073 



an ideal inidare, agjiiii leaving- molecular lolcitions and iiitiainolecular 

 motions out of account, may be easily dei'ived it' Gjbbs' theorem, 

 according to which the entropy of such a mixture is obtained by 

 calculating the entropy for each component as if it were present by 

 itself in the volume occupied by the mixture and adding the values 

 so obtained, is supposed to remain valid \vlie)i the equipartition 

 laws no longer hold. We then obtain : 

 «. for loiv temperatures 



S=:ccT'V :S -^, (16) 



(?. for /u(j/i temperatures, retaining the first term which gives a 

 deviation from the equipartition laws: 



13 3 



;i^(^TF^/3)-2.^.V/.J/,-2| (17) 



If at constant volume the temperature continually decreases, at 

 sufficiently low temperatures (for densities of the order of magnitude 

 of the normal density at extremely low temperatures, cf. Suppl. 

 N". SOa § 5^) a positive deviation from the equipartition value begins 

 to develop itself. This deviation finally causes the entropy for a 

 mixture also to approach to proportionally to 7'' as shown by 

 (16) instead of becoming — oo. 



Physics. — ''Further experiments with liquid helium. H. On the 

 electrical resistance etc. {continued). VII [. The sudden disappear- 

 ance of the ordinary resistance of tin, and the super-conductive 

 state of lead." By Prof. H. Kamerlingh Onnes. 



(Communicated in the meeting of May 31, 1913). 



§ 13 ^). First observation of the phenomena, a. Passing from the 

 investigation of the super-conductive state of mercury to that of the 

 change in the resistance of various other metals when they are 

 cooled to helium temperatures, although I hoped to find more super- 

 conductors, I did not think it likely, judging from our experiences 



^) The §§, tables and figures are numbered successively to those of Comm. VII 

 of this series. (These Proceedings May and June 1913). 



