Dispersion of Metals. G73 



of the values of n 2 (/c 2 — 1) under the same circumstances. It 

 is worthy of note also, that the dielectric term is of relatively 

 greater importance at the shorter wave-lengths, in the poorer 

 conductors. 



Finally, we must compare the form of the curves for K as 

 shown in the figures witli that demanded by theory. The 

 expressions which have been deduced for K are of the form 



or— p z 



where k involves the charge, the mass, and the number in 

 unit volume of the relatively fixed ions; co is their natural 

 " free " frequency; and the summation is to extend to as many 

 terms as there are such free periods. Now, both from the 

 forms of the curves actually found as well as from considera- 

 tions of inherent probability, it is evident that we have here 

 to deal, not with sharply defined isolated natural periods, but 

 with resonance extending over considerable finite ranges of 

 wave-lengths. If we therefore transform the formula in the 

 manner of Schuster * so that it becomes applicable to the 

 cases under consideration, we obtain a quite complicated 

 equation involving the values of the frequencies at the edges 

 ot the absorption bands, as well as the constants k. 



Now the data at present available for a satisfactory deter- 

 mination of: all the constants thus demanded are sufficient 

 neither in extent nor precision, as was remarked earlier in this 

 paper. Nevertheless, it can be stated that the theoretical 

 equation with suitable values of the constants can be made 

 to yield a curve approximating to that found, e.g., tor silver. 

 It is scarcely worth while to give details of such calculations 

 here, however, as owing to the limitations of the data which 

 have been mentioned, the determination of these constants is 

 largely guess work. 



It is to be noted that if we had data available sufficient in 

 extent and precision to permit a satisfactory evaluation of 

 the other constants in such a dispersion formula for K, then 

 that equation would allow us to determine the value of k. 

 This in turn would yield information as to the number of 

 vibrating ions in unit volume, just as equation (8) gives us 

 the number of free electrons. With this added information 

 we should get some light on the magnitude of the part 

 played in the absorption by metals, by the relatively fixed 

 ions ; information which could not fail to be of use in 

 unravelling the mechanism of that process. 



* Schuster, ' Theory of Optics/ p. 152. 



