Dr. Oliver Lodge on Opacity. 409 



whence we can w T rite E anywhere in the slab, 



1 - Mw—p) f eq , . Q±±£ e 2 q i e - q A . 



E i " (qv+py^-iqv-p)* \ * gv-p J 



Put x = l, and call the emergent light E 2 ; then 



% ~ {qv+pye« l -(gv-p) 2 e-* 1 " Pi ^ ' l } 



and this constitutes the measure of the opacity of a slab, 

 p z being the proportion of incident light transmitted. 



It is not a simple expression, because of course p signifies 

 the operator d/dt, and though it becomes simply ip for a 

 simply harmonic disturbance, yet that leaves q complex. 

 However, Mr. Heaviside has worked out a complete expres- 

 sion for p 2 , which is too long to quote (he will no doubt be 

 publishing the whole thing himself before long), but for slabs 

 of considerable opacity, in which therefore multiple re- 

 flexions may be neglected, the only important term is 



4,s/-2e-y/ 



av 



with 



?= l + (l+p/*vf ••••• ( 18 ) 



* = 4/(2wpp/a) =3xlO G 

 for light in gold ; and 



V 2-7T 2-7T 1 . 



± — — — = -7777 — e = rrr about. 

 av a\ 60 x 5 25 



So the effect of attending to reflexion at the walls of the slab 

 is to still further diminish the amplitude that gets through, 

 below the e~ al appropriate to the unbounded medium, in the 



ratio of rtg , or about a ninth. 

 25 ' 



Effect of each Boundary, 



It is interesting to apply Mr. Heaviside's theory to a study 

 of what happens at the first boundary alone, independent of 

 subsequent damping. 



Inside the metal, by the two fundamental equations, we 

 have 



and by continuity across the boundary 



E 1 + E 3 =E , 



E 1 -E 3 =„H =At ,E (^)WJ'E , 

 where still q 2 = A7rfjbkp. 



