670 Prof. Lynde P. Wheeler on the 



because S L becomes absolutely divergent at very long wave- 

 lengths, and because the value of n 2 n 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 practi- 

 cally linear manner throughout that portion of the spectrum 

 in which the absorption 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 trans- 

 parency (smaller nx); 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 elucida- 

 tion 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 taking up of the incident energy by the free 

 electrons, and the second the expenditure of the incident 

 energy in forcing vibrations in the relatively fixed ions. 

 The absorption due to the second cause must be supposed to 

 vary with the wave-length in such a way as to be relatively 

 much greater in the neighbourhood of those wave-lengths 

 corresponding to the natural free periods of the ions. In 

 other words, the ions should produce a " band " type of 

 absorption, the breadth of the bands being proportioned 

 to the range of frequencies to which they are capable of 

 responding. On the other hand, the electrons being free 

 and of small mass should take up energy (if at all) from a 

 much wider range of frequencies, and hence cause a more 



* In the case of cobalt, after an increase of r -with decreasing tik 

 similar to that taking place with the other metals, there is a subsequent 

 falling off in r, while hk is also rapidly decreasing. Too much emphasis 

 should not be placed on such an anomaly, however, in view of the 

 uncertainties of the data. 



