208 Johnston and Adams — High Pressures on the 



these changes can be predicted from thermodynamical con- 

 siderations. For instance, the change of melting point pro- 

 duced by uniform pressure can be calculated if we know the 

 heat change and volume change accompanying the process of 

 melting. The differential equation connecting the change of 

 melting point (dT) with change of pressure (dP) is 



dT _ TdV (1) 



dP~ AH {) 



where T is the absolute temperature of melting, dV the 

 volume change and A H the heat change which accompany 

 melting of the substance at T. In order to integrate this 

 equation rigorously, it is necessary to know how d V and All 

 vary with pressure and temperature. The exact magnitude of 

 these variations is not known in general ; but, fortunately, 

 their effect is slight and may for most practical purposes be 

 neglected. Consequently we may use the following form of 

 the equation to calculate the change of melting point (AjT 3 ) 

 produced by a change of pressure (AP 2 , expressed in atmos- 

 pheres*) : 



AP 2 ~" 41-30 Q V ; 



wherein Q is the heat of melting in calories per gram, and 

 Vi and V s the respective volumes of one gram of substance at 

 the melting point in the liquid and the solid state. An exam- 

 ple of the agreement between calculation from this formula 

 and actual observation of the effect of pressure on the melting 

 points of tin, bismuth, cadmium and lead is afforded by the 

 following table, taken from a former paper from this labora- 

 tory ; f the divergences are such as are to be expected in view 

 of the present uncertainty in the values of Q, the latent heat 

 of melting : 



*That is, true atmospheres (1033 g. per sq. cm.). 



f Johnston and Adams, this Journal, xxxi, 516, 1911 ; Zs. anorg. Chem., 

 lxxii, 29, 1911. It should be observed that, through inadvertence, the 

 numerical factor (42720) made use of in the paper here cit^d is wrong: it is 

 appropriate to pressures reckoned in grams per sq. cm. Substitution of the 

 correct factor (41*30 for one atmosphere, as given above) leads to calculated 

 values 3 per cent higher than those given in column IV of the table of the 

 previous paper ; but this makes no essential difference to anything there 

 stated, for it is reasonably certain that the values of Q there used are not at 

 present known with an accuracy of 3 per cent. For instance, the values 

 recorded in Landolt-Bornstein-Meyerhoffer Tabellen show divergences in 

 some cases of 10 per cent and it is hardly possible to determine which of 

 these are most reliable. 



