§17 OF ARTS AND SCIENCES. 42 1 



matical difficulty and practical objections. It may per- 

 haps be allowable to suggest that, from almost any point 

 of view, there will be in melting ice only from fifty to 

 seventy per cent, of solid particles, and in freezing waiter 

 nearly one-half as many, but in boiling w^atcr not more than 

 one-third; so that the number which disappear in melting is 

 not more than twice the number which are eliminated 

 when the liquid is raised to boiling. The true expansion, 

 therefore, from o° to ioo°, instead of being 1.04, niay be 

 from 1.08 to 1. 10, and the real coefficient at 0° is probably 

 from .0006 to .0008, increasing regularly with the tem- 

 perature, as in the case of an ordinary liquid. 



§ 17. The investigation of the hypothesis that the cohe- 

 sive forces var}' inversely as the 4"' power of the distance 

 has now been carried as far as was originally intended. 

 The results of other hypotheses remain to be determined. 



In equation IV. § 2, 



If a different value be assigned to a, we can see that 

 the relation between the latent heat and the other con- 

 stants will be materially altered. There being no reason 

 on the whole to suppose that the value already considered 

 is either too great or too small, and since a determines, in 

 a certain way, the average rate of change of the cohesion, 

 it follows that we are not allowed any great w^dth in the 

 nature of our fundamental hypothesis. 



It is not so with the cohesion at short distances. In the 

 condition of equilibrium, 



P+ P' + P" = o, 



if we write P" : P^' = ll : P ^ we shall obtain equations 

 as before for the elasticity and the expansion, which may be 



