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Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW) Citation: Heuse, W. & H. Kamerlingh Onnes, On the measurement of very low temperatures. V. The expansioncoefficient of Jena- and Thüringer glass between +16° and -182°C, in:KNAW, Proceedings, 7, 1904-1905, Amsterdam, 1905, pp. 674-684 This PDF was made on 24 September 2010, from the 'Digital Library' of the Dutch History of Science Web Center (www.dwc.knaw.nl)

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Physics. - H. KAMlmUNGH ONNJ<:S aIld W. HEUSE. "On t!te measu­rement of ve7'Y low temperatltres. V. Tlte expansion coefficient ot Jena anrl TluÏ1'in,qel' glass between + 16° ltnd -_182° 0." Oommnnil'ation N°. 85 from the Physieal IJaboratory at Leiden.

(Communicated in the Meetiug of June 27, 1903)

~ 1. At Leiden tile hydrogen thermometer (cf. Oomm. N°. 27 May '96) is taken as the standard for very 10w temperatures. To reach the de~l'ee of accuraey otherwise obtainable with this, it is necessary to 1010W the expansion eoeffieient of Jena glass 16m to about 1%

, Bence we have determined the two eoefficients in the qnadmtic formula assnmed for the linear expansion of glass below 0' C. At the same time we have, in preeisely the same eil'enmstances made a similar determination for the Thuringer glass, from which the piezometers mentioned in Oomm. N°. 50 (Jnne 99), N°. 69 (April '01), and N°. 70 (May '01) were made, in ol'der to be able to calculate and applJ' the correction f'or expansion to the resuIts atk'tined with these piezometers.

Some time previously we made measurements on expansion coefii­cients, among others on p1atinum. The va1ue for this metal was l'equil'ed for the reduction, from the measnrements mentioned in Oomm. N°. 77 (Febr. '02), of the galvanic resistance at low tempel'atures.

But the results whieh we have lately obtained for th~ two above mentioned kinds of glass appeal' to us to be the first that are worth to be published; the final l'eduction of the measurements named above was postponed till the requil'ed accmacy was reached. However the measurements on platinilm must be l'epeated.

Although the field of measurements at 10w temperatUl'es is hal'd1y touched, still we consider that in this field pl'eliminary and app1'ox­imate "alues are wo1'th 1ittle. In the majo1'ity of cases appl'oximate values of this kind ean be obtained by extl'a,polation, and thus only those determinations whieh are accurate enough to allowajudgment on the question whether sueh an extrapolation is allo wed or not, are really of use in advancing our lmowiedge. We have hence

. al'l'anged our obsel'vations 011 the expansion coefficient so as io reach 1

an accuracy of 200'

For general the investigation of expansioll at Iow teUlperatures it will be required to determine on the one hand the linear coefficient of solids and on the other the absolute coefficients fol' those substances, which remain Iiqllid to very low tempel'atmes, e. g. pentane, in such an hydrostatic mannel' as DUI,ONG and PETIT'S (impl'oved by REGNAULT).

The determination of the l'elative expansion of the Iiquid chosen can

&ti •

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then serve as a con trol and as the starting point for further meaSUl'e· ments. The pl'esen t in \'estigation fOl'ms the fil'st part of this general program and gives the linear expansion of glass with an aeeuracy whieh suffiees for our present purpose. From the deseription of our measurements it wiII be seen that with practieally the same apparatus and in nearly the same way it will be possible to determine the absolute expansion of pentane.

§ 2. We bave determined tbe two roeffieients a and b in tbe fOl'mula for the linear expansion L = Lo (1 + at + bt2

), for the two val'ieties of glass from three obselTations for eaeh. These were made at crdinal'y temperatul'e) at about - 90° , C. and at about -180' C., by measuring direetly and at the same time the lengths of the rods of the two substa.nees.

The rods were drawn out at eaeh end to a fine point whieh eould be aecurately observed with a mieroscope. At the bottom and top, the two rods project out of a v01'tically plélCed cylindrical vessel. The bath is closed at the 10wel' end and is filled with a liquefied gas giving the l'equired temperature. Care is taken that the points shall be kept as nearly as possible at the temperature of the surrounding air, and also th at the air between the points and the objective of the micl'oseope shall be at the same temperature. The lengths are then read directly again&t aseale by a eathetometer arl'anged as a vertieal comparator.

