Laws of Molecular Force. 259 



of the molecule is proportional to M its molecular weight ; 

 so that from the second we have Ml proportional to a(Mv)*v, 

 and hence a (Mr) I measured at 2T t ./3 is for all bodies pro- 

 portional to T c . Now in our notation the relation discovered 

 by Eotvos (Wied. Ann. xxvii.) is 



d{*(Mv)*\/dT=-227, 



or «(Mi>)* = -227(T-T/), 



where Tc' is a temperature very close to the critical ; and this 

 is only a more general statement of the relation we have just 

 deduced. 



As Eotvos has verified his relation experimentally for a 

 large number of bodies, his result is a verification also of our 

 general principles. The form of his relation also induces us 

 to examine a little more closely an important consequence of 

 the form of our infracritical equation, which, when multiplied 

 by M with the pv term removed at low pressures, becomes 



* M (i + «£.*=«\t. 



zv \ 13 v—p/ 



Now B/M is constant, and Ml/v is proportional to a(Mv)*, if 

 a and v are measured at 2T c /3, or any other constant fraction 

 of the critical temperature, and under these circumstances 

 a(Mv)! has been shown to be proportional to T c ; hence if T 

 is aT cy a being a constant fraction, we get T c proportional to 



\/^ k'—v 



so that 1+ -tt- 77j measured at a constant fraction of the 



±> v— j3 



critical temperature, is approximately the same for all bodies, 

 a result which our study of Tan der Waals's generalization 

 showed us to be approximately true. This shows that Eotvos's 

 relation is rigorous only to the same extent as the constancy 

 of this last expression is rigorous ; as a matter of fact, exclu- 

 ding the alcohols and water, Eotvos finds the constant whose 

 mean value is taken as '227 to depart from this mean value 

 by not more than 5 per cent, in any individual case. This 

 brief discussion of Eotvos's relation has therefore furnished 

 us with additional proof of the general accuracy of the ap- 

 proximations we have been forced to make in parts of our 

 work. 



One of the main difficulties in the way of pushing on with 

 the many interesting inquiries opened up by these relations 

 lies in the fact that we do not know the relation between the 

 densities in the body and in the surface-layer of a liquid. 



