Kinetic Theory of Solids. 531 



Even at the melting-point 1/bd for most metals is about 

 50, so that at ordinary temperatures 4 is small in comparison 

 with 1/bd. Neglecting 4 for the present, and remembering 

 that c and b vary only to a small extent with temperature, 

 and that cm, by Dulong and Petit's law, is the same for all 

 metals, we can write, putting h=l, 



, 2 Jem . . 



k ~"^We^[ 9 {b} 



approximately, and assert that theoretically the bulk- modulus 

 varies inversely as the temperature, and that the product 

 kb 2 6m/p is the same for all metals. This result makes the 

 bulk-modulus infinite at absolute zero, which, of course, is 

 merely the result of our assumption that the change of 

 volume of the molecules produced by collisions is negligible. 

 At any rate the bulk-modulus at absolute zero is probably 

 very large, that is, the molecules are probably only slightly 

 compressible, as will be seen later on. 



In our equations (7) and (8) for k we know all the quanti- 

 ties on the right-hand side (if h = 1) for the metals, and we 

 also have some quasi-experimental determinations of k, so 

 that we can proceed to test how our assumption of E being- 

 constant will hold. The values of k are not purely experi- 

 mental, because they are not obtained by direct measurement, 

 but by calculations from other elastic measurements on the 

 assumption that the metals are homogeneous isotropic solids. 

 In such solids k is connected with the rigidity n, and Young's 

 modulus q by the relation k = nq/(dn — 3q). 



When k is calculated from the experimental values of n and 

 q, the worth of the result depends entirely on the nearness to 

 perfect isotropy of the solid. Thus, on the assumption of 

 perfect isotropy, it is possible to calculate a value of k for 

 many metals at 15° C. from the average values of n and q 

 given above in Tables III. and VII. Tomlinson has given 

 (Phil. Trans. 1883) values of k calculated from his measure- 

 ments of n and q ; and there is this advantage in using his 

 values, that n and q were measured on the same specimen, 

 Amagat has found (Compt. Rend, cviii.) values of k for a few 

 bodies by measuring q, and also the change of volume pro- 

 duced by external pressure on hollow cylinders, and then 

 calculating on the assumption of perfect isotropy. It will be 

 shown afterwards that the metals are at least nearly isotropic, 

 but yet we must assume that all our values of k for the metals 

 are only more or less rough approximations to true values, 

 because small departures from perfect isotropy produce large 



2N2 



