L. P. Wheeler — Dispersion of Metals. 503 



in which form the equations have been used in this paper for 

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

 S, 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 (n + l)st to the nth terms is 

 in S„ (n+l)/a, and in S 2 (2n + l)/2a. Hence S x does not begin 

 to diverge until the number of terms is equal to (a — I) and S 2 

 until the number of terms is (2a — 1)/2. Thus the best 

 approximation attainable in the use of the series will be, in the 

 case of Sj when (a — 2) terms, and in the case of S 2 when 

 (2a — 3)/2 terms are employed ; the approximation being better 

 the larger the value of a. Now the values of a* for the five 

 metals and the range of the spectrum considered, vary between 

 12 and 2020. Taking the smallest value of a which occurs, we 

 find by using ten terms that Sj— 0'865 and S 2 =0'895 ; while 

 by using only three terms, S 1 =0 , 875 and S 2 =0*901. Thus the 

 error committed in using only three terms is, in this the most 

 unfavorable case, but 1*2 per cent in the case of S 1? and 0*6 

 per cent in the case of S 2 . 



We proceed now to the discussion of these equations in the 

 light of the experimental data which we have reviewed. In 

 the first place we observe that equation (8) gives directly the 

 theoretical dispersion of the product of the two optical con- 

 stants. If we assume that r is constant (as seems to be at least 

 tacitly the general impression), the equation expresses a law 

 of great simplicity, namely, that the product of the index of 

 refraction and the coefficient of absorption is proportional to 

 the cube of the wave length of the incident radiation. On 

 account of the variation of a and therefore of S x with the wave 

 length, this statement is only an approximate one ; but that it 

 very nearly expresses the facts for the five metals under dis- 

 cussion is evident from the circumstance that the maximum 

 variation in S x found, is only about 10 per cent. Now that 

 this law is not even remotely fulfilled by the data at hand, will 

 appear on inspection of the fifth column in the tables, where 

 the values of n 2 tc/\ 3 as computed from the data of the second, 

 third, and fourth columns are given. Hence we are forced to 

 conclude that r is not a constant, but is a function of the 

 frequency. That is, the number of electrons taking part in 

 the conduction current depends on the frequency of the radia- 

 tion which sets up that current. 



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

 from equation (8) with Si = l ; then with this value of r the first approxima- 

 tion for a is calculated by equation (7) ; then with this value of a, Si and 

 a second approximation for r axe computed and thence the second approxima- 

 tion 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. 



