032 Dr. J. E. Mills on 



to consider them to be shifted back into their position of 

 even distribution ; and the fundamental supposition upon 

 which the mathematical work is based is, that the molecules 

 of a liquid and the molecules of its vapour have per se the 

 same * energy when they are in this ideal position of even 

 distribution throughout the space occupied by them. 



Except for associated substances or substances undergoing 

 decomposition, it is generally believed, and the belief rests 

 upon considerable experimental evidence, that the number 

 of molecules in the liquid and in the gaseous condition are 

 the same. The equation is not true where this condition is 

 violated. 



The fifth assumption warrants the closest study. In the 

 first paper, when equation 1 was originally deduced, this 

 assumption was not expressly made. The deduction of that 

 equation contained an error which was later corrected in the 

 sixth paper. Attention was called in that paper to the 

 following facts : — 



1. The equation, \=u,'( \/d— v^D), was true experi- 

 mentally. 



2. The above equation followed if a constant mass of 

 liquid was taken and the law of the force acting between the 



particles of the liquid was, force = 2 , where fi was the 



s 



constant of molecular attraction and was equal to a constant 

 times yu,', m was the mass of the attracting particles, and s was 

 their distance apart. 



3. If the mass of liquid taken was varied then the same 

 law of force between the particles showed that the heat 

 required for vaporization should vary as the 5/3 power of 

 the mass. 



4. We know experimentally that the heat required to 

 vaporize a liquid varies directly as the mass of the liquid 

 taken. 



The question to be determined therefore is, in what way to 



LL .771 



modify the assumed law of the force, namely, force = g > 

 in order to obtain the experimentally true equation 



m\=m/*'( yj- vb), 



with either a constant or a variable mass, M. An inspection 

 of the factors involved makes it very probable that the 



* See footnote (*), p. 631. 