Although this arrangement gives a convenient method for the deter­minatioll of length it necessÏtates a considerabie difference in temperature between the middle and the ends of the rods. To correct for this, use is made of the l11ethod employed in Coml11. N° 83 (Febr. '03) for the deter­l11ination of the COI'l'ections along a piezometer or thermometer stem. This depends upon the use of a nniform platinum.wire wound uniformly ~'olmd the rod. lts use depends upon the assumption, that the change of resistance of a wil'e wounel in this manner is nearly propol'tional to the l11ean change oftemperatnre of the rod. This will be furthel' considel'ed in §4. I/ Aftel' this general view we may considel' cel'tain details.

1 st • ZIlte glass rods were about 1 m. long and had diametel's of 5 mmo 1). Round these 0.1 mmo thick platinum wil'es were wound spirally and soldered to brass l'ings A, B, C, D (PI. I fig. 1.) whieh were tightened by scl'ews.

Between Band C, the part wbich was immel'sed in liquifiedgases, there were 140 tm'ns with a pitch of ab out 0.5 cm. Between AandB or C and D wh ere the tempel'ature changes rapidly there were 25 anel 40 tm'ns respectively with a pitch of 0.25 cm. Care is taken

1) A platinum tube provided with glass ends similar to those described above was used for thc determinations on platiuull1.

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that the pitch l'emains constant in each section A to B, B to C, or C to D. At A, B, C, and D platinum wÏI'es a, b, c, d, e, J, g, and h about 15 cm. long and 0.5 mmo thick are soldel'ed in pairs. At tlle o'ther ends they are connected to cap per wires. In order to pre­vent fau1ts in insulation the spirally wound wires lay in shellac they were also covered with a layer of tissue paper for purposes of pro­tection. The pOl'tions A to Band C to D were enveloped in succes­sive layers of fishglue and writing paper to about a thickness of 0.25 cm., in order that the distribution of temperatUl'e shonld be as even as possible along the rod. This protection was found to be proof against the action of either liquid nit1'ous oxide or oxygen. Ta allowaf contl'action on cooling the paper layers were only pasted togethel' at both ends.

2nd• T/~e cylindrical vacuum jacket. Tbe bath for the liquid gases bas the form of a tubuJaJ' vacuum glass. Usually vacuum glasses are made so that thel'e is but one edge connecting the cooled and uncooled walls. When it is necessary to l'emove liquid at the bottom of a vacuum glass the Iower sUl'faces are connerted by a spiral tube. However we required something qnite different i.e. a double-walled tube open at both ends and capable of holding a rubber stopper in one. If such a vacuum tube were made by blowmg simply together inner and outer walls it would cerlainly Cl'ark when cooled, owing to the dIfferent e:&.pan­sion of the outer and inner waIls. Also it did not appeal' to be pos­slble to make the outer wall suffieiently elastie by blowing several spherical portions in it (see fig. 1).

?

Fig. 1.

Rence the outer wall was divided by a thin brass case Vl , Pl. I, which allows a compression Ol' expansion of 2 mmo This copper box was inserted by platimsing and coppering the two glass surf aces and then soldering them to the copper box. The vacuum tube thus produced was silvered and evacuated in the usua1 mannel'. In the first arrangement the top was left clear in order to allow ofthe observation of the surf ace of the liquid. In later al'rangements we preferl'ed a float, Such tubes with compound elastic wallt:! appeared to be suitable for Ollr purpose and will probably also be found to be useful for the solution of various other problems. An example of how easily tensions arise which cause such glass apparatus to crack, was found when the rubber stoppel' at the bottom was pushed in too faro On admitting the liquid oxygen the rubber became hard bef'ore it had l'eached the temperature of the liquid, which tempel'ature the glass immediately above had reached

