Kinetic Theory of Solids. 533 



where dp/dO means now the rate of increase of the melting- 

 pressure with the melting-temperature. Now, according to 

 our theory, melting occurs when molecules are able to escape 

 from imprisonment by their neighbours, that is, when the 

 space between molecules attains a certain value relatively to 

 the size of the molecules. Hence, if the size of the molecules 

 is invariable, melting must always occur for the same value 

 of e. whatever the pressure is, and we have dpjdd of the last 

 formula the same as ~dpl"d6 taken from our equation with the 

 condition e= constant. 



30-3^-E) ana ^-"WO-E) ' ' ' • W 



But on this view of melting the latent heat may be calcu- 

 lated in another manner, for on this purely mechanical view 

 it must be the energy supplied to produce the change of 

 potential energy that accompanies the change of density on 

 liquefaction. Hence \ = B(p 1 —p 2 ), and neglecting^ in our 

 equation, this 



_ 2D P1—P2 



~3e 2 (e-ft)' Pl 2 ' 



" A ~ 3^-E) " v 2 ~ 3e\e-E) nearly ' 



as before. Hence, remembering that e 3 = m/p, J) = Jcmd, and 

 e — m = eb6 nearly, we can write 



2cm p± — p 2 



Pi 



X=^.*^* calories (10) 



60m 



Person (Ann. de Ch. et de Ph. ser. 3, t. 24) has found the 

 latent heats of several metals, and Vincentini and Omodei 

 (Wied. Beibl. xii.) have found the change of volume at the 

 instant of melting for lead, cadmium, tin, mercury, and other 

 bodies ; and Hoberts and Wrightson (Nature, xxiv.), amongst 

 other data, give the densities of melted zinc and silver, whose 

 densities just before melting can be calculated approximately 

 by means of their coefficients of expansion, though this is not 

 so satisfactory as a direct measurement. The mean coeffi- 

 cient of expansion b of solid mercury is not known, but can 



be found by the relation &T?72 6 = '044, where T is melting- 

 point, to be afterwards discussed. Person, in his calcula- 

 tions, intentionally ignored the increase of specific heat with 

 temperature, but if we put c = c (l-ra.t) and use the values of 

 a given by Naccari (Wied. Beibl. xii.) from experiments 



