60S Prof. Lynde P. Wheeler on the 



great as on the other. He then uses the values of K yielded 

 by the two formulae to discriminate between the two hypo- 

 theses. This argument, if the formulae as given above are 

 correct, is illusory. Further, since the value of N is not 

 independently known, it is impossible to discriminate between 

 the two hypotheses by means of the difference between the 

 two results for n 2 K. The equations resulting from the 

 assumption of the Maxwellian distribution have been adopted 

 for the computations of this paper, because that assumption 

 seems on the whole to the present author to have more 

 inherent probability. 



In using equations (3), (5), and (6) for numerical evalua- 

 tions it is convenient to use, following Schuster, the ratio of 

 the number of free electrons to the number of molecules per- 

 unit volume in place of N. Calling this ratio r, we have 

 N = r/Mr, where M is the mass of the hydrogen atom and r 

 the relative atomic volume. If, to simplify further, we 

 gather together those constants which are the same for all 

 metals, writing a = e 4 /7r 3 »t 2 M 2 C 2 , and use the wave-length 

 in vacuo (X), in place of p, then equations (3), (5), and (6) 

 become 



rr 2 t 2 /,P r 2-\3 



"-^w- • • (7) B "=-^F S " • • (b) 



K + *V-1) = ^~^S 2) -. ... (9) 



in which form the equations have been used in this paper 

 for purposes of calculation. It is to be remarked that the 

 series Si and S 2 are semiconvergent. That the use of only 

 three terms in either series yields, however, a more than 

 ample accuracy for the purposes in hand, is easily seen. 

 For the ratio of the absolute values of the (w + l)st to the 

 nth terms is in S x , (n+l)/a, and in S 2 (2n + l)/2a. Hence 

 Si does not begin to diverge until the number of terms is 

 equal to (a— 1) and S 2 until the number of terms is (2a — 1)/2. 

 Tims the best approximation attainable in the use of the 

 series will be, in the case of Sj when (« — 2) terms, and in 

 the case of S 2 when (2a — 3)/2 terms are employed t the 

 approximation being better the larger the value of a. Now 

 the values of a * for the five metals and the range of the 



* These are calculated as follows: — a first approximation for r is 

 obtained from equation (8) with S,=lj then with this value of r the 

 first approximation for a is calculated by equation (7) ; then with this 

 value of a, Sj and a second approximation for r are computed, and 

 thence the second approximation for a. The process is then repeated as 

 often as may be necessary ; three approximations being the greatest- 

 number required for any of the metals discussed in this paper. 



