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Lorsque le document est trop grsnd pour Atre reproduit en un seul clich*, il est film* d partir de Tangle supArieur gauche, de gauche d droite, et de haut en bas, en prenant le nombre d'images nAcesseire. -Les diagrammes suivants illustrent le mtthode. 1 2 3 4 5 6 1.0 !!!l I.I lU Vi Ui 116 liO I 24 1.8 MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS STANDARD REFERENCE MATERIAL 1010a (ANSI and ISO TEST CHART No 2) FROM THE TRANSACT1CN3 OF THE ROVAL SOCIETY OF CAN ADA SECOND SERIES— igo3-igo3 VOLUME VIII SECTION III MATHEMATICAL, PHYSICAL AND CHEMICAL SCIENCES ON THE POTENTIAL DIFFERENCE REQUIRED TO TRODUCE Electrical Discharges in Gases at Low Pressure AN EXTENSION OF PASCHENS LAW By W. R. CARR, B A. FOR SALK dY J HOPE ft SONS, OTTAWA; THE COPP-CLARK CO., TORONTO BERNARD QUARITCH, LONDON, ENGLAN:) 1903 MB Section III I'.HV.' [161] i:\N!(. K S. »• XX. — On the Potential Difference required lo produce Electric Discharge in Uases at low pressures — .l;i Extension of Paschen's Law. By W. U. CAnn. B.A. (Coniiiiunicated by I'resident Li'uilon.) (Uead May 27. 190:;.) 1. Intkodictiox. The researches of recent jears have conclusively settled the general connection between tiie spark [joieaiial ami liic pri's- sure of a gas. Jt is now well known that as tin.' pressure of a gas diniiuishts the dillerenee of potential necessary lo produL-e a discharge between electrodes in the gas, a fixed distance apart, also diminishes until at a critical pressure the spark potential reaches a minimum value. It is further established that below the critioal pressure the potential difference required to produce discharge rapidly increases as the pressure is lowered. This connection betsveen the spark potential and the correspond- ing pressure of a gas has been well illustrated in a scries of n >es drawn by Peace,' who investigated the sparking potentials between a pair of parallel plates at pressures ranging from one-linlf an iitnin- sphere down to a little below the critical pressure. Among others, Strutt ■' and Bouty ' have carried on ilic iiivc.-iii,'-a- tion at pressures consideraljly below the critical point and the results show that, once the critical pressure has been passed, the rise in potential difference necessary to produce discharge is exceedingly rapid. The efTect of varying the disfarice lictween the electrodes v.-as first dctcrniined by Paschen,* who observed the existence of a simple law connecting the pressure at which ilischarLre took |i|m' e •,',iiii tin- corresponding spark i)otential and the distance Iieiween ili^ ilcird.li.s. Paschen's results showed that when a given potential difference was applied to two spherical electrodes whose distanci^ apart could be varied, the maximum pressure at v'lich dischaige occurred varied inversely with the distance between ti.o spheres. ' Peace, Pior. Hoy. Poc, Vol. r.2, p. TP. ' Strutt, Phil. Trans.. Vol. \K. p. r,77. ' Bouty, Conip. Rfnil., Vol. ICl (2), p. 443. * Paschen, Ann. d. Phys., Vol. S7, p. 69. ,^, KOYAL SOCIKT .' OF CANADA The ,„6. .< pre«ur« »"' "'j't"^ r 't 'l^^'.'d ^ ,hil, oon.id.r.bl., aid not "''°\t' "ho crUi, . procure h»d been U, p,e..u,e. higher to tlje .,i.ic.l pre.-'- ^,^__^ .^.^, ,.hr;;reritf::rj»...ddi.^^^^^^^^^ ee„.i.i.n. hoidin, ,er di.h.r„. - .^-^ -> Jo« pr ^^_ ^^ ^^^^^^, sr.p.r;":d" ,- ^.h.. j ';'«;--r «, £=. . ,„„ ,f which, fleeted fr.™ re.dmj. '*™.,'' °.'^„ J",,,,,., „/e»», .„re. are siven in the '"""JJ^ '„ee T , Sl^ eh»,en .re very ^eXi^e^r;"r':::d-'!