442 Mr. G. H. Livens on the Electron 



and practical results *_, which is possible in the present state 

 of the subject, as our knowledge in this branch of work is 

 hardly complex enough for a discrimination between the 

 -different forms of the theory. One or two general remarks 

 bearing on the application of these results may, however, 

 not be out of place. 



The formulas here obtained exhibit very clearly the exact 

 limitations of the simpler Maxwellian theory, which is 

 applicable so long as the period of the light- waves is large 

 compared with the mean time of description of a free path. 

 This has been experimentally verified by the experiments 

 -of Hagen and Rubens, who found that complete metallic 

 conduction is fully established in a small fraction of the 

 period of ultra-red radiation, up to which limit all radiation 

 is reflected from all metals in proportions determined by 

 their ohmic conductivities alone. 



The simple relation 



required by Maxwell's theory is modified, firstly, by the 

 factor 



1 + aO^-l) 



1 + aG^-l)' 



which arises from the resonance electrons, and, secondly, by 



the factor 



2 





_1 1 gl + se ° da 



which is a function of the period of the light used. The 

 theory thus contains an effective account of the observed 

 departures from the simpler relation. 



For long-wave radiation the square of the quasi-index of 

 refraction is a purely imaginary quantity ; for the opposite 

 extreme case of very short waves it appears that, in the 

 absence of absorption due to the resonance electrons, the 

 square of the quasi-index must be a real negative but small 

 quantity. The optical determinations of Drude indicate 

 that this is not very far from being the case with light- 

 waves for some of the nobler metals, although, as the more 



* See Enskog's paper previously referred to, where a comparison is 

 attempted. His results, however, require the modification necessitated 

 by the more complete theory, which includes the full effect of the 

 resonance electrons. 