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all'eady, and the lowel' rim cracked olf. Later we made the connec­tion tube and the stopper more elastic (cf. HP!. I fig. 2) by inserting between them acollar formed of severallayers of paper glued together at the borders. In this way a closure was obtained which was perfectly tight, a quite necessary item, for otherwise the eseaping liquid streams past the reading points as a eold vapour, which disturbs tbe uniform distribution of temperature supposed to exist in the ends of the l'ods and obtained by continually blowing air on to the points whieh is necessary a180 for keeping them dry. At the top, tbe rods are \ bupported sideways 80 that no strain is eaused in thcm. They are protected from the eold vapours which a!'Îse from the bath. From the front and side elevation of the uppeL' end, FIg. 1, the arrangement of paper used for tbis protection can be clearIy understood, and the course of the vapour can be followed as it streams over the wall of the bath through channels of eardboal'd. This arrangement has mOl'eover the advantage, that the outer sUl'face of the yacuum vessel is also cooled. This is of great impol'tance in the beginning. The eoid gas and cooled air are so conveyed away by varions paper sereens, that they do uot come info the neighbourhood of the cathetometer Ol' the standard scale, and also that air at the ordmary temperaiure remains between these and the points. At the commencement the liquefied gas 1S introdueed in drops through an opening in the eork at the upper end, and aftenval'ds carefully in srnall quantities. When the bath is onee fuU, fresh liqmd is continual1y added in small quantities to keep the level at the same height. The liquids used were nitrous oxide and oxygen obtained in the manner deseribed in Comm. No. 14 (Dec. '94) and No . .51 (Sept. '99). In both cases considerable purity was aimed at, in consequence the temperatul'e of the bath did not change during the measmements. There is no doubt that the temperatures at the top and the bottom of the bath were not the same but this introduced no difficulty sin ce in the calculation only the mean temperature as determined by the platinum resistance was required.

31d , Tlte compamto1' (cathetometer and scale). We used the instl'uments which are described in Comm. No. 60 (Sept. '00). The scale was very eal'eflllly enveloped in wool and paper to pl'otect it from changes of temperature. lts temperatme was read by two thermometers divided into 1/20 and symmetrically placed above and below, while the room temperature was maintained as cOllstant as possible. The telescopes were pl'ovided with the microscope objec­tives which had been used fol' the measurements on the viscosity of liquid methyl chloride (Comm. No. 2, Febr. '91) and wbich

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can be used at a distance of 10 cms. In this case one l'eVOlll­tion of the head (divided into 100 parts) of the micrometer screw (ef. Comm. No. 60 § 15) was equivalent to 60 to 70 p. The levels on the telescopes were cal'eflllly cahbrated; at the dis1áÏlce nsed, one division on the levels corresponded to from 4 to 6 (t and tbe uncer­tainty in reading was less than 0.2 division Ol' abollt 1 p. Aftel' each setting, 30 seconds was allowed to elap5e before reading and former measurements have shown that this is sufficient for the attainment of equilibrium.

The field of view of tbe microscopes was a1so investigated by measuring at various points a 1/5 mmo scale, but no il'regulal'ity conld be found.

4 th • Measw'ement of resi~tance. The doubled condllcting wh'es a, b, c etc. at tbe ends of each measUl'ing wire AB, ete. (cf. PI. I) were lead to eight cups of mercury for each rod, which cups cOllld be connected in pairs to the wÎI'es from the WHEATSTONE bridge. By measuring

u\=a+AB+lJ

W 2 = () + AB + d

Wa = a + () ~1!4 = b + d

the resistance of the wil'e AB

can be determined 1). The galvanometer with reading scale (see Comm. N° 25, April '96) had a resistance of 6 wand a sensitiveness of 2.5 X 10-7• Thermoelectric forces in the circuit of copper leads, platinllm leads and platinum resistances are uuavoidable, they were, however, only small and conld be eliminated.

§ 3. Survey of a determination. A complete determination com­prises focnssing the microscopes, referring to tbe standaI'd scale, and reading the thermometers, as weIl as the various determinations of resistance between A and B, Band C, C and D.

In tbe following table all the readings for the determination of length of the Jena rod in liqllid oxygen are given. Column A contains the readings of the micrometer heads, B the corresponding positions of the levels, C the nearest division on the standard scale, D and E the micrometer and level readmgs for this and F the temperatures.

1) In our ease the influenee of the shunt between A and B, 0 and D was so small that it eould he negleeted and then wa + W4, eould be determilled at onee.