^;;Lure .nd .p.r. .....h .hema be .eenst.nl in.ntily. it P.-b™'" l'" "<>■ i..m.i: -r I'kac ks 1:i>ii.T!«. _ difference in »olts , ot mcuurv. j 649 «»0 870 731 2 5 e S 2 5 082 «n •021 •030 205 oao •lOS 075 "" „ .e c.n,...,e the fct .nd „.ona ,. th». r^Us wber. the diiterenc. in .p.rk p.tent.nl u »■"» " '"f 'J'i," „a Igain. the the iirsl c..e nearly seven Innes that '° "» f ^J,,, ,|,.n p„,l«e. cor,.,,,„n.li»« to the «F^^. P"'™™^' ":;»,'i,;le. in the • "l\rfSS.°;rZlr Pe.ee-s rc.,ats point to ;h.e^^^^^^^^^ '' Peace. Proc. Roy. Soc. Vol. 52. p. 99. [cakh] AN KXTKNSION «»K r.\S(llKNS LAW les the exibisnce of the relation which Paschea found to hold at high pressures. Owing to the special precautions taken by Peace to obtain accu- rate values for the spark potcntiul-s it is possible to arrive at but one of two conclusions regarding the departure from Paschen's law indi- cated by Peace's numbers. Judging by the results, either the law ceases to hold when the critical pressure is passed or else the appa- ratus uatd by him in his experiments did not admit of an accurate measurement of the actual spark lengths corresponding to different spark potentials. A short discussion of the apparatus will reveal one considerable -defect. The object of the investigation:* of both Paschen and Peace was to determine the electromotive intensity requisite to cause dis- ilmrgf in a ga-. lliroughout tlie rang.' of presMirc^ invi-stignted by Pusfhen the diM'liarg.' always look plac>- alon- the .>lioMest distance letwocn the .'^plui nal elcitrodos and tlic eloctrornotive inUmsity requisite to break down the gas was, therefore, directly proportional to the spark potontials obtained by him. .\t points below the crit- ical pres.-iurc, as Peace's results indicate, discharge occurs more easily over a longer distance than over a shorter one, and if t^e values of the electromotive intensities necessary to break down a gas at differ- ent pressures are to be compared, it is necessary to know in each case not only the potential difference applied to the electrodes, but also the path between the electrodes along which the initial discharge occurs. To insure passage of the discharge over the same length of path Peace used plane parallel plates of very large diameter as electrod'*; but while i^ this -vay he obtained a uniform ficla of considerable extent, and ^o was able to obtain an accurate measure of the electro- motive intensity between the electrodes, he failed to make certain that the path along which the gas initially broke dovm was always confined to the uniform part of the he Irass plates, wa.s inserted. In the construction of the apparatus special precautions wore taken to insure that the plugs n y; mvsscd nululv airainst th. ebonite nng. As a result of this device that portion" of tho electric field which was not uniform was fc AN EXTENSn. UK rVSt'llKN?' LAW ■ee entirely tonfincd to tlip space ocjupied l>y ebonit •, so I .' this way it wa« rci iered iinpo.^^ible for a discharge to ;)«-ur li -e'l the t-on in -.Miy bi a iinifon.i I'.i'bl. The thil•I.m^.s ol the «'Im.iii;.' riii-. wliicl. >uld ; made ac.urato to ',,„„« mm.. tU'lLTinincI tlu' er by glash tubes sealed into the ebonite plugs, and these tubes were connected with the air snace by two very fine channels leading through the ebonite ring. Before closing the discharge tube, which was made air- light with ordinary commercial soft wax, tlie inner surface of the ebonite ring wa carefully rubbed 'vith glass pajr r to r'-move any coi.ducting material from its siirfa. . The potential differences ''..