Laics of Molecular Force. 241 



This table makes it clear enough that, in applying Van der 

 Waals's generalization below the critical volume, we have to 

 do with a first approximation only. The curves for all these 

 diverse bodies excepting CS 2 , while not identical, would form 

 a compact bundle about a mean curve from which each body 

 would have its own characteristic departure ; and this is just 

 what our study of B and /5 in Table XXI. should lead us to 

 expect. 



7. Five Methods of finding the Virial Constant. — The first 

 method is that which we have already exhausted, namely, by 

 means of extended enough observations of the compression 

 and expansion of bodies in the gaseous state. 



Second method : to obtain the virial constant I from one 

 measure of the compressibility and of the expansibility at the 

 same temperature of the body as a liquid. 



Writing our infracritical equation thus, 



_B'T/ 1 , VT *'-iA I 



dp _R' 3R' VT k'-v_S I _B! 3p 

 3-T v 2 B ' v-p 2'2?; 2 T 2/2 T' 



But at ordinary low pressures the term p/T is a negligible part 

 of this expression, and we can write 



dp _ 3 I _R/ 



Now 



dT 4 ' v 2 T 2v 



"dp 

 BT - ' 



"dv /"dv _ 

 'dp/ dp' 



V 



1 dv 



v dT 



v dp 



_Vo 



V 



a 



where a and fi are the coefficients of expansion 



and the com- 



pressibility at T 



as usually defined. 











3 I 



•'• 4 » 2 T 



2v 



Vq a t 



V fJb ' 







= |(, f +i R^T = |(^ + |fE>T. 



In addition to giving us a value of 1, this last equation gives 

 a test as to whether the equation applies to a body or not, as 

 the expression on the right-hand side is to be constant at all 

 temperatures if //, is measured at low pressures. But on 