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TABLE I. JENA GLASS

2,)}3 03 I .ti. I B I C I ])

I E I ---1,1

HdU' I I I POInt b,-Iow 27 82 6.1 16 14

Mllllmetcr 116 ö4.23 52 117 20 07 51

POJllt ubo\c 1944 6.1 16 70

M11I JIn e tcr 1127 33 33 5.8 1128 1714 5 8

p Olllt below 27.83 6.0 16.54

\' above 19 47 6.0 I 16.80

lh45' I I The l'eadmgs on the micrometer head are now reduced to a

standard position of the level and the temperatul'e readings are (,ol'l'ected. This gives the following.

TABLE Il. TENA GLASS

25/5 '03 ! d I B I c I JJ

1"&U I Pomt below 2781 16.37

Mllhmeter 116 3430 117 2015

Pomt above 1943 16 63

MIIIim(\ter 1127 33 35 1128 17 16

Point below 27 83 16.47

" above 19 47 16.73

11,45

Point below 116.458

" above 1127.859

Length 10H.4C1

Nothing new was in Ihe method nsed fol' the determination ofresistance. Tt IS llence only necessal'y to give the flnal results, as th(:' means of the val'ious meaSUl'emellts redllCed to the same time.

To calculate the tempel'atnre we have nsed the following preliminary fOl'mula, obtained in the measurements described in Oomm. N°. 77

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B

Me:m timp.

20 V. 4410

22 V 3h15

23 V. 11'15

25 V 12hlO

25 V. 1/15

26 V. 3k10

C Tempe sca1e. I

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TABLE lIL JENA GLASS.

IO.,/B

10BO

leOD

4.82

8.77

4.37

6 29

33 95

10.17

TABLE IV. JENA GLo\SS

iJ E

15 58 1012 594 10-12 587 top 6 66 6.29

63

.69

595 588 middIe 36 04 33 95

593 587 bottom 10.66 10 17

17.74 1011 834 1011 865 top 5 10 b 29

16.03

1782

1800

.83&

.844

868 mlddie 22 15 33 95 - 87 87

880 bottom 698 10.17

18 32 1011 827 1011 808 top 5.01 6 29

1841 815 .858 mlddie 22.13 33 95 - 87.87

),= 78 1

bottom û!)J 10 17 ).=

16.68 1012.567 1012.579 top Ü Ci8 6 29

16.68 .573 .585 mlddIe 3Ci 00 33.95 Hl 41

bottom 1072 10 17

16 08 1011.408 1011.409 t()P ~ 82 6 20

.13

.17

411

406

.413 mHldle 8 77 33.95 -182.9::1

.409 bottom 437 10.17

10 38 1011.407 1011 414 top 4 68 6.21

.55 .401 .411 middie 877 33.95 -18298

82 0

1'.= 2 18

1.= 51.0

1'.= 18.3

bottom 4.34 10.17 1.= 52 8

17.30 1012 565 I<H2 588 top 670 6 29

49 .567 .594 11llddlc 36.12 33.95 16.64 1

bottom 10.66 110.17

._...!..._L-J

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with pJatinum wire of the same kind as that used in the present instance

Wt = Wo (1 + 0.003864 t - 0.0 6103 t') thus tBC = - 182°.90.

The calculation of the temperatures of the projecting portions from the values WAB and WCD wIll be described in § 4.

In the following table the final resuIts 1) fol' all the determinations are given, the standard scale at 16° C. being taken as the reference length. Column E thus rontains the values for the l'od lengths l'edllCed to this reference. We have used as the expansion coefficient of bra&s between 16° and 17':: the value 17.8 X 10-6• Column 1 refers to the ends, and its contents wil! be considel'ed in § 4.

