362 PROCEEDINGS OF THE AMERICAN ACADEMY § 2 



The possibility of such a connection, independent of 

 the choice of units, is easily established by the considera- 

 tion that the dimensions of work per unit of volume and 

 pressure per unit of surface are the same, a consideration 

 by which the discovery of some law like that alluded to 

 might have been anticipated. 



Denoting by a some value of the variable x between a, 

 and a^, a value which, although perfectly definite in any 

 case, is known only to lie within these limits, we have for 

 the internal latent heat,* Z, of the unit of volume, whose 

 mass is D, the equation, 



JLD = —1— p;', III. 



a — I 



where J is the mechanical equivalent of heat, and remem- 

 bering that — Pq =1 P -\- P' we have, numerically, 



3 



^^^ = -^z^ {p+n 



where P may generally be neglected. 

 Combining with II. we have 



'& 



-^^^^^r^iP+E.T), IV. 



an equation by which the value of a can be determined. 



For a given value of a there will be an indefinite num- 

 ber of possible theories by which this value can be real- 

 ized, but of this number one only is likely to be plausible. 

 On the other "hand, given any theory of the cohesive force, 

 the value o\^ a will be absolutely determined in every case, 

 so that we shall be able at once to decide for or against 

 the theory. 



♦The internal latent heat (which will be understood throughout this paper) is that neces- 

 sary to convert the unit of weight of a substance into vapor of-the same temperature without 

 doing external work. 



