Electrons concerned in Metallic Conduction. 265 



body the dielectric capacity observed for non-oscillatory 

 forces will be 1 + 2$, the summation being for all kinds of 

 ions in the substance, so that $ r may be called the dielectric 

 capacity of an ion of type r. This is done, for example, by 

 Drude, who thus arrives at the definition of ordinary dielectric 

 capacity as the sum of the capacities of the free aether and of 

 all the types of ions. 



A more correct formula must be K x -+ %$, where K x is 

 different from unity, and may be more important than 2$. 

 It is an effect of material polarization in doublets. Calcula- 

 tions of £ from the known positions of absorption of such 

 bodies may therefore be subject to error. According to 

 some views atomic doublets are rigid, and can only move as 

 a whole, say by twisting round, the positive and negative 

 charges preserving their distance apart. Sir J. J. Thomson 

 has suggested the use of such doublets in a recent paper on 

 the theory of radiation*. 



But whatever Kj may be, the quantity K which we have 

 employed denotes K 1 + ^/(l — {tj/t) 2 ), which in the case of 

 non-periodic forces becomes K x + S, where S relates to the 

 positively charged atom only, whose free period is t x . The 

 negative electrons have been accounted otherwise. For 

 steady forces Kx + 3 for this atom cannot be very different 

 from the kind of value it may have in the case of non- metallic 

 elements, that is to say, it may range perhaps from 1 to 20. 

 Now K, when the force is periodic, differs from Ki + S by an 

 additive amount Stfftt 2 — t^). But many free vibrations of 

 a metallic atom must, on most theories, be far down in the 

 infra-red, so that when t is a period in the visible spectrum, 

 this additive amount is negative, and thus K is less than 

 Kj + 3 for periodic forces in the visible spectrum. Thus our 

 magnitude K is more certain than Ki + S not to exceed, s-ay, 

 20 at most, and may in some cases be negative if t 1 is nearer 

 to t than usual, or if 3 is larger. 



It is evident from this reasoning that the values of K, to 

 which we are led by the theory of equal velocity of agitation 

 of the free electrons, cannot be admitted, and that a method 

 of discrimination between hypotheses of velocity has been 

 found. The nature of the values given by the use of Max- 

 well's law is exactly what it ought to be, and so exact that 

 it became possible to credit the law with a very high degree 

 of accuracy. On this basis it is found that the description 

 of the behaviour of the various metals in yellow light is very 

 complete, and, as stated, in a later paper it will be shown 

 that the description is equally good for other frequencies, 

 * Phil. Masr. Julv 1910. 



