412 PROCEEDINGS OF THE AMERICAN ACADEMY §14 



have 0.45 for the specific heat under constant volume, for 

 a range of temperature from 70° to 220°. Now since the 

 specific heat of ether is 0.53 at o" and 0.55 at 35°, we may 

 assume that at 70° it would be about 0.57, and at 140° 

 about 0.61, the excess being in the neighborhood of 0.14; 

 the latent heat being 82 (Regnault — Zeuncr) and the rel- 

 ative coeflftcient of expansion about .0017, we should have 

 for both sides of equation VI. the number 0.14, so that, as far 

 as these figures show, the relation may be perfectly exact. 



The case of bromine is of unusual interest, it beinof an 

 elementary liquid; in equation VII. we have without any 

 correction H — //' 1^.05 74, which multiplied b}^ the 

 molecular weight (160) gives 9.2, nearly. The coefficient 

 of relative expansion being about .0013 at the given tem- 

 perature (80° -|- ), gives about 3.7 for the second term in 

 the parenthesis; adding we have 9.6, which finally mul- 

 tiplied by the principal ratio (-95) gives 9.2, nearly, for 

 the other side. 



There are many other cases of agreement, and indeed 

 it may be said that there is no case in which the truth of 

 the formulae for specific heat can be disproved; neverthe- 

 less, the evidence is negative, and all that is claimed for 

 these formulae is to represent approximately the diflTerence 

 between the specific heats of the liquid and vapor. 



When it comes to solid bodies, or such a dense liquid 

 as mercur}', a glance will be sufficient to show that these 

 formulae for specific heat do not hold at all; and neither 

 does formula IX. connecting the elasticity and expansion. 

 It would appear as if the cohesive force varied inversely as 

 some power of the distance much less than the fourth, as 

 would be the case if the molecules were in absolute con- 

 tact during even a considerable portion of the time which 

 we suppose to be occupied by a vibration. By referring to 

 the original formulae, it will be seen that the rate of ex- 

 pansion will be greatly diminished in tliis case; and hence 

 the constants will nearly all be aftected. 



