L. P. Wheeler — Dispersion of Metals. 507 



about 17*5 per cent (at the red end of the visible spectrum) to 

 about 6-5 per cent at the extreme infra-red wave length 

 measured. As in the case of equation (S), it is impossible to 

 predict from equation (9) the relative magnitudes of the two 

 parts for infinite wave length, both because of the divergence 

 of S 2 at large values of X, and because of lack of knowledge of 

 the value of ?i\k* - 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 with that demanded by theory. The 

 expressions which have been deduced for K are of the form 



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

 volume, of the relatively fixed ions ; w is their natural " free " 

 frequency, and the summation is to extend to as many terms as 

 there are such free periods. Xow both from the forms of the 

 curves actually found as well as from considerations 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 thar it becomes applicable to the cases under consideration, 

 we obtain a quite complicated equation involving the values of 

 the frequencies at the edges of 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 that found, e. g., for 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 men- 

 tioned, 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 Je. This in 

 turn would yield information as to the number of vibrating 

 ions in unit volume just as equation (8) gives us the number 



* Schuster, Theory of Optics, p. 152. 



