 0 .0 ,,:; ~ ~ ~o ~ e H~ , 6-a 0 (GA USSES) ~ Q 2000 FIGURE 7- ; : : AS A FUNCTION OF Hl 1000 o-Q D ,"~I ,., - I 0 VAS H-l 3000 PERMALLOY 1.000 - - - - - - - - - - - - - - - - - - - , . - - - - - - - - - - - - - - - . . . . - - - - - - - - - - - - - - - - - - , I O'I I ~ i:t1h~ core a.n1..,. coil were plac:ed in tne ooc llla ting sucstitute..1 into equation values .1'or (2d) to <Je·terraine B;. . 'l:he r?.x andf E: were aubstlt'.ltea. into equatlon (27) .A to .::'e ter.:'!lne /-'- - f"--+ I • cf ~:as ·detorfflino.i by prevlou:s aixperL:1ent .a ... t'- -' t-hL. infor.ca·tton tho quantity r,',-+J ·1r.10 vaL..1c of quantity /--4-J f-' +I l.li&S not a constant , tut a. fu."letion of H .11.en:·1mr1S'nen ts were mede for v:iu•ious z lues of H,, 11 and a curve· of U-I ~· •rf+i a~ainst ll z was plotted ., ( Figure ( 7} ) • l.'o measure J , oe.c.t1 eyllnd.r•ical sample was placcc. _in z s. solenoia 4:4 . e c.m long ai1c. l . 60 cm ir, diameter . The sole- The solenoid. arii":i aa.i11plc YnJl"'e ace urn tcly cen. tereo in the t:t.10 direction of the axis of t; 1€ sample .. •rne ter:nlnals of tte soler~oid wero connoctoD. to a ball is tic f~s.lvanol"1H.:iter o 750 z 1- w z C/) I- >- 0 LL ':E 0 250 Jl <l 500 (!) w z 1- <l N 1- 0 z 0 / 500 -- V, 1000 FIGURE 8- n H~ 1500 (GAUSSES) - ..., 2000 - ,.... MAGNETIZATION CURVE FOR PERMALLOY n 2500 ("\ I 3000 -;-I ~ cp 47TNM 9 , . cp - 41fNVJ~ 1· {... .l ".. v.n ~ l ... ,J \JSs dlrcon. ectea, 0 'W '1 0 41fNVJ-a cp J,.,,.. a,., . . ., ..... ,,. .. ;, ,;_,~J. ... 1,;.., t., L...,z f.-,,.. v-. is reprcduceu in ~l ,.1rc , ; .. f - ' was 1,.ound., across tie t":Jr:.inal. oi. t.fw scco:1..'!.ary coil \,as 1r,cr-€o.seu 1n 01 .... (. .:1 ,. 0 ,-------------.A M, s 8 C. . ' •'-' :.et ..... '. S .,.., 1l t. !C ... \.).,,.·e ; ( c...t_,, t; vol~a O!'t!., .l.(, t J... \l : t.o r.cc tc ... 3.L • . .i. ... l t i.;r. r- .. ..:or • ..... I' 1. t-, .. I .(" ~ 'J "i • €. 1-'<I'. t .. uUt .t t . Pt ,d . , a. . . t, t ••• 1..,t 1J ~~ ,\ ._ ,., t ) ·e \ . ..)'L.•. .... . i 0 lt 1. .J ,. .: ... u t ..... n t • •• r .. fic-J - Vout V ·1n - .J 17 e v ~es atten~ate~ by a resistance network, an~ a~plle~ to the osclll0scopeg o: tna induced voltafos were notea on the oacllloscope ucrosa tr.e output 01' the ft.J.tlplil' ier· o I•'or· convenience in t1.d.s cisct1.ssion, al.:ernatinr:". vo .... - coilo ~1ar~ i0~t1 vC.P C1lt.1r1;,.etj tt:c f;:ti t11al . 1.: .. . l J.c tar:ce te ~.t~ .fin t'--1z c!