Kinetic Theory of Solids* 547 



cm is constant, so that we have this result, that the product 

 ~Nbm/p is the same for all metals, and so also the product 

 Qbm/p. The best manner of testing this last theoretical con- 

 clusion will be to tabulate the values of IQfmi/J&mp and 

 21Nbm/Jcmp, and see whether all the metals give the same 



value for B+l. 



















Cu. 



Ag. 



Au. 



Mg. 



Zn. 



Cd. 



Al. 



IQbm/Jcmp or B + l. 



.4-6 



4-6 



3-2 



5-0 



10-5 



10-9 



5-9 



21'Nbm/JcmpoT'B + l. 



..4-5 



4-7 



3-2 



5-0 



9-0 





5*5 





Sn. 



Pb. 



Fe. 



m. 



Co. 



Pd. 



Pt. 



IQbm/Jcmp or B + l. 



.6-2 



3-7 



4-8 



5-4 



4-4 



3-2 



3-6 



2imm/JcmporB + l 5'4 4-7 5-1 5*2 4-3 



The values for zinc and cadmium are about double those 

 for the other elements; if for the moment we take half of 

 them as the true values, and take the mean of all, we get for 

 B + l the value 4' 6, the serious departures from which are in 

 the case of gold 3*2, aluminium mean 5*7, tin mean 5*8, and 

 palladium 3'2; in the case of palladium the fault lies probably 

 in the absolute value of q at 15° C, which is the mean of 

 Wertheim's static and kinetic values 980 x 10 6 and 1130 x 10 6 , 

 while before annealing they are 1180 x 10 6 and 1240 X 10 6 . 

 In the case of tin uncertain isotropy and experimental un- 

 certainty explain the discrepance, but for gold and aluminium 

 no adequate explanation is available except one suggested 

 below. On the whole the theoretical conclusion is well borne 

 out. In the case of zinc and cadmium, the fact that the 

 product is double the normal value is connected with the fact 

 that the molecules of zinc and cadmium are known in the 

 vaporous state to be monatomic. The product IQbm/Jcmp is 

 independent of m the molecular mass; but as we do not know 

 the dynamical significance of the constant B + l, we cannot 

 tell whether or not it ought to be twice as large for mona- 

 tomic molecules as for diatomic. The assertion that B + l 

 must be the same for all metals goes on the assumption that 

 they are dynamically similar systems of molecules at absolute 

 zero ; if they are not so, then the assertion no longer holds, 

 and this may be the cause of the difference in the case of gold 

 and aluminium. 



The theoretical relation that Qbm/p is to be the same for 

 all metals corresponds to Wertheim's empirical discovery that, 

 if q is Young's modulus at 15° C, q(in/p)^ is approximately 

 the same for all the metals [Ann. de Ch. et dePh. ser 3. t. xii.). 



202 



