504 L. P. Wheeler — Dispersion of Metals. 



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

 that r varies as \/ri*/c/ X 3 , the constant of proportionality differ- 

 ing for each substance. The numerical values of r, calculated 

 in this way, 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 quantitative 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 dis- 

 crepancy 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 approaching 

 such a value. What the value of the ratio would become at infi- 

 nite wave length cannot be deduced from the equation because 

 S x becomes absolutely divergent at very long wave lengths, 

 and because the value of 71 2 k for zero frequency is unknown. 

 In the second place, it is to be observed that for each metal r 

 increases in value uniformly and in a practically linear manner 

 throughout that portion of the spectrum in which the absorp- 

 tion coefficient has a value in excess of about 4. The point 

 where this approximately linear relation ceases to hold lies in 

 each case either in the red end of the visible spectrum or else 

 not far back in the infra red. And in the third place it is to 

 be noted that the rate of increase of r becomes much greater 

 in the regions of greater transparency (smaller uk) ; and that 

 the value of r does not fall off again after passing through a 

 transmission band, though at the shortest wave lengths observed 

 there is an apparent decrease in its rate of growth.* The 

 magnitude of the ratio at its maximum is, for silver about 16, 

 for copper about 12, for gold 7 to 8, for nickel 2 to 3, and for 

 cobalt 4 to 5. 



The fact that this equation of the electron theory leads to 

 the conclusion that the number of free electrons in a metal 

 varies with the frequency of the current does not seem to have 

 been noticed before. The circumstance indicated, that r 

 increases with decreasing absorption becoming in general 

 largest when the absorption is least, does not seem to carry 

 with it any immediately obvious suggestion for an elucidation 

 of the mechanism of the phenomenon. A possible physical 

 explanation may lie in the dual nature generally ascribed to 

 the absorption of light by metals ; the first cause being the 



*In the case of cobalt, after an increase of r with, decreasing na similar to 

 that taking place with the other metals, there is a subsequent falling off in 

 r while wc is also rapidly decreasing. Too much emphasis should not be 

 placed on such an anomaly, however, in view of the uncertainties of the data. 



