JOHNSTON: ELASTIC BEHAVIOR OF METALS 263 



to cause the metal to melt at, or about, 25°. The method of cal- 

 culation follows. 



The application of thermodynamical principles to this case 

 yields the differential equation. 1 



^ = A (I) 



dP QD u; 



which when integrated so as to be applicable to the case in hand 

 becomes 



^i = -^L_ (ir) 



AP 42.72Q l A 



according to which the change in melting-point (a7\) produced 

 by a pressure (AP) acting only on the solid phase is expressed in 

 terms of the melting point (Ti) at atmospheric pressure, the 

 heat of melting (Q x ), and the density (A) of the solid at ordinary 

 temperature and pressure. 



Lack of space precludes a discussion, and justification, of the 

 assumptions involved in obtaining this integrated form of equa- 

 tion I; suffice it to say that the matter has been carefully con- 

 sidered, and that any inaccuracy in this integration is quite 

 unimportant in the present connection, more especially since the 

 accuracy of the available values of Qi (and even of DO leaves 

 much to be desired. 



The above formula has been applied to the calculation of the 

 lowering of melting point produced by 1 atmosphere excess pres- 

 sure on the solid in the case of all the metals 2 for which values of 



1 A succinct mode of deriving this equation is given by G. N. Lewis (J. Am. Chem. 

 Soc, 30: 680. 1908). 



2 Excepting iron, on account of the uncertainty of what "iron" is, and the dis- 

 parity of the recorded values. The value given for nickel in Landolt-Bornstcin- 

 Meyerhoffer Tabellen (p. 470) as a heat of fusion (taken from Pionchon, Ann. 

 chim. Phys., (6), 11: 106. 1887) was found, on reference to the original, to be a 

 heat of transformation (occurring somewhere between 230° and 400°) ; consequent I y 

 nickel could not be included. (Similarly, Pionchon's values for iron given in 

 L.-B.-M. (p. 470) are heats of transformation.) Mercury and gallium are omitted, 

 since they are liquid at ordinary temperatures. The value of Q, for aluminium 

 is somewhat doubtful : it was calculated from the "total heat" (as given in L.-B.-M.) 

 by means of the specific heat of aluminium (0.30) as given by Bontschew (L.- 

 B.-M., p. 383). No alloys could be included, owing to lack of the necessarj dal a; 

 in any case the formula is applicable only to those alloys which melt at a definite 

 temperature. 