-cd in *e experimenis were obtained from a series of small stora^o colls, similar to those used in the Keichsanstalt, Herlin. As t, se eells have ii lari,'e cairiiity their voltage remained ■ 'nstaiit o . i )ni,' intervals of lime, miil as a loii- sequeiice it was p - ile to iiini. the readinj;s uith llie grwilest aceu- racy. The ivotmtiai diirereiuc. \wiv measured \i\ a We.-ton volimeter which was carefully calibrated by means of a potentiometer furnished with a standard Westtm ladir.inm il('iin';ii. Throughout the investigation the discharge chamber was con- nected in series with a dryiii;,' IuIju eo'Uaiiuii^ piiu.-pu.iric peiuoxide, a glass reservoir about two litres in volume, a McLeod pressure gauge giving readings accurate to Viooo of a mm., and a mercury pump of small capacity. By using this reservoir and the pump of small capa- city it was possible to diminish the pressure in the discharge tube by such exceedingly small amounts that it was easy lo obtain a series of discharge potentials over he whole range of pressures investigated without the necessity of admitting fresh gas to the chamber. In making measurements one terminal of the battery was joined to earth and the other terminal was eonnwied tlinugh a resistance of xylol to one of the electrodes of the disohargr- tune. Tlie other electrode was permanently joined to one pair of quadrants of a quad- rant electrometer, the second pair of which was kept to earth. In determining the potential ditl'erence nivc^ssary to produce discharge at a given pressure, the electrometer electrode was first earthed, a given potential applied to the battery electrode and the earth connec- tion of the electrometer elect, dc then removed. If, after waiting some minutes, no discharge passed, the operation was repeated with a slightly higher potential applied to the battery lee KOYAL SOCIETY OF CANADA electrode. This procedure was followed untU a potential sufficiently high was reached to break down the gas and cause a discharge. The passage of the discharge could be readily noted as it was accompanied by a violent deflection of the electrometer needle. The well known phenomenon of delay in the passing of the discharge, which has been investigated at length by Warburg,' was observed throughout the experiments. It was especially marked m /aoo- C3 -I 1. 1 1 i I 1 ^ ^ 1 ! 1 1 1 1 1 fj/roo- ? ! ! ' 1 1 i 1 ■l 1 1 1 ^^^^^"""^ 1 1 1 i -^ ^ ! 1 ;l s 9 /z Pressure in MiUimefhes the neighbourhood of the critical pressure, discharges being frequently obtained ten or even fifteen minutes after the requisite voltage had been applied. In every case, therefore, as the minimum sparking potential for any pressure was approached, a considerable time was allowed to elapse, with a given applied potential difference, before any increase was made. III. EXPKHIMENTS IN AlH. In the experiments on atmospheric air the whole discharge apparatus was first exhausted to a very low pressure and then refilled by fresh air, which bubbled in very slowly, first through a wash-bottle of sulphuric acid and then through a tube tightly packed with phos- ' Warburg, Ann. d. Phys., Vol. 62, p. 386- T 1 [carb] AN EXTENSION OF PASCHEN'S LAW 167 phoric pentoxide. The discharge chamber was then exhausted to about 20 mm. of mercury and allowed to stand at this pressure for a period of from eight to twelve hours. During this time the air was always in contact with phosphoric pentoxide in the drying tube, and was, therefore, entirely free from moisture when the measurements were