Potts — ■RovrtancPs New Method. 95 



capacity. On this account formula (5) is not strict!} 7 accurate 

 but should include a term involving the capacity of the coil. 

 Let the capacity which in parallel with the self-induction, L, 

 will have the same effect as the given coil be k and let K\ be 

 the resistance of the coil and R", the resistance of the remain- 

 der of arm 1. Substitute in (3) in place of 



1 be 



R 4 (R 1 +R 1 )+r(B 1 +B,)=A 



and also put 

 Then 



(R,R ,, 1 -R g R 4 )(l-^L)+R , 1 R,H-^^R , 1 R" 1 R,+^R 3 - 

 A(l-b'kL)-b t klR , 1 (R t +R t ) + i{Abk'R\ + (l--b*kL) 



bkR,R„R, 



W(R,+R 4 } (6) 



As before, the condition for no deflection is that the real part 

 of (6) vanish, or 



[(R a R 4 -R,R" l )(l-ft^L)-R' l R 3 ][A(l-^L)-6 a ^R' 1 (R3+R 4 )] 

 = [AbkR' 1 +(l-b i kL)bl(R 2 +Rj][bLR a -bkR' 1 (R,R t -R 3 R'' 1 ) : ] 



Expanding this it becomes, 



A(l-^L) 2 (R„R 4 -R 3 R" 1 )-AR' 1 R 3 (l-i^L) 



+b i k£R\(R t +R t )R a -(R B R t -R i R'\)(l-b a k'L)b i klR\ 



(R 3 +R 4 )=A^LR' 1 R 3 -A^ 2 FR , 1 2 (R 2 R 4 -R" i R 3 ) 



(l-^L)(R 3 +R 4 )R 3 WL-(l-^L)(R 3 +R 4 )(R 2 R 4 -R" 1 R 3 ) 



¥JclR\ 

 JSTow since k is in all cases small and I is also small, the terms 

 above which involve ¥ and kl may be dropped, whence we get, 



p _ A(1-6 2 A;L) 2 (R 2 R 4 -R 3 R" 1 )-^L(R 3+ R 4 )R 3 (1-^L ) 



AR, 



= (l-y C L)' R ' R *~ B ' B ^ -^L R '+ R «(l-yA;L) 

 K 3 A 



ISTow since the last term is very small and 1 — fffcL is nearly 

 1, it may be dropped ; and we have for the final formula, 



R' =-*— < L~ R 3 R ", , ( l Vn \ R 3 + R 4 



i-« L )i 



/R 4 (R,+R,)+r(R, + Rj 



l 



R 



^H5?cW (7) 