TABLE V. THURINGER GLASS.

c D E

20 v.1 2h45 15 12 1013 107 1013.091 top 6.47

44. .108 .098 middle 36 53

bottom 10 21

22 V. 12"30 17 08 1012.244 1012.263 top 4 59

.33 .238 .262 nlldd1e 22.55

.37 239 .263 bottom 6.51

.35 .240 264

23 V. 11k40 16.68 1013.086 HH3098 top 6.52

.68 .088 .100 mlddIe 36.70

bottom 10.23

25 V. 3k20 17 04 1011 744 1011.763 top 3.81

.12 .748 .708 mlddie 8.95

.19 .740 .761 botlom 5.29

.25 .738 .760

26 V. W50 10.56 1013.095 1013 105 top 0.46

.67 098 .110 lTIlddle 36 60

I bottom 10.18

G

612

34.53

9 68

6.12

34 53

9 68

6.12

34 53

9 68

6.12

34.53

9 68

6.12

3453

9 68

15.08

-87.71

16.36

-182.7

15.61

9

À= 85 4

À= 1.0

À= 25.9

1) The numel'iC,11 values at e slightly d.tlerent from [he values given in the origiual Dulch paper accordtng 10 a new and mOle exact calculatioll. The fin al results for the dilalation glVen III the original al e quoted § 6 fooillote.

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§ 4. Discussion of tl~e 1neaSU1'el1wnts. In ~ 2 we have already remarked that the mean temperatul'e of the platinllm wil'e, wound round lhe portion BG of the rods, which is at the temperature

of the bath, may, with sufficient accuracy, be put as equal to the mean tempel'ature of that portion of the rod

(l. ~ itseJf. Throughout this Jength, the differences of temperatnre or the Jength over whirh they are found, are on the whole

À srnall, so that only the mean tempel'ature comes into .~ . . 0 account. Further consideration is however necessary in

respect to the relation of the temperatm'es of the enels AB and GD anel the resistances determincd.

Fig. 2. Let us suppose that the level of the liquid reaches to a position À, fig. 2, and hence that t11e upper portion of AB is outside the liquid. We may suppose tlw,t, for the length A, the rod has the tempm'ature of the bath. The resistance of the wire between Band I.. is then 'Wt = 'Wo (1 + pt + qtJ

) 'v here t is the tempel'atllre of the bath. Also we may suppose that at A, which was damp but just free

from ice, the temperature was about oa C. Further let us suppose that between Î. and L the temperature gradient is linear, in othe1' words that the external conduction may be neglected in comparison with the internal conduction of the glass. There is every reason to assume that this was true to the first approximation, since the glass l'ods were weU enclosed in paper the conductivity of whi('h is about 1/100 ofthat of glass. Then, neglecting the ronduction of the platinum wire, itself the resistance of an element of the wire between À and L is welte,

x=L

where w = Wo (t + lJtx + qtx 2) anel the whole resistance }velJJ. x=À

Further for x between 0 anel À, tr= tI' between Î. anel L, t

tx = t - L-(x-I..) and for x = L, tx = 0, so that -.I..

l , W AB = W(AB)o L (1 + pt + qt2) +

J;=L

+ J W(AB)D1[1 + P (t - L t .I.. (,'IJ - ).)) - q (t - L t .I.. (,11 - A))]d,U. x=À

From this J., the only unlmown, can be obtained. One of the most unfiwourable cases, that for the upper end of the Jena glass rod in N20, shows when calculated that tlle linear farm for the resistance can be employed in our measurements without difficulty, in place of the quadratic fOrm. We fOlmd Î. = 8.4 cm. with the

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quadratie anti). = 9.0 cm. with the linear formula. The uncertainty thus introduced into the determination of length, is Iess than l(l.

In order to determine the influenee of varions suppositions with regal'd to the distribution of temperature in the rod, we have ca1cu1ated tlle change in 1ength ",hich would be produced, if the temperature was - 87° C. fl'om 0 to J. and 0° fl'om .I. to L, in place of the distribntion assumed above. The change was hardly 0.11t and tbus lies within the degree of accuracy. However an important con trol indispensable for more accurate detel'minations would be obtainecl by measurements on a rod with similal' ends AB and GD, but where BG was only a few centimeters long 1).

To apply generall.y the method of this section for the determination of mean tempel'attll'e it may be necessary to subdivide the portion of at variabie temperatl1l'e AB into lllore parts wbile for each of these separate portions the resistance would have to be found. In our case tbis "'ould have been an unnecessary complication.

