§2 OF ARTS AND SCIENCES. 361 



If between the limits, F", and V2, ^ can be regarded as 

 constant and equal to a, we have 



_ 3 



« — I 





whence if [^ = i we may write 



a — I 

 hence we have, for the total work required for completely 

 vaporizing the unit of volume of a body, at constant tem- 

 perature, 



,v=ca 3 



I — a 



^^' a — I 



It is easily seen that if a-, be the maximum value of 

 a, during expansion, and t?, the minimum value, greater 

 than I, 



IV > — ^ PJ' 



a^ — I 



<— ^— p: 



a^ — I 

 for, since Kis necessarily greater than i, each term in the 



series is e^reater than ^ /l"A V 3 and less than 



to 



«. 



«, — I 



It follows that, independent of any theory of cohesion, 

 if the force be known to vary inversely as some power of 

 the molecular distance not greater in any case than a, and 

 not less than a,, the internal latent heat of vaporization of 

 the unit of volume of any substance is known within two 

 limits, in terms of the cohesive pressure P^\ under which 

 the substance exists in the original state. 



Thus wc have a mathematical proof of the statement 

 in § I, concerning the mutual dependence of latent heat 

 and cohesion. 



