4IO 



PROCEEDINGS OF THE AiMERICAN ACADEMY 



§ H 



Le. 



From (3) directly, 



From I. and VI., 

 {H—H') m = (5.922 + 7.8966 T) 



From IV. and V., 



{II—H')JD = EeT 





2o^m 



VI. 



VII. 



VIII. 



From (4) and (5), 



£ c'mT= 82,898,000 (3 -^ ^eT)D. IX. 



And finally, fi-om (5) and (6), 

 T^e (3 + 3eTy P' = 0.11876 (:^ + ^ery (P' + P).X. 



These formulae nearly all involve e, which is one of the 

 most generally, if not most accurately, known of all the 

 physical constants, thanks to the efforts of Kopp and 

 Pierre. When, however, as in the case of water, the 

 coefficient is hidden under some molecular change, the 

 value ma}^ easily be eliminated. It should be remembered, 

 however, that any molecular change that affects the ex- 

 pansion will also alter the compressibility, so that we 

 can no longer depend upon the value of £. 



The relations between the other constants will not in 

 general be disturbed. 



§ 14. The truth of the ten equations of the last section 

 is easily shown, in the case of most liquids, to hold within 

 reasonable limits. In many cases, if not in most cases, the 

 error committed by using these formulae is not large as 

 compared with the error of actual observation. To ex- 

 amine in detail the application of these equations to the 

 hundred or more substances whose constants have been 

 determined would require an almost endless amount of 

 labor. A brief consideration may not be out of place. 



