Wave-trains through a Conducting Dielectric. 325 



and the expression for y- simplifies to 



J-o 



h l-& 2 r l-y + 2g 2 sin2Scot X -| ' n 



I ~1 + 6 2 L l-2£ 2 cos28 + f J' * ! ^ } 



This case was recently worked out by Dr. Barton, and our 

 equation (51) may be reduced to his. Dividing out by the 

 denominator in the square bracket, we get 



]t l-h 2 [\ 2g 2 (g 2 — cos 28- cot x sin 28)1 

 1 ~1 + 6 2 L " l-2f 2 cos28 + f J* 



Dr. Barton's expression is* 



It __ l-fr 2 f 1 /2 -q, 2 Q*//3) sinffl 2 + cos /3t 2 -b 2 e-« f n 

 I "1 + 6»L + l-2^-^cos^ 2 + 6%- 2 ^ J' 



which is equivalent to ours ; his t 2 being equal to twice our 

 t 2 , and his a//3 equivalent to our p\lp- 2 or cot^. 



As a second special case, suppose we are dealing with a 

 steady simple harmonic ray instead of a damped wave-train. 

 X is then ninety degrees, and the other symbols take the 

 special values 



^ = 90° . sec^;=co, ~] 



Pl =0, ••■ W =g=y , [_..... (52) 



The long second term in (49) vanishes altogether now, being 

 divided by (sec%— cos%), and 



I' _ <?P 



I b 2 l-2f cos28 + f ' ' 



If in this case we again put a 2 =0, we have 



» = £=&, 



B=p 2 t 2 ; 



and so if the plate be a non-conductor, 



L c 2 / 2 



I ~l-2b 2 cos2p 2 t 2 + bv # * * 



* Proc. Roy. Soc. vol. liv. p. 92 ; < Thesis/ p. 13. 

 Phil. Mag. S. 5. Vol. 39. No. 239. April 1895. 



(53) 



(54) 



