7:? Mr. 0. Heaviside on the 



effected by an integration along the line from x = Otox=l, 

 with a similar process applied at P and Q to the potentials of 

 Ci and C 2 and the current in E 2 . Collecting the expressions 

 for the separate divisions, we have, from # = to x = x x , 



V^-*h*m(^. + ty-%Ap*.w?\ .... (12) 

 from «r = «r 1 io a?=# 2 > 



\ XlX2 = 2A,| sin \-±- + & f J + £ sm-^ j 



=2A i M;say; . (13) 

 from ^ = ^2 to #=#3, 



TT VA f ' ( a i X , 7 ^ ' ' «*(# — #l) 



V^ 3 =SA,.| sin {-j- + ^ +?,sm -^ 



+ ^ sin <£p)| = 2AM';,say; . (14) 



and so on to the end of the line. 



At the beginning P, by (4) we have 



V 1 = ^A J .(sin^-m 1 a f cos^) = ^ A ^ sa y- ■ • * ( 15 ) 

 At the end Q, by (8) we have 



V 2 = SA f [ J sin (a. + h) + q. sin a. ( 1 — j 1 j 



+ q] sin a Yl- ^ 2 j + . . . j + (™ 2 a.-$af) { cos (^ + 6,-) 



+ ^cosa.^l-^+^cosa^l-^J4-...|] 



= 2A^',say (16) 



Also, let Y s =Gkl; then by (6), 



V 3 = 2 A .^ — a. -J cos (a . + 6/) + ^ • cos a { ( 1 — ~J 



+ rfcoBa f (l- f ) + . • • } =^N7, say. (17) 



To find A,-, the ith value of A. Multiply both sides of each 

 one of the last equations, (12) to (17), by the coefficient of A,- 

 in that particular equation ; e. g. multiply (12) by M^, (13) by 

 Mj, and so on. Next integrate each side belonging to the 

 line between the limits for which it is true. Thus (12) from 

 x = to x — x v &c. Apply a similar process to V,, V 2 , and 



