Dispersion of Metals. 669 



spectrum considered, vary between 12 and 2020. Taking 

 the smallest value of a which occurs, we find by using ten 

 terms that S x = 0'865 and S 2 =0'895 ; while by using three 

 terms, S^O'875 and S 2 = 0'901. Thus the error committed 

 in using only three terms is, in this the most unfavourable 

 case, but 1*2 per cent, in the case of S l5 and 0'6 per cent, in 

 the rase of $ 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 

 constants. If we assume that r is constant (as seems to be 

 at least tacitly the general impression), the equation ex- 

 presses 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 

 Sj with the wave-length, this statement is only an approxi- 

 mate one ; but that it very nearly expresses the facts for the 

 five metals under discussion is evident from the circumstance 

 that the maximum variation in S] 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 fc/~\? 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 radiation which sets up that 

 current. 



If, then, we regard equation (8) as determining r, we have 

 that r varies as \/ii 2 K/\ 3 , the constant of proportionality 

 differing for each substance. The numerical values oE r, 

 calculated in this wa}^, are given in the sixth column of the 

 tables, and are shown in the figures by the full lines in the 

 upper halves. Owing to the fact already pointed out, that 

 the only result of such calculations on which much quanti- 

 tative dependence can be placed is with respect to relative 

 values, the absolute values of r have been computed for only 

 one observer's results in the regions of overlapping, except 

 where there is marked discrepancy in the dispersion. 



An inspection of these curves shows in the first place that 

 the numerical values of r are, at the longest observed wave- 

 length, of the order of magnitude unity or rapidly approach- 

 ing such a value. What the value of the ratio would become 

 at infinite wave-length cannot be deduced from the equation, 



