406 PROCEEDINGS OF THE AMERICAN ACADEMY §13 



a formula by which we may determine the difference of 

 specific heats if we know the coefficient of expansion, the 

 factor A^and the ratio of/' to /. 



The formula may also be written, substituting L for its 

 value, 



still involving the ratio of the molecular diameter to the 

 free path. 



But since the work done in expansion is the product of 

 the coefficient by the pressure overcome, less the affinity 

 satisfied, we may also write 



/ {H— H') = KP\, II. 



in which, substituting any value oi P" ^ we have from III. 

 § II, from II. § I, and from III. § i, 



J ^H— H') D^K ?iii^ ^ JLD^ = KEe T, III. 



whence we see that {^H — //') := Ze. IV. 



By means of these formulae the difterence may be deter- 

 mined between the specific heat in the liquid state and 

 that under constant volume in the state of vapor. 



§ 13. We have now considered the principal physical 

 constants, and we find, with the exception of a few rela- 

 tions between them which are independent, that all involve 

 in some way the ratio of the molecular diameter to the 

 free path. It docs not, therefore, seem surprising that 

 the relations which still remain to be established should 

 have escaped the notice of a scientific world which has 

 until recently* been bent upon the solution of the molec- 

 ular theory of liquids and solids on the false supposition 

 that the molecules were very far apart, and the repulsive 



* Sec Riihlmann, ibid. 