taken. The first measurements were made with the electrodes 3 mm. apart, and the spark potentials were determined over a range of pressures extending from 51 mm. down to -35 mm. of mercury. The Fig.ll - Air Z 3 * fissure tn AfiU /metres of Mercury spark potentials corro.sponcling to the various pressures arv' rocoriltMl in columns 5 and C ui' Tal)le 1., and the results are loproscntcd jjrapli- ically in Fig. II., a. In making these determinations the precaution was always taken of allowing eight or ten minutes to intervene between consecutive readings in order to make certain that the air was in its normal con- dition when the discliarffc occurred. As can be set-n frnni tlic I'u'ure the curve is quite regular and exhibits all the peculiarities already noted by Peace,' Strutt,^ and Bouty". The curve, however, is carried much higher than those drawn by any of these experimenters, dis- charges correspondirg to I'otential dilTerenoes of over eighteen hun- dred volts being recorded. « Peace, Roy. Soc. Proc. Vol. r.2, p. 111. • Strutt, Phil. Trans., Vol. 193, p. rsi. ■ Bouty, Comp. Herd., Vol. 131 (2), p. 44S. 168 2 ce -r ■i'-S— 11 Spar ill \o m T b s ^ s ii ? e f. a 0, = t c .'■ - = u. UOYAL ,«)CIKTY (»K CANADA § S S I s 11 i ^ i G S = i i§ I i § ^, ,. — ^1 .^ * -ri r. r: 3 tJ "• !i? _ ., _ - i' '-: ri A -2 y, _ ft — 5E IS Tl C5 ? i! S S S X c S T^ rt ^: •:i Ti — — — 7" I- -^ ?! — park enti voll 5 95 3r X •^ *TC i ^ i^ t/1 o c a"" x*^ 4, O >. s = ? ?5 s !s X '.- ^ -* ^ = %i c ^ i- -r ■?! — — — — 1— t.S •" ■M - — 1- I- o '-. — « $! 2 ;- ;: r- = r. 5 ~ 5 ^ ? v? X >n ?' "■ ^j £.2 • -3 ., I = I -grs ! = .-: .- = = - ^' '5 r - ;-^ .^ 3 !2 S ? S (5 5 5 H b .'" S i! 1 £ ° C- < i: : 5 S S -, 2 :y ?! S I ? S 5 S Sf r ^ i(-Si = I- .- S - ■; - ',:: r ? 2 S ~ rt ?! ^ - ':?. ?■ 5 ■= p S -N o ^ !_: '.1 C; Lj ir i :; # ;,{ - '■'• 2 2 S i c. j; . t. « ~J " S ,•" *J ^ U i'-: a ii ci * !■- «5 '* "" ?^ - ?- I 3 r: X '- -T ^: ti *i *> '^ ^ S i ^r^ '_,,,-_-, ji I- I- 1; I- »j =; ;l S 5! ?i X fS X 1| S 5 ?i 1^ '^^R' '1 [carb] AN EXTENSION OF PASCHEN'S LAW 169 The distance between the electrodes was then varied and five different sets of readings were taken in air with the electrodes 1, 2, 3, 5, and 10 mm. apart, respectively. The complete set of numbers for these different spark lengths is given in Table I., and curves showing the readings taken over that portion of the range of pressure below 5 mm. of mercury are exhibited in Fig. 11. It is apparent from the relative positions of these curves in the figure, that at poiuts at and below the critical pressures, with a given potential difference applied to the electrodes, the pressures at which discharges occurred regularly decreased as the distance biween the electrodes was increased. But a critical examination of the curves and also a reference to the numbers which they represent show that Paschen's law is rigidly applicable over the whole series of discharge potentials recorded. For example, the pressures at which discharge took place with an applied potential of 1800 volts were, for the different distances between the electrodes, approximately:— Uintance between eleolrodcs in mm. Dischnrpe pressures in inin. of niercnrv. 1 2 3 5 10 lai ■5:« •:t.ji 2in 10.1 and it will be .seen that the numbers in column 2 are almost exactly in inverse proportion to the numbers in column 1. Again, with an applied potential of 500 volts (say), the approxim- ate pressure.s at which discharge occuired were:— Distance Ix'tween the electrodes in mm. Di>(cliarp;e potential in mm. of mercury. 