( 208 ) 



As a case (o wliicli wo will applv c(|iiatioii (2; \vc consider the 

 expansion of a liquid from the volnnio v, to the vohnne r.^ at constant 

 temperalnre. When \'.\N dkh Waai>s' foimula 



P I "^ ]{v-'b) = nT (:{) 



holds foi' this, \vc aet 



while 



A = \ p di'—llT (n \- ~ 



J ^\~^> ''.2 



a a 



follows for L'. These relations are of course in harmony with 

 equation (1), of which one can easily convince oneself; on the otliei- 

 hand we have : 



dA v,—b , dU 



Urn =r R In , Inn = (for 7' =r 0', 



dr v,-b dT ^ 



relations which are incompatible with equation (2), i.e. the new 

 theorem of heat. 



Now, however, it would be entirely injustitiable to consider the 

 new theorem of heat refuted on this ground ; it is indeed oidy 

 experiment which has to decide this question. And as we know, 

 experiment proved long ago that van der Waals' formula and even 

 the general theory of corresponding states too are often in flagrant 

 opposition to experiment ') ; it is further easy to see that especially 

 at low temperatures the deviations become particularly striking. The 

 new theorem of heat, on the other hand, has already been conlirmed 

 bv a great number of examples, and in many hundreds of cases, in 

 which we conld not yet prove it with perfect exactness for want 

 of a more accurate knowledge of specific heats at low temperatures, 

 at least certain a))proximate results were contirmed, which I could 

 derive from it. 



For the rest it is also easy to derive from molecular theory even 

 without having recourse to the new theory of indivisible units of energy 

 which is of coui-se incompatible with foi-mula (3), that this formula 

 cannot possibly hold for licpiids at low temperatures. For it is known 

 that stronglj' undercooled liquids assume a rigid glassy state at low 

 temperatures according to Tammann's iinestigations, and nolxuly but 



1) Gf. e.g. my Tiieoiet Gliem. p. 23<i and paiiicnlaily KiisliiK.' Meyer, ZclLschr. 

 piiysik. Chem. 32 1, (1900). 



