404 PROCEEDINGS OF THE AMERICAN ACADEMY § 12 



The first series 's evidentl}' equal to 

 the second is equal to 



I + ay + ay + ay + «*<:• 



which is equal to 1.201 -|- ; so that we have 



P" = ^:^-^ TIL 



w^iich, combined with II., gives by an independent method 

 of reasoning the same result as before, namel}^, 



JLD = K P\ 

 since we have disregarded signs, and have considered the 

 external pressure equal to zero. 



Now the thickness of a molecular film, having been 

 determined by various methods for a few elementary sub- 

 stances, can be calculated for any substance whose graphi- 

 cal symbol is known;* and hence if the surface tension is 

 given, formula III. enables us to determine the cohesive 

 pressure, and indirectly any of the other ph3'sical con- 

 stants in terms of which it may be expressed. 



§ 12. The difference between the specific heats of a 

 substance in the liquid and in the gaseous state is, as we 

 have seen, other things bei7ig equal ^ the measure of the 

 work done in separating the particles by the amount cor- 

 responding to an increase of one degree in temperature. 

 The sum of all such elementar}^ quantities of work done in 

 an indefinite expansion is the internal latent heat of vapor- 

 ization ; and, conversely, we may regard the difierence of 

 these two specific heats as the change of the internal 

 latent heat per degree of temperature, or, what is the same 

 thing, the derivative of this latent heat with respect to 

 the temperature. 



In order, however, that this rule may apply in all strict- 

 ness, the temperature of the liquid and vapor whose specific 



• See also Riihlmann, ibid. "Untersuchungen iiber die absoluten Grossen der Molecule." 



