410 Dr. Oliver Lodge on Opacity. 



Therefore,, for the transmitted amplitude 

 E _ 2p 



and for the reflected 



Ej p -f gv 



5_3 ^ p — qv 



B x p + qv 



or rationalising and writing amplitudes only, and under- 

 standing by p no longer d/dt in general, but 'only 2tt times 

 the frequency, 



Eo _ 2p 



E, ^((p + av y + M-P^' ■ ( u ) 



Any thickness of metal multiplies this by the factor e~ ax , 

 and then comes the second boundary, which, according to 

 what has been done above, has a comparatively small but 

 peculiar effect ; for it ought to change the amplitude from p 1 

 into p, that is to give an emergent amplitude 



_4/ 2. p/*v_ 



l + (l+p/avy 



instead of the above incident on the second boundary 



^ e,«-i. am 



v(i+(i+^M 3 ) ' " ' (0) 



that is for the case of light in gold, for which p/av is small, 

 to change 2/ s/2 into 2 n/2, in other words, to double it. 



2 /2tt 

 The effect of the first boundary alone, p 1} is — - — , or say 



1/18, and this is a greater reduction effect than that reckoned 

 above for the two boundaries together. 



Thus the obstructive effect of the two boundaries together 

 comes out less than that of the first boundary alone — an 

 apparently paradoxical result. About one-eighteenth of the 

 light-amplitude gets through the first boundary, but about 

 one-ninth gets through the whole slab (ignoring the geo- 

 metrically progressive decrease due to the thickness, that is 

 ignoring e~ al , and attending to the effect of the boundaries 

 alone ; which, however, cannot physically be done). At 

 first sight this was a preposterous and ludicrous result. The 

 second or outgoing boundary ejects from the medium nearly 

 double the amplitude falling upon it from inside the con- 

 ductor ! But on writing this, in substance, to Mr. Heaviside 

 he sent all the needful answer by next post. "The incident 

 disturbance inside is not the whole disturbance inside." 