µr :.:1~.Br"3 o.r· not be c.c tee tee. i:, i tr:. a.n osc i l lus cope 9 pro<.n.tcec. s. smnll :n nstei;i by reodjui; t lng tno var iomctvr , leaving sirsc S~Pll value il !Vi.mll in pc1ase r.:-1is conc..1..udea the preli,11ir..ary expe.r 1:n.en ts des 1f!nec. to eliminate voltazes tnat aiPht ~ask tae gyr~~aRnatic effect. I'hc e:xpez."iments.l met.hod fin ally ::u,.o;..'te:.. to ,neas\.:lre E s::iable.:'.l one to meas!..U"e F. in the presence of' eerta.ln (.Li.sturb- Tne .nethod will be •-OBcribE:d first, a;1.J. tnen ln;; ef fee ts. t.:1e disturbances v~ill bo clscusse~. ln measuring E , the sample and. saconnary coll \H::re 1 C"ilplaccu in tr1e apparatus, as c.escr lbe.:.t above. Tt1e currl:m t in t;he 300 lb coil li,as sot ~o some prec::-ter.. ~J.n ·,.i value, pro- ducins a etea.Jy ..:agnetic field., 1!.,., ,., a.no. en intensity o • l"!'lag- output .. e ter inc:ica:.ed a ~:"rn.ll ln phase vol ta~e E1. ~ .. en reversed, chnr:.;in • ~1z co -J'7. ... i,1tt:i. tnla c.-1an"e in current in "Ghe 3Ju lb coll ms to -..:.'.,,, .., r,,,ct UJ,..,. '· ' 1 ."0 , • C""'·l:' •~1""•fT io-.&.C.: 1..t-:) .a ... c.... r .. z rno - --1... .....,. its rendinG to E 2 , ~. cr~er to us~ th!s ~roce~uro to measure 2 ~G, c&rtai~ precautions ~ore necessary to el~mina~e possible errors. wita t~e gyro~agnctic effect ure plotte~ elon~ P:lgure { de.) e:1ov:s tne r•elations Lo tween :~ 1 ~10 Y axis, and E2 triat °\"!ere deslre,i, w: th. t'ie pl1nse a:-1 c lc bet~'.t.:en r: 1 &n.d £ equal to zor1). V:-ith this p11ase relation it is propo.;.• t,o r, - - ~ T:'10 -1 - - I• o 2 -56y y 2EG 2 EG E, d - - - - ~ - - - 4 - ~ - - - x - - - - -~ -- - - + - - - + - - - -x 0) CORRECT PHASE b). INCORRECT PHASE RE LATIONS E 1 AND E 2 RE LATI ON S BETWEEN E 1 AND E 2 BETWEEN 2EG 2 EG ' I I d) ELIMINAT I ON OF QUADRATU R E COMPONENT C) INCORRECT PHASE RE L ATIONS BETWEEN E 1 AND E 2 OF FtG URE 9 E2 - :.'utu.rc co :r,on.on t of S 1 f ti1z- va:r.tar,:eter ,'an He;: ,113 teu trr~ t ~.l a • ..1..,on tne .Slnco i11e .no..--~r1~tie fi,.~J.Ll H""... \;es sct.;.sll~! sc ;e\vt·~st ln - sxio of eac- tiJd ~erore ~~G ~as ~0co~~ai o 0 i:c. C. J J ~) t, ~ {..;.,_ 1' .,; Cl 3ir ce re c t.ion ., - . . . 1- t ~M, Ir"• ~~as rcc.;.JI•J.e,..1. ~(; tc 1 r ~ vrlues ~ ... f1.~ u ~--et·Leen ~e1•,, Stl"! .1 .::r,J~J e:l~iJ.SSCS o curve e~poctau fop ~-·t·;u-,. ,, 4 .,., e =:: IQLL'W , •e--.• ,."' •• v r"'··lln,:r l~~ _.....,_, ; : ~u:t'e~ a heavy bloc~ ltne, .,,.. .... ti\-., e-1 oe•e- .,.. - • Vl . . ,..... ... ,. v:... - 62- --------.---------.----------,....