1 2 :« 2 1 30 3 ■804 .5 517 10 2.10 Sec. III. , liW.'. 11. 170 ROYAL SOCIETY OF CANADA where the pressures are in the ratio 100: -55: -34: 22: 11, numbers which are again very nearly inversely proportional to the distance between the electrodes. Further, we notice that the spark potential corresponding to the critical pressure in all cases whs practically the same, 350 volts, and the values of the critical pressures for the differeni, spark lengths were, from Table I. : — Distance between electrodes in mm. Discharge pressures In mm. of mercury. 1 2 3 8 10 408 2-71 1 89 1-34 •679 1, are and these numbers while not exactly in the ratio 10: 5: 3: 2: still very close to it. j .i. i- i In finding the values for portions of the curves around the critical pressures he results given in Table 1. show that a sm..ll variation in potential d.«ference was associated with a relatively very larg.> change in the pressures, so that a very small error in reading the potential differed ce would result in a large error in the pressure readings. It is Intel asting to note, however, that even under these unfavouraole conditions a striking agreement is presented between the results obtained at critical pressure, and the results demanded by Paschens ' In order to make the agreement between the numbers demanded by Paschen's law and those obtained in these experiments still more evident, the results recorded in Table I. are again given in a slightly different form in Table II., where each potential difference is asso- ciated with the product of the pressure at which discharge took place and the corresponding spark length. Paschen* found that at high pressures these' products were constant for different distance? between the electrodes, as Ion? as the applied potential difference was the The numbers recorded in Tabic IT. show that the sainr law is rigidly appl'Pable to all pressures both bi,-h and low. > paschen. .n. d. Phys.. Vol. 37. p. 69. {cakb] AN EXTENSION OF PASCHEN'.'* LAW 171 B e o ) £ h g. t/j as" M?B 2l§gSI^I^SIigiii li H •J n < a. ■^ ^ a M s a u * 1 c/3 2 t s^iiiiiiisissgeig in lo Q S3 S S issS^islsisSliil ■-■'5 — n !t c/i 3 S S3 "^ "^ CO 00 ^4 CO 9 ^ i" •* '-I 06 n C^l (M EN ^ f ^ 5 s .- 5i w iQ 25 Cr t? yj iQ t- ® '-' S rt |J 2 S a o n ® X I o.= o 5 ec 0.00 =e = ? a 1 > :5^ 2Sg3SSF:E i.T 5l O t^ » 1* ^ ^ t- N ej ^ ^ ^ g ? K s a s Ti <0 ^ -^ l-^ tS ?i 35 :^ -»■ '?!'-« « 172 ROYAL SOCIETY OF CANADA A like conclusion must be drawn from the curve shown in Fig. Ill which graphically represents the numbers in Table II. In plot- ting this curve the products L spark lengths and discharge pressures were taken as abscissa; and the sparking potentials as ordmates. The regularity of the curve which represents the products for the five rig.lll-A,r ?M \ 1 r ^ — ' — i d - d '■ / rr^ni Z mrn |.J \ S mm ■\mt y 1 ' i 1 !_ ! 1 \% \ ^ ' ' i 1 I \ ^ X — i 1 K i i 1 i i 1 1 ' r ' — \ — — ^ ' 1 r 1 ■ • i P% jI2ta>£i~^ i 1 1 — 1 •^ •« - 1 1 HH-O. ']" 1 « mC— • «— « 1 ' ztc 1 s 1 ? different eloctrodi distances shows clearly that thero can be no doubt regarding the applicability of Pascbcn's law lo electric discharges in air at pressures at and below the critical point as well as to pressures above it. IV. Experiments in Hydrogen. In order to demonstrate, if possible, the generality of the law which has just been proven to hold for discharges in air, a scries of measurements were made on the spark potentials in th^ gases hydrogen and carbon dioxide. In these experiments exactly the same apparatus was used as in the previous experiments in air. Preparatory to making the measurements in hydrogen the appara- tus was first exhauste(! witii phosphoric pentoxide, before being led into the discharge chaml. r. Also, just as in the experiments in air, the gas was always allowed to stand for several hour-? (>t <■> pressure of about 20 mm. of mercury in the presence of phosphoric pentoxide, before any readinp were lecorded. Fi^ IV' Hydrogen Pressure /n M///'/n?