±74 Mr Larmor, On a mechanical representation of a [May 4, 



If i denote the angle of incidence of the waves, \ their length, 

 and v their velocity, we must have 



In + n x z — pt = — (ob sin i -f z cos i - vt). 

 Thus P - ■ " ■ 



I 2 sin i 2tt sin i ' 



where v = {fi 1 K 1 )~* is of the order 3.10 10 C.G.S., and for light waves 

 X is of the order 10~ 4 , and for copper a 2 is about 1600. 

 Hence for all realisable wave-lengths, long or short, 



which for light waves is of the order 10 5 , and is very large for 

 all realisable waves, unless for media of slight conductivity com- 

 pared with metals. The amplitude of the surface wave in the 

 conductor is reduced in the ratio e~ l at a depth n~ x ; this wave 

 is therefore absolutely superficial, and is fully developed even 

 in a very thin sheet of metal. 

 The surface conditions give 



n 1 (A 1 -B 1 ) = n 2 A 2 , 



l(A 1 + B t -A 2 ) = - l -4m<r 

 V 



-cpK^+BJ^A^ 



2 



of which the first and third equations determine the amplitudes 

 of the waves produced by the reflexion of A lt and the second 

 determines the surface density 



cr exp i {lx—pt) 



of the superficial electric charge. 



n„ 47r 



Hence p + ^ l) A 2 = 2A X , 



i.e. 



a„=2 ,vr»fi , A 



nj \pa- 2 K 1 



n 

 and B=A--*A C 



1 x ?2j 



