Transmission of Electric Waves along Wires. 373 



have been introduced and the amplitude diminished. Evi- 

 dently, then, to complete the account of what happens at the 

 electrometer, and frame a theory of the throw d) to be 

 expected, we need an infinite decreasing series of integrals of 

 each of the three types given in (31) as due to the first 

 interference effect. 



40. All these integrals, when evaluated, have the same 

 denominator : hence bringing; that to the left side of the 

 equation, we may write 



4/^(l + 7< ; 5! )Erf , = F 1 -r-G 1 + H 1 



+ F 2 + Go + H 2 



+ F3 + G3 + H3 



+ > • • • (32) 



+ 



+ 



= F + G + H ; 

 where F = F 1 +F 2 +F 3 + ;" 



and the same applies to G and H. 



41. In constructing the integrals for the first line, we have 

 to note that the reflexion at the condenser and the return of 

 the waves to the electrometer introduce the space coordinate 

 2Lin two exponential factors and in the argument of the 

 cosine, besides introducing the amplitude factor A and the 

 phase change a. 



Again, in passing down any one of the columns in (32) we 

 have to affect each succeeding line by the factor 7 ,<i , and intro- 

 duce k in the angles whose cosines are taken. 



We thus obtain the following scheme of integrals : — 



Ed'= \ e- 2k P f co^pt dt + s 2 \ c -2#(*-2* a ) C0S 2 ( _ lZ^f 2 + a ) dt 

 J° J2t 



+ 2sl , 



J2t„ 



e~ 2/i '^ ~ f J cos pt cos (p . t — 2t 2 + a)dt 



+ 7* 



1 n 00 



e -2ipt cos 2 ( pt + K y t + r 2 >s 2 \ e - 



J2L 



■2kp(t-2t 2 ) cos 2 ( p . t _ 2^ 2 + a + K)dt 



+ % & s 1 e -2kp{t-t 2 ) cos ( pt + «) C os (p . t — 2t 2 + * + ic)dt 



J2L 



+ 



+ 



+ 



to an infinite number of lines. 



Phil. Mag. S. 5. Vol. 50. No. 305. Oct. 1900. 



•2 D 