----------0 0 0 It) 0 1---------1---------t-----+-------,1-----------1~ CII >- 0 ..J ..J <t 0 0 ~ 0:: 0 t- w a. N (.) w u. u. a: w 0 (.) u. LL t- w z (!) fll w 0 ~ <t ~-0 0 rO 0:: t>- <t ti) ti'; 0::, 0~ 10 - w - 0 t- w ,..,z :i:: (!) ~ (!) <t ~ >- 0 _J _J >(!) 0 0:: <t :!! 0:: w 0.. 0 0 0 I 0 w a: ::> (!) LL ---------------------------------0 IO 0 IO io O I t::) 0/ I I I I I O 0 0 0 0 ....__ ___._,.___ __ _ . I O ~ - - - - - - - - - C l l ~ - - - - - - - - ' ' - - - - - - - - - - - - i O o 0 0 0 -63- rt, 01 0 / I 0 0 0 of I Io It) N p d z I I 0 0 z 0 /v 0:: - 0/ I I I I 0 0 u. u.. ::E 0 u.. 0 I- 0 w u.. u. w 0 0 I ' ~o 0 f/) w 0 0 U') I'- <z ~ (!) It) I- z >(.!) ~ CJ X: w 0 - "' ::, I- ~ - .,. <( c., 0 0 I LIJ - - 0 I (!) a:: <( I 0 ::E I 0 0:: I 0 o >- - 0 0 ('l .., 0 0 0 0 0 (SltNn A~V~l18~V) .::1~3 ()ll3N9V~O~A9 '.:) LL 0 N Lil a:: (.!) 0 <t a:: N 0:: I I a:: 0 0 0 It) 0 coil woul~ also bo zoro o A study of tns t~eory for this ne5 not z.er0 .. vol ta;re appearit1F· in tho tH::icond0ry c ircu t t v, 1th trw appl lci:1- - 65- ac~ secon~ary colls o As ~111 b~ aescr11ec belo~ , annll ~o- t.. qua.litativo foz•;:iule. for the effect of certain mowee; 12b, 12c ano 1 2d )o It le well to rccell at tnis point tnat l'hc soconcary coil ·,N&.8 used t.o .:..;et4:}ct the magnet.le i.nct~iction " -66- A / -Y -x x/ A' a) ___ A' b) Y' I A l, y I I 82 I ; "'- ' I --i ~ II II I e3 I CD y I II A c) d) FIGURE j 2. POSSIBLE ANGU LAR MISALIGNMENT OF APPARATUS )( .u E C 2f ! •1 \;'" ~ .;....i,,,, cp E:: 2 ootn lr:s 6E c~t.1 e, N - ,.., :-;> V - ~' _, r . ,at ., ' \ . l' A <., l-2 .n l _, ~!c .~vor . ., ,i.) . f' r, i r· ' C t !1 t. ~ ,:....J, l ~ { 1.4 - 1) v H s ( ri. e, si n wt ~ Mc-=- _J_ 41T ( ... " ..., 1 . '! I c.;vL it . ra"" . ·11"'~ ,." lC 1 . {;, !""..':lf! :n .,' r() ..., $ &T) w lo.,~ C . c., • • .1., .i. C"1 t t ,·: (1 rl. .. L l, or 'C ,. l (.' 1· ·o _ _,<"I .;K) ox L t.. -~. L .I' :tr,, ..... ,. . ~- .. a'-· e2 ... ~ .... .J. •IV t ,.. ->-~::it -v~ 7€11" 0 ... .... . . .. -..·, ' . i ..., J. ~ +- . 0 14 •ii i' __, ~; I:. r or -· :s ~ Jl., •J t \.,, . . , . r O"'-, (; t"-, • 0 Ci;..., t' 'ii ,._, J, .. . '.:cat , -...,be {' "'! { .. cy~, . ) : .:, :1 c.,,_ :: ' ! , . ' ." . . ,I,.; 0 .I ~ Ct.. C1- ,,.,,.,C . :., II ...... . l ' a r .... .. t .l ) .., 0 t - .di - !.) e 0 > ,)4. . .. 1· ' ...... .,,.,,.., ..., ' ,._, L I .J. ,J, ' r .... 1t 0 ~·,, 8 t: . , 01 t , . .; l )J.. . o e t e.1. '1 .. . - <( 0 w z ~ w a: >~ a: I- <( <( a: a: IQ <C m ~ a: LL LL I- w en o- I- 25.0 22 . 