318 PROCEEDINGS OF THE AMERICAN ACADEMY 



ences of specific volume increase from .048 c.c. to .071 c.c, nearly 50%. 

 Hence, if either of these quantities be more than a vanishing increment, 

 their difference must also be. 



From a different point of view : if the dissociation energy, q, is 

 large as compared with the expansion energy, then the thermal con- 

 stancy of X is of little consequence here. I make the supposition, 

 therefore, that q is not large relative to fpdv, a point which I will 

 endeavor to test in § 12. 



Returning to equation (1), § 3, it therefore follows experimentally 

 that 



XV, pV 

 pdv = q + I pdv (2) 

 "'^ 



where q^ and q are the dissociation energies, p the molecular pressure, 

 Vq and Vq the specific volumes solid and liquid respectively at zero 

 Centigrade, and where v and V have the same meaning at any given 

 temperature between zero and the melting point. If by § 2, ^'o = q, 

 then equation (2) may be reduced to 



I p dv — I p dv = 



(3) 



an equation in which the molecular pressure is expressed in terms 

 of the thermal expansion of the liquid and the solid within the same 

 thermal limits, and by which any reasonable law of internal pressure 

 may be preliminarily tested. 



Now suppose these integrations be successively taken at zero, and 

 all succeeding stages up to the melting point : then will the distance 

 apart of the limits of either term vary in any ratio relative to the 

 distance apart of the limits of the other. An equation 



p(V-i()=c (4) 



will therefore at least partially satisfy (3). In how far it may do so 

 throughout the whole interval 0° to 50° may be gauged by determin- 

 ing the constancy of x throughout this interval. This is done in 

 the next table, where ?', V, and >t are given for successive tempera- 

 tures d. 



The constancy of x is thus marked, and quite within the range 

 of experimental errors ; and hence the equation (4) expresses the 

 law of force as well as any other function fitted to equation (3). 