§ 5. Infiuence of en'01'S. These can be fuUy considered by the LI-Lt1 1

aid of ä = -=-....:. Lt t-t1

The accuracy of the cathetometer reading ean be put at 2~t (tlle wh01e contraction heing 1200 (l). This gives dä = 2 X 10-8. For the mean temperature of the porti on BG the error is certain1y Iess tban 0.5 deg. G, whence dä = 1.5 X 10-8, and for that of the ends we founel 1 tI. Henee a gl'eater nncertainty than dä = 4 X 10-8 is not to be expeeted. Although the dlvision of this error between ct anel b cannot weIl be made, it IS certain that an error in tlle temperature detel'minatioll has by fm' the greatest influence on b.

§ 6. J?inal J'esults. For the observed lengths Luw)! at the tempe­rature tNO! in nitrous oxide, Lto! in oxygell, aud L I60 at ordinary tempm'ature we have the three equations

LtNo~ = (LBCo + ).1 + ).s) (1 + atNO! + bt'NO) + + LJo + L50 + (Lso - .l.s + L lo -).z) (1 + ~ atNO~ + ~ bt2 NO~)

and two analogous ones fol' L1o! and L 160, with LECu = 840 mM., L lo = 97, L.o = 59 for Jenaglass, alld Lneo = 834, L /o = 96, LbO = 60, for Thüringerglass. For LBC'o (the Iength of the part BG in the iigure at 01 C.), Llo, L.o (th at of the parts CD and AB in the figul'e) are assumed approximate values; the exact values L4

0 and L jo to be

1) For Jenaglass in oxygen we found a negative vulue of "I wc m,lde lhel'efore the calculution on anolher supposition viz. th at fl'om A in lhe dilection of B lhe rod has the tempeL'alure 0) over a length of ).' cm. (cf. Table IV).

47 Proceedings Royal Acad. Amsterdam. Vol. Vil.

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ascribed accol'dingly to the lengths at 00 C. of the points pro,jecting beyond A and D follow from the equations. These equatiol1s givc L 40 + L50 = 16.587 and L 40 + L 50 = 23.095 for Jena and Thül'inger glass respectively, and further; -

L = Lo (1 + at + W)

V = Vo (1 + kl t + k~ t') Jena glass 16111 a = 7.74. 10-6,b = 0.00882.10-6

k l = 23.21. 10-s,k,= 0.0265. 10-6

, a = 9.15 10-s, b = 0.0119 10-6

Thüringer glass (nu. 50) 1 I k l =27.4510-6, k,= 0.035710-s

The value found for Jenaglass iBlIl differs much fi'om that obtained by WIEBE and BÓTTCHElt') and from those obtained aftel'wards by THIESEN and SCHEEL 3) for temperatures between 0° and 100'.

Physics. - "Tlte motion of elect1'ons in metallic bodies, lIl." By Prof. H. A. LORENTZ.

(Communicated in the meeting of March 25, 1905).

§ 16. We may now proceed to examine the consequepces to which we are led if we assume two runds of free electl'ons, positive and negative ones. We shall diRtinguish the quantities relating to these by the indices i and 2; e.g. NI and .N, will be the numbel's

of electl'ons pel' unit of volume, mI and m, thei!' masses, 2~ and ~ ft l 21/ 2

the mean squares of theiI' velocities. For simplicity'& sake, all elec­trons of the same sign wiH be supposed to be equal, even if con­tained in different metals. As to the charges, ~lCse wlll be taken to have the same absolute mIne for all particles, so that

8, = - el' • • • • • • • • (48)

OUI' new assumption makes onIy a slight diffel'ence in the fOl'mula for the electric conductivity; we Ilave onIy to appIy to both kinds of electl'ons the consideratiolls by which we have formerly found the equation (21). Let a homogeneolls metallic bar, havillg the same tempel'atul'e throughont, be acted on in the dil'ection of it& length by an elet'tric force E; then, ,just as in § 8, we have tOl' each kind of electrons

1) In the original was given Jena 16III a = 7.78 b = 0.0090 Thilringer nO 50 a = 9.10 b = 0.0120.

~) WIEBE und BÓTTCHER. Z. f. Inst. k. 10, pg. 234. 1890. 3) THIESEN uud SCHEEL, Wisse Abt. der Ph, techno ReichsanstaH. Bd. II S. 129. 1895.