5 KC 1 I I 30,0 y = 350 GAUSSES Hz 32.5 I Hz = 2 75 GAUSSES : 500 GAUSSES 600 GAUSSES ----.....i Hi! I = 950 GAUSSES Hz : 750 GAUSSES H~ J"• 1771 .r' FIGURE 13- QUADRATURE EFFECT VS FREQUENCY 27.5 I I I 21 20.0 -----1 I I I r / I I I I 31 4 51 6 7 8 9 IOI 11, I I 0 I -.J .... .,. . fro.1 tc field ~z a If t·1i~ was tne case , corques woul~,be exerted i~.is device ls described ln detail on pavB (31). 71ppin~ , var 1~, ty ,.,f ui. !'er.en tly slio;c,_ curv..:e coul._ be obtair", e · r. i th -7 4- "' (l) IJ.. 0 z 0 0 z ct 0 <t er: I0 z ::, IL CJ) u. <t 0 CD C/) J: I- z I0 w IL LL. w w ::, er: ct C/) 0 co :c I- :J I- <! 0:: 0 <! <I>"' ~ ... t s;t w a:: :J (!) LL S3SSn'19 006 = ~H HllM ( SllNn AH'1~Hl8~'i ) 103.:1.:13 3~n.l'1~0'VnO -75- 3t-------+------i--4--------+----------J X / I l- o w LL LL w w ex: ~ I- ot-------+"-=L-----...L.--------L----------J 1000 ~ ~ 1500 2000 I H~ (GAUSSES) ~ ~ C, -11--------+---+-------+---------+----------l QUADRATURE EFFECT WITH VARIOUS VALUES OF 82 -3L--------L--------L-------.L---------' FIGURE 15 r 0;. i • l i..' t.. ' . . .... .... '-" ,. L -.:,.J. - ... ... -J ... . '' ) ~ ·-J , 'E ,_, I J ... ' L, • I ~- s - t"'3r·" ; t - ...... ·z o ( l o ;; • , t ~• .. •..,..I,....., ,. V ....... .. .... ~ c :..ar. - t,J - ''" ..... v n 'ha r cCc...,Sf\ :c ., ... O:.lr, - : , VU .. •.oJS 1..1tH'Y c•l -· .:. s ,. ,., 1.r ,'r''.':. 3se :1, a. c:. tc, r?f.lt: 1 ° ·naxir.m.. ,.~ t~1E- -' 1 \ ) \17} .. oy ot .J.")I' netno0.~ o • J:. e -· yr• 0( 6 2;rl -S. .., : C ?'at i C, ne ativ: dW:.. l.::er . I.1.e s:.__ n o,.: e e, a 3 C..e fine J. :.1 8 r O I i..., a \,e.s ex) :..--l~St tal.J.J fou:.'1.~ by c0111;»..1.' • n. 6 t.ie :;:,ilaac rela t io ,.shlp (}i t a ·yroina[t:1.e tic volt - ~. , .. Calculations e 1ue. t .ton I,; .1.~ 7) ',,l:Hm chc e.::peri.nen t slly a.etermine,:.j, values oi the c on - c.£G Hox l'tle nu_i,erlcnl vali,ea for ~ ~; (40) , r. , a:,d H0 , wez•e ob- ts ine~ fro~ ~aa4urc~ents es describaa in t~e pre\~oua i-.i:ec t ton. i ll o.r tt..0se qua1 ti ties depenje.;_ clpcn tLie e i = (,. o 4- ~ o o 6 ) A .::.ew examples fu ~ calc~latlo~s yro- .. a;d. _,.; c1 a. , • r:... o.n .... tne ::-e !r.,n of near sat!.:re.tlon of ,L, t ~at is, <.J . . .::- - v r- 11 t.t~ e u ... , !.t onsl 1_,e ta were not incl r.,,;:::d ln com ··~ne. \air.: .. inst!'.J.C:J.C"ltal errors to attain the e. ror in e :_3 1 ~nen re )Siile &'e ~ e I.!± 2(, )if, )Z \100)•1,ioo ... \i'o0 } + {""..s-\2( 1 )zL, )a /I )z(1 \a{ 1 )e r+ ;;-.. -+\.;;;:, -+ \,000 .. ~r ioo ioQ g=-o,osz e 1D.a,;;netic .fiol.:;.s obtainable, s0 trie f'orreulas could not be ar- J;liod 'li,1 th certainty. Hovrnver, it vms pos aible to obtain s. rJ1EH1surable g-yro::1agnetic eff'oct for iron 1n the ree;lon nvail e.ole e ( :.:ee P'lgure ( 1~}}. frn Hz lacreased, this ef feet starter" in much che same \,ay as utd t.:1t';.; effect for r,ermallcyo SL'1ce satu2.