/^s In the experiments T»'ith this gas readings v*ere taken for the same electrode distances, 1, 3, 3, 5, and 10 mm., and the values of the spark potentials and their corresponding pressures are given in Table III. These numbers are also graphically set forth in Fig. IV. We see from this table that the readings corresponding to the spnrk potential ISOO volts are: — Iiistanri' bctwcpii electrodes in mm. 5 m n schnree pressure mm. of morcnry. ill 260 1 St Htn .513 ■204 which pressures are in the ratio 9-9: 5 0: 3 2: 19: 1. 174 ROYAL SOCIETY OF CANADA i s § s o a s = s i s 1 § i •« a K: s » N — — O S I- "5 •I ^ .1 ^ 1 7 i i ^ a s i a i I § i !5 S I P- e = | ' " 3,5 b 2 Q a ■< I s E II e EC ^•Sl *|.S « fl r p G i, = = * ■^■s:^ '^IS s -• s S s u eg o. Sao i s; § i ^ § I S r- 3 w fr X o o S3 S S * 'a-s « s ^ CO ^ ts pH O (5« ^ -^ ^ 1^ lO U3 t^ "T^ S 3 2 C5 m M [cark] AN KXTKX8ION OF PASCHEN'S LAW 178 ' a e o ill sssags'^ssss =«|5 I a. 30 "N t* O 3 5 r: n 1^ ift r- is. '^ S I s U3 II 1c 111 I s i i g s i ^ ? S 5 — i« H ~ ri .^ ■" B ^ t^ p.- O ■^ O O ';> ^ Q a ® i »j 2 f ?5 "^ ""^ ^ "^ "^ s s S i* 3 = s 00 r* CD »« "^ "^ ^ S 5 b: = a >> " 1 s J3 ' !« > S P-H u J< 11 f^ 1 = ) •* S i ■ = o a § s I g g i i S ^ ^S I i 1 I Is 5 lis P ifj O CO 51 O as (P "9 "^ I— o « r- tf5 ■^ "3 t'* CO ^-i p 00 i"* * •* *** »5 -JC CA ;?3 ^ I i i ?"• ''=^* i I 5 L- I- c ?o r- O T U o '^ ca A o *a CD CO r1 o ■^ r^ mm ^^ *^ S ^' ^ 00 I-- i 1 II Spark poteulia in voltx S i i ■cs: a oi^ j4 tU l^ ■?! ^ ° st: _■ e & ■§is M .-I M fill ^ggi^SSIiBr^ ■« ■js is ^ •* o n ?4 176 ROYAL SOCIETY OK CANADA Again, with a spark potential of 500 volts, the readings give: nutanre iM'twefii i'lfCtr(> 3: i-8: :>-3: 10: 1. The minimum spark potential in hydrogen was about 280 volts and tho critical pressures corresponding to the different spark lengths were: — DiBtunce liotwi'en electrode/ in mm. 1 i 3 5 1(1 Disclmrite pro-surfs in nun. of nieri-ur). 10 :i .-. o:i 4 02 2f« 1 10 where the various discharge pressures are once more nearly inversely proportional to the distance between the electrodes. To indicate further that the law Ls applicable at all points, a table of products similar to those recorded for air was calculated, and is given in Table IV. A single curve, Fig. V., represents these live sets of readings, and again the close grouping of the different results about this common curve shows that the law is equally applicable above and below the critical pressure to all spark potentials. It is evident, then, that with hydrogen just as with air, Taschen's law is rigidly applicable over the whole range of pressures. V. E.xrERiMESTs IN Carbon Dioxide. These further experiments were made with a view to corroborate the results already obtained in air and hydrogen. The same apparatus as had been used with these two gases again served for the experi- ments in carbon dioxide ana the distance between the electrodes was varied as before, so that readinss were obtained at the five different 1 [CARRJ AN EXTEN8I0N OK I'ASCHKN'S LAW 177 O^ V - Hyd/Zj§e/7 *1 mati I ^ 1 i _ 1 . _ 1 . .. _ t j: 1 1 • 7 ^*^ 1 \ D £ S mt ) L 1 1 v\ V \ \ ». \ V r V l\ \ \ s«- -- \ ^ :^ ^ ^ ■ > s^ =^ 2 J ,78 |t.,YAI. M«lI.TY(»r{\N.M>A , . .. - „iiitmin The carbon dioxide was prepared di-lai-ce», 1, -i, 3, o, and 10 mm. /"^^ •=" -j.