542 Mr. G. U. Yule on the Passage of Electric 



conductivity. Let the damping of wave-trains in their 

 passage through it be given by a factor p, such that 



a 2 = a l e-* x , (4) 



where a x is the initial amplitude, and a 2 the amplitude of the 

 same wave after traversing a length x of electrolyte. From 

 Maxwell's theory it follows that 



P = 2tt^CV, (5)* 



where V= velocity of propagation in the electrolyte, 

 C = conductivity of the electrolyte. 

 fi= magnetic permeability of the electrolyte. 



Taking the second surface of the electrolyte (x 2 ,G.g. 1) as origin 

 of coordinates, and carrying out the summation of successively 

 emergent rays, we arrive, after sundry transformations, at 

 the expression for the curve 



where 



I,_ (!-&«)««-»' f 2Ql 

 I ~ l-tfe- 4 * 1 I £ J ' ' 



(6) 





I = intensity transmitted when the absorbent layer 



vanishes. 

 If = intensity transmitted for a thickness I of the layer. 

 b = fraction of the incident amplitude reflected at the 



first surface. 



21 

 t 2 = — , L e. = the time taken by radiation to traverse 



twice the thickness of the layer. 



On putting the conductivity, or p, = zero the above ex- 

 pression (6) reduces to that given by Mr. Barton for the case 

 of no absorption. 



On analysing (6) we see that the expression on the right- 

 hand side may be split into two terms : the first gives us a 

 continuous drooping curve which may be considered as a 

 centre line, on which the humps formed by the second, 

 periodic, term are imposed. If we put the primary damping 

 ry=oo , interference is impossible, the periodic terms vanish, 

 and we have 



h _ {i-vye-w 



I " l_to-4j»* > W 



* Maxwell, ii. [798J. 