--a iun of J ·co-11,J not 've obtalne:l, 1 t was not z pos.:iL:,le to a.,_.ply, w.lt~. certainty., eqLu1tlon (26} to iron . cu.J.s.tect i'ro;'l t11e valuen of E obtslncu g.fter the :neximum value of E bad been re$Ctled (as was observed. fox• permalloy), and by also assuwlnc tuat the-; correct saturaticn value of .Tz could. e obta in~d by ext:rapols ting tiie di; ta obta lneblc for .r .,,7 , one ob ;;;sino~ tor iron e .= c,.o s ± o. ,o)~ '.I'he error for tte measure:nen ts on iron v,ss co:::.puted iri ..., I • .... .;C • •. t ' ' \J J . ,.-- - , l t: ' ),, . - r, I 31 't, I:, ,.) rr . t::, • l [•\., . .. ' ' ..:.i.'8.J. 1' LS., 0 . roa'=r .. l, a1• . st. \; ' r, .... .. I;;: + + lo ,, 1 t~ ., c C -', ... a 1, ~ !'I , ) '" i~ s c ~ :. n I .) I., + -•~ .. ( 1.. j U~ ,. in ) (..;J. • ,.. i. -) 'ta J, . 0 • J., . J .... ~ + .J • .. I-':.,+ To v • , ·,. .: 9 v ·.,••;,_'; --- - -..--.. ---------- ., 0 ._.I" - ,1 . ~ ..,,,- ..1 .;J.. • ' a 1 , .:.. c .. is.• ·e - .., .... ~ lar lC .. . .;!. 'l, U 0 r. i~t"'".s !' )J 0 J ,.n •!~ ..... -. J l - ·1 .., v r t, f 01° 'l • v C. "' • J.' .J e ·x t, .. . to t V . , L~ ·~ C .• a ··t '"i\.. r"~,,. t, ~ ~ , .. ,, t"l(. - . us t r. . u1., l e L .c.Jl > ~ ' \, JC~, • 1.c 8 • v C ~. ... cv" (; . ~:. i.o ,-'-'- J" fl M ., : - t . .., ..,,. 0", l,'!('(, e' - !· ""' .,v'""'C .. : t..., .. f - ...-t,; - ir:s I v -' ' .. ..L.1:, ..... .J....., 'l ~he most difflcJlt qum1tlty to measure in this axpe- volcmet.erso slso ~tfficult to dater~ino b~cause it i.ng ms.gnetlc flelo.s , witl.l intense steauy cross fields . because of tn.e l~u• 0 e transverse cternagnetiz ing fe.c tor , ac-- curate measurements with & cylinder are difficult . Yore prect~e data might be obtained "ith the procedure used by Eozorth e.nd .)111 tnt1er . { 10 ) In possing., it is wor'ch notini: thet 11 ttle inforrrn - tion conccrninz trensvcrEe permeabilities has been published., Bozorth and .Gillin.,~cr { ''4) ~ have publlsheo. oata on the lrans\rorse pormea.blli ty 1r.. longi t wina.l fields varying in 1 .. strength from zero to several timeD tna t rH.H:lJ.cJ, to saturAte fields aa strong as .flve times tne saturation field stren :-.r th o .t"urt.ner i.n.f'or•i'l.ation on tnis phenornoo.on rnl 0tit b0 obtained by experimenters quite easilyo -88- I11:.,ensi ty of ... a::netization in a Unii'oi-•m ~J::Ltl.