§ 15 OF ARTS AND SCIENCES. 413 



The laws for dense solids could easily be established by 

 the same methods of reasoning; but their discussion would 

 exceed the intended limit of this paper. It ma}', however, 

 be observed that the products of the coefficients are usu- 

 ally from one-third to one-half as great for solids as for 

 liquids, and that the law of variation of the force which 

 binds them together, being compounded probably of at- 

 tractive and repulsive forces, appears to vary inversely as 

 some power of the distance not far from the square. 



The critical temperatures calculated by formula X. 

 come out, for the four liquids examined by Cagniard de 

 la Tour, about ten per cent, higher than his estimate; it is 

 possible that under different conditions a more elevated 

 temperature might have been required, but it is more 

 likely that the theory is at fault. Many considerations 

 have been left out of account which would indicate just 

 such an error. In particular I would mention the same 

 causes which led us before to expect a still greater diver- 

 gence in the expressions for the pressure at this temperature 

 (§ 10) and the difference between the mean and probable 

 velocity of the molecule, all of which considerations must 

 at present be passed over. 



The ten equations of the last article appear to be borne 

 out by experience in the case of a hundred liquids, as close- 

 ly as one Avould have a right to expect, in view of the minor 

 considerations which have been of necessity disregarded. 

 By means of a more general analysis, outlined in § i6, I 

 have been able to prove that the same would not have 

 been true if we had assigned an essentially different 

 law to the variation of the cohesive force; the relations 

 calculated between all these constants would h"ave been 

 in that case entirely out of proportion. 



§ 15. To facilitate the use and application of the for- 

 mulae of § 13, connecting the latent heat, elasticity, expan- 



