Coefficients of Self-induction and Mutual Induction. 233 



T=i(Lw 2 + N.i-i 2 ) 



2 . — 



F = i{7 1 w 2 +S.i — w +7 2 i 2 + G.i— ^ + dy* + b.y — z' 



+ a, . i— m +a 3 . i — i +Bi 2 }. 

 From these, 



Y2<# + S • # — W + «2 • #~~ 2+ G. #— "^ = N. Zq — Xq, 



dy + b.y—z — Q ,a:—y = 0, 



7j?/ — a x . 2 — m — 5.oj — u = — Lw = — L<£ ; 



whence 



w(«i + 7i + S) = S<£ + a 1 2 — JjXq. 



Substituting in the two former equations, and putting 

 as—y=—6, 



-a^+U+7 2 +s. "* +7 > ) *-(«,+ * iS +. > 



\ «i+7i + 8/ \ «i + 7i + b/ 



=N(i -i )-Li ^ + ryi + s , 



(£ + d + G)0+(6 + d).z -bz = 0. 



Now if we put 



g » + „ XT: T c =/> «i + «2=a, 71 + 72 = ^- 



a i + Yi + o 

 Since 



d d 



lv=*\-y 7 2 =«2-^' 



The condition of no flow, and therefore no deflection, on 

 making or breaking contact is 



m-u. — - — 5 =o. 



»i + Yi + o 

 If b = d, and therefore ci 1 = y 1 , 



N=L S 



2^ + S* 



and the transient currents from each coil will be a maximum 

 when 



6 2 =/G(2B + c)/(G + 2/). 



