1197 



during' which the path is covered iniiier tiie influence of the attrac- 

 tion, approaches logarithmically infinite, ii^ does not then approach 

 ordinarily in the same way as ?^/, but to a much slighter degree, 



proportionally to 1 : log — . I.e. the temperature will approach 



much moie slowly than the Energy ; when the temperature still has 



a very small value, the "Energy" (i.e. E — E^) will practically be 



already = 0. The latter, namely, is only determined by ?/„" in the 



neutral point, whereas the temperatuie is determined by the time 



average of the square of velocities which has increased under the 



influence of the attraction. 



Hence relatively only exceedingly little supply of energy is required 



to augment the temperature by a certain amount: in other words 



the. heat capacity loill rapidly approach at loio temperatures. 



2f 

 When we substitute its value for 7-% u^'* ff^ becomes = -^ (/ — sY, 



m 



so that with -\;/*(/ — .s')" = ^j^ E^ and Nm u^ ^ RT (see above) we get: 



V,E 

 (7=0) RT= ? (10) 



^ ^ 2Nf{l-sy ^ V, E„ - ^ E, 

 ^^ '^ Nrnn,^ y^E-E,) E-E,' . 



Accordingly, by (10) T is expressed in E for the case of small 

 volumes and low temperatures. It is noteworthy that (10) is not 

 ^?«Ve identical with Planck's relation, but that the logarithmically infinite 



denominator log i^'r'^ -I- 2) = loq \ "- — h2 | would have to be dimi- 



nished by the small finite quantity log 2 = 0,69, in consequence of 



/ ■^E, \ 



which the denominator would become log (2^/* -\-^)=z log [ \-l I. 



\E—E^ J 



The original denominator log [ 'l<f -\- -— 1 would, therefore, have to 



be diminished by Vs ^^9 2 = 0.35. 



Different circumstances might be adduced as an explanation of 

 this exceedingly slight difference, which is for the i-est immaterial. 

 First of all possibly an exceedingly small modification in our funda- 

 mental suppositions concerning the mode of action of the attractive 

 forces, the logarithmic form of t^ being retained, might give rise to 

 a moditication in this sense that still a constant term is to be applied. 

 And in the second place the taking in account of Maxweli/s distri- 



