644 Prof. 0. W. Richardson on Distribution of the 



They are only identified with T when the further assumption 

 is made that Vi is independent of T and equal to 4*16 x 10 3 c.cs. 

 There are good reasons for believing that in the case of metals 

 Y 1 is comparable with this number, but the further assumption 

 that Y 1 is to be regarded as independent of T can only be 

 considered as a rough approximation. It seems probable, 

 however, that the numbers will give a very fair idea of the 

 values of T both relatively and absolutely. 



in these computations, as in fact throughout this paper, 

 the following values of the numerical constants have been 

 used : — 



6 = 4-69 Xl0- 10 e.s. unit. 

 7t=6*55x 10 -27 gm. cm. 2 sec. -1 . 

 E = l-35x 10 -16 gm. cm. 2 sec. -2 deg. -1 . 

 N = 6'12xl0 23 . 

 elm = 1'7 6 x 10 7 e.m. unit gm. -1 . 

 M 



m = ^-- = 8*86 X 10 28 gm. = mass of 1 electron. 

 M = 5'42x 10 -4 = atomic weight of an electron. 



The numbers in column III. are plotted against the inverse 

 of those in column IV. in fig. 1. It will be observed that 

 below about 1000° K, g{Q, Xi) can be represented accurately 

 by e const/C or to the approximation referred to above, by 

 ^const./T^ j] ven a kove T = 1000 the curvature of the graph 

 of log e #(C, Xi) against T -1 is not very great ; so that if the 

 range of T is not too extended log e (C, a , 1 ) = A + B/C, where 

 A and B are constants, will be very closely followed. This 

 is shown by curve (2) on the right where the values corre- 

 sponding to T -1 <10 -3 have been plotted on a larger scale. 

 It appears from curve (2) fig. 1 that, subject to the assump- 

 tion C oc T, g(C, Xi) can be taken to be of the form A^ 00 ™^ 

 over a range roughly corresponding to 1000-1800° K. 



Even over a more extended range the deviation from this 

 formula would not be great. If we take <7(C, #j) to be 

 expressed by A 1 e Bl/T as a valid approximation, then from 

 curve (2) fig. 1, A 1 = *r* 75 = *4724 and B x is about -Jg as 

 great as (w 2 — w^/R. 



It follows from equation (34) that, to the extent to which 

 the approximations referred to are valid, i as a function of 

 T can be written 



i= A 2 T 2 £ -3 ^ T ...... (35) 



where A 2 and B 2 are independent of T. This result is also 

 given by thermodynamic considerations to the accuracy of 



