530 Albert P. Mathews 



a(i/V 1 -- i/VJ. By our assumption this difference in energy 

 must be equal to L - - E. Hence (L - - E)/(i/V 1 - - i/V w ) 

 must equal "a." We come, therefore, to an expression 

 different from Mills and one incompatible with it. Since 

 it is certain that the cohesive pressure varies at least ap- 

 proximately inversely as the square of the volume this ex- 

 pression must be the correct expression, if Iy E represents 

 only heat consumed in overcoming cohesion. As a matter of 

 fact (Iv E)/(i/V e i/V v ) does not equal a constant, hence 

 our assumption must be wrong. But if the assumption is 

 wrong then the fact that (L E)/(i/V' /3 i/V^ 3 ) happens 

 to equal a constant can not be adduced as evidence that 

 molecules attract inversely as the square of the distance. 



I think therefore, that Mills' empirical expression, 

 I, g = ^'(i/V' /8 -- Vj, 7 *) does not mean, as he supposed, 

 that the work done in overcoming molecular cohesion from 

 the volume V 1 to the volume V v was equal to /(i/V^ 3 - 

 i/V^ 3 ), but that the total internal latent heat, i. e., that used 

 in overcoming molecular cohesion as well as that absorbed 

 in the expansion of the molecules, or in doing other work is 

 equal to this expression. 



That Mills' expression, /(i/V^ 1 - i/V^ 3 ), does not 

 represent the work done in overcoming molecular cohesion 

 may be shown, also, if the attempt is made to deduce the 

 formula on this basis,*~assuming the attraction to vary in- 

 versely as the square of the distance. A value is obtained 

 for // widely^different from that found. Mills realized this 

 difficulty and tried to avoid it by assuming that the law that 

 matter attracted itself as the product of the masses was 

 incorrect. 



^ll will make the simplest possible assumptions. If the 

 molecules are assumed to be cubical in shape, to lie a mean 

 distance apart and the lines of attractive force to run per- 

 pendicularly from*each face of the cube in three directions 

 of space and to end upon the* six surrounding molecules, 

 but not to penetrate them; and if the molecules attract with 

 a force varying inversely as the square of the distance between 



