of Refraction, Reflexion, and Extinction. 277 



The evaluation of t'ie magnetic field excited by the stratum 

 follows a similar course ; its component along y is 



[H«]=2^*-*o)<teoNprC (8) 



%J | z-zo I 



-Applying (7). § 2, we obtain as before 



[Rf> J = +27ran&oNA^^- a • *"*<> I " te o+a] 9 . (9) 



where the upper sign is to be taken if the difference z — z ^ s 

 positive and the lower if it is negative. 

 We shall have in a similar manner : 



[Hf]=0, [H< 2) ]=0. 



§ 5. The effect of a stratum having been ascertained, we 

 are enabled to evaluate the aggregate secondary field arising 

 from the presence of matter in bulk. Let us suppose for 

 clearness of conception that the medium under consideration 

 extends from z = to z — cc. Consider a point M in the 

 medium, situated in a plane z~z where z> 0. Secondary 

 electromagnetic waves, emanating from various strata of the 

 substance, are uninterruptedly transmitted through the plane. 

 Let us calculate the electric field (measured along x) which 

 arises at M under the simultaneous operation of secondary 

 waves travelling in the positive direction of the axis of z. 

 Things having become steady, this field, in accordance with 

 § 4 above, is 



NA (2) j dz € in ^~ hz °~< z - z o)^'] m . . (i) 



Jo 



A convenient way of explaining the meaning of the ex- 

 pression (1) is to remark that it represents the cumulative 

 effect of concurrent secondary waves, advancing in the 

 direction in which the incident wave traverses the medium. 

 For simplicity and definiteness, we shall use the terms 

 positive and negative to distinguish effects due to secondary 

 waves which are propagated, relatively to the medium, in the 

 same direction as the incident wave and in the opposite 

 direction. Putting then (E^ } ) + for the secondary positive 

 electric effect, «e have 



(jnW) , = 2<7rNA 1 tjnit-bz + q) _ 6 in{t-az + q)\ / q\ 



^- ;+ i{bc-iy '* * K) 



A similar argument may be applied to find the value of 

 the secondary negative electric effect (Ej) _ which is gene- 

 rated, in the plane c = c in the medium, by the operation of 



— Iiran 