(l..J.l.g_ljl_, _____ ~ z ------- y lf a hoE\or;onoorts :lsotop1c ferromagnetic ellipsoid 1s ori- and i~ dir:~ctions, urnl if D;;i and Hi aro tlLc X COL,• poncnts, :tnaitte the ellipsotd, of tl o rn1cn0tic i·1d'1C= p is tht" per. -ee.bili t.r, then a well Jcnom1 !."1.:lnti.or~ 1 t·.1c0n ...;X ui anc1. .u.x ts ( 41) Now, tf Dx, Dy, and Vz r1r1;; the de; incn~ttzinc factors in the X, Y, and Z directions , if r.l~ :ts the .. io.010tlc in- inf'ini ty, and if Jx is t 1 1c intens:t ty of t: 1 r• 1 ngnot:lz~~t:ion, tlien the 1... elrition botw(, ,n tJ-rnso quautitles is <ns> ( 42) ( ,i~J) into tJ>qun tion ( 41}, ono obte.'.lns tt.nother equation t ... s t 01,pl ies to lnside t).1 e t, .ece 4'..,an ti.. t ie8 m"'u.iu.m is (44) (44) , one obtains .ro;; equ.a 101 (41), Appen ix I, one O.Jtalns ( 4'7) nnd .t'rorn equation (lti), poi,-~e (17), D = 2ir(1- S) X On suLstit ting for Dx frorr. <?quaticn (4:,) equa t1on { 47), :i.nto na ob-en Lns (49) 21T Fro!'l.l eq'.lat.ion { :ib), • ppenuix I, one cbta· ns (5)) .:ubstitutin ) for !.,x' from eqiatlon {43 ) into eqt.:a1.1ion (bO}, one obtalns • . B' )( (51) that p-1 B; -- l+ -P,➔ I (52) ,- -/A-,6 f'+I ,\ O\• , if &'is amal..L , 8,-_ C.. if ~ ls pr0ater than one (as duces up;:il'oxirna i:icly to µ-1 I -t f + I B' 1- S I<. (53) Divldln/ tt1roup;h by Hi.. an:.. further ai'nplifying , thi3 re•~uces approxir1stely to -\ _ --- ---~--- ---·-~- ________ 1 or;.•.1.a_c.,_·\lolt' .. _......., • .... u.:,, ___ ..c. q 1 ... oll. 0--- -- 2b 0- - - C)l tn ..;er ul . co:.1 it~ . Li~ - • .) 1 1~~'1 ...., .. , t.n 1,~ .. (: 1 tc -L.V ~l.4 - o., .... ·tu ~c. -"-~ se ,.,oe, t, .... o:. 01· t;r. 0 cc-:. r, ·d )., -~ ,a ne.l t!, :i.~::;io lnsl t .e I...;'! ... i C f- J + f+I I B'X -- I- s • r t '61 .B' )( \-\ 0 )( ~-Gr 1 .,.___ • t.na t 1~_1e rr.ca_71e tic lnd.uc t i on , ...,u to .ox (60) coiJ. !.s ::1 ven by du't1sti tu tin· tt.o e.xpross ion for i cp fro· eq:.iat l.:irJ. ( oO} to eq~atlon ,gl), one ootains •bstit 1.,1 .g 8 B, = _ _ _~_c.._E_x_l_0..._ _ __ X N(.) j C, [(1-+ t: )+ f (1- ~)] I·· one da11nta l's.J t .at C -=: b t '(' nere "if is sJtal. , tneH eq.:i.atlon (o:.:-/ siu)llftoa to "2 E B A E F QfJ~·~ 11~- ~-I I Fl E''I A' ~ r. Q I I B I se·.. t - •S,;l.i.;i1•lual ,no-~~10-_ 'Nas u~n.,J. to dct0r·.~ir1e t~.e fl:.;.x ., : i:r•2t..11 t 1e ZL!i.cn°Jt.:tc flux c:p trz>ua...J.L1g t;w cwll 1=-:T:..' P'l' , 5 calc:ila tcc1 o ·en.e 1·at1.o of tne flux cFs tnreaz..lng this c.:i.osely to t~10 flux cp l.