01 



Dr. Oliver Lodge on Opacity. 391 



and 2a 2 = the same with the last sign negative, 



^(^[{i+^yy-i]*. . . ( 5) 



which is the logarithmic decrement of the oscillation per 

 unit of distance, or the reciprocal of the thickness which 

 reduces the amplitude in the ratio 1 : e (or the energy to -f) 

 of the value it would have at the same place without 

 damping. 



Using these values for a and ft, the radiation-vector in 

 general, after passing through any thickness x of any medium 

 whose magnetic permeability and other properties are con- 

 stant, is 



F = F £- aX cos(^- / &z'), (6) 



the speed of advance of the wave-train being pi ft. 



Now not only the numerical, value but the form of this 

 damping constant a, depends on the magnitude of the nume- 



4:7T 



rical quantity — t?, which may be called the critical number*, 

 and may also be written 



p*K/K > ••••••• A<) 



where K, the absolute specific inductive capacity of the 

 medium, is replaced by its relative value in terms of K for 



vacuum, and by — .=the velocity of light in vacuo =v . 



vKoft 

 Now for all ordinary frequencies and good conductors this 

 critical number is large ; and in that case it will be found that 



and that ft is identically the same. This represents the 

 simple diffusion case, and leads to equation (2). 



On the other hand, for luminous frequency and bad con- 

 ductors, the critical quantity is small, and in that case 



* An instructive mode of writing a and /3 in general is given in (11") 

 or (12") below, where the above critical number is called tan e : — 



av Vcose = p sin|e, 

 fiv Vcos e =■ p cos y. 