^^ ^^ ^ried ,.y treating -«^'\-^\^>'^'"*=tbire of wntrJd ^^^^^ through of a bulb of phosphorus pentox.de for Beveral hours^ The complete set of results is given m Table V. and the corre ine toiiiH»=i- ^ compare the i.niullniT curves set forth in rig. v 1., anu u we ufeo. i M arge FcLres and spark lengths corresponding to anyj^- of the applied potential, the same law is seen to nold hero also with cscn uieater rigidity than in the olhnr cases. For ISOo'vnlts the figures arc approximately :— ____^^^^^^^ Distance iH-tween elrctro * . ',' ,^c« JipW'iJ": ISO 140YAL SOCIETY OF CANADA VI. Sl'Aliii I'OTKNTIAI.S WtTII DIFFERENT ELECTRODES. li has now been shown, using brass electrodes of constant size, thai lor discharges in a unifonn iield in any gas, tlie values of the spark ])otentials are determined solely by the product of the pressure of the gas and the distance between the electrodes. From thi^s result it appeared that if the size or material of the electrodes did not alfect the results, the spark potentials were dependent only upon the (juan- tity of the gas per unit cross section between the electrodes. In order to determine this point the brass electrodes which had been used up to this time were replaced in turn by electrodes of iron, zinc and aluminium of exactly the same size. The resiil's of the experiments showed that there was no variation in the dilierent sets of readings and it was evident that there was not the slightest effect produced in any case by a change in the material of which the elec- trodes were made. Ill order to sec if the size of the electrodes affected the values of the s]iarlc potentials for the different privssurcs, provided the dis- charge look place in a uniform field, a reduction was made in the surface of the electrodes exposed to the gas. This was done by replacing the ebonite rings C, C, Fig. I., which had an inner diam- eter of .3 cm., by others whose inner diameter was but 1 cm. By this device the areas of the electrodes exposed to the gas were reduced to about '/,„ of their value in the early experiments, and the condition that the discharge could only take place in a uniform field still held. Fsing this apparatnf=. with air, no difference could be observed in the values of the discharge potentials corresponding to thr> different pres- sures, and it was therefore certain that the value of the spark potential was in no way influenced by the size of tlie electrodes. Tt is therefore clearly established that the only factors that affect the spark potentials are prcssur(^ nnd the distance between the elec- trodes, and hence Paschen's law is most accurately expressed bv saying: "That, with a given applied potential difference, discharge in a uniform field, in any gas, at pressures l)oth above and below the critical pressures, is dependent solely on the constancy of the quan- tity of matter per unit cross section lietween the electrodes." Every assistance towards the carrying of my research to a success- ful issue has been given me throughout by President London, and I gratefully accept this opportunity of thanking him. I also wish to re- cord my appreciation of the many kind suggestions of Professor J. C. McLennan, in whose laboratory the experiments were performed and to whom I owe much for their success. 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