~'lreac.,1 ~.g a ..t'cr-.n-... ia was d.evelofCC! fur t,1r vol ts.::e lnduccct in cl1e lar{~C. coil . .... t • ..., I I"- c:p, ', .s.i .:..::: ,'1,:"1:nct1.c f ,1. l'!O'..l t,c:..J'.l. c ... l:133:_:,, ti:, ~i. 'P.s - 2 ...• J~ :~ LJ I H;' + (4ir-D) J;_ .,. o ... - .B \ ~ 0-t \ J_ .. n r..s,,,;_, Q I' ........ ,.:').,: q. , ~i-. J r -~ .:J ~ (4ir-D) ~ :·t)" v (1..) t:· t.;i.: q...1~;:-.cit.7 'f ==A Rf Ax/i; ' :~ <1's -== 1; - 'f' '2 \, '.) . ) 'fs=2F & NH;,v-(1+~) +2(b+A)N--eH;&H; r4--1 - I f +I J - 2,r t:_10 I- fA+I ~ "'. --· f">' ~ ~ "t..i- 0 i. 3 s . .-oJ.)., t.,_I t. <.> re .ice, f- I J..1 -=- 27r f'--+ I H {I+ 0) ~ I 0 I ;. • ~() ' \ ,' I ..: ..),,t- cp-=: 4 lf Nb~ A (I+ S cp cp COS W-C 0 ~= J cos wt ( '1 VJ ct 0~ E 8 ../2 w rh 16 2 't'o I( • l' ( I ( ' f I .., ' , \ I ,, I . 1 ( -·--------, .... "' ......... - ,L • • vrns _ ec or-Jo .... o t-ke.- vas _/.i.ac,1., ln t ~ Sf.l1:e positlo.£ 1• ·:he deflection(:.'.'.) er "-' - .... ')1 - for the ,-• OJ -A roe - .1.02- 1. r. . ~e ter· Reoaing .Position 1 10 :i 10 - '1 ox. -= t1 • Sl ,-"BUS30$ . tet~r Hoau ii:0 Posit.ton 2 volts 11 0~ 21 x 10- 4 volts 2d 2d 12 3J 14 11 . zv x voltu e ::: l..~•H)~ 0 e h x __ lJ ., 70 gr.:.1sses 0 _ _.,...,.,.,.___,._ ___,.._ ........_, tex- ~. . oa.c ing $ ~ 1 ,.:eter f-:es_i_:np- ou i tL).n l Posltion 2 18 1J ', Vt:'.i'.'-tL e :;; ~.G 2,,_n e- .1,J ., 7_. 1 o '..,; •/'7• -'.,l 0 P.i:1:;·s ice. XIII 241 d (1~15) S ., 224 Pr0Ct'H)dfr1 2'.8 o:· ( 1,~-•44,) t~lE. A,l9!" _:.(;$,.i1 .• ca - Jemy of' 11.r-tt:. a:1J. ~•c lcncs~ 76 7 .:. 10J (lv44) A ., Fins te ln and ,. • .J' 0 -.::e Haa1:3 1.,./ert~ o d D Phy.a lct:i frt) !j 0 1l cc.,., J. .......~.;... { ; :·l ,, ) • ,..... #>'- • .., \!0:r'tL ,. ..... r, ?t.1ys ics 0-es .. 1'7 203 ( l;:jlt·) V01;-,b. o •·t .. , \ \.; PrL:ta lea Gvs o 1 r..,.. 173 ( l. ,:i .!.QI Vicrh .. i...). -.... r '. ~ 1-'h.ys:.c:s -10s .. 1e ,12~. ( 1~;,1.J) Proc0e0.1.:-:r:s oi' tt~e A·•ie:•!can i'\.cs 1..em.y o.f' ,11"" ta an ... ::'cl,:,acos ?I;! r;:01 ( 1 ..:4:,'J) t; l :., Pt1.ysical Ret L:ki Pr:.yslcal Heview F ~ BJ..0Cl1 140 J o H. -o Grlff1ths (j__f:37) 70 ( 1: '.<6) V?O lCO 1 \ .,_ ... cl, 1 •c·7) ,.. l Io _ _,.(c ) ( 1 ............ ?roccc(l~~a of ~1e ~oyNl Soclbty (h) lJ;;< 'I (l~}2e) pr'-~ C (] '8 ~. i11 t .:~- G, f t:1 0 . \13'.! :? ~) :._ C 0.(1 d,2.u:" o1: Ar•"'.,s an~ ':c..l<..1·1G:.;s V.I /t C e .. •104- 22 . " J . Bn1~nett Physical Rov:tew 2'7 115 (1026) R. Bozo1•th and Dillinger Physical H0v1ew 41 3<-15 (1032) 24 . s. J . IJarnett Physical Reviow 27 425 ( 1908) 25 . J . A • Osborn Physical Hav1ow 67 };51 ( 1945) 2::s . 0:.1 .