Measuring the Coefficient of Self-induction. 59 



equal zero ; then the condenser is discharging through a 

 resistance equal to 



r(A + B-r) ^. r{B(0 + D)-O} 

 A + B B(C + D) 



since 



AC = BD. 

 Therefore 



" r{B(C+D)-C,} ' _W±5» 



q=g e b (c+d) = q oe > *, 



and 



do B(C + D) -A. B(C+D > 



"^ = ^K,|B(C + D)-C n 6 K r {^°+^-^- 



Also 



^ , A + B B(0 + D) 



q = Ky r and — - — = -^ — ^ 



Substituting these values in (4) ; we obtain 



B(C + D) -9+Rt B(C + D) 2(c+d) ( 



X Q ^ e L =y . B(0 + D) _ c? , . e Kr{B(C+D)-Cr} . 



Also 

 therefore 







1 



-C+5, 



D 



_B(C+D) 



e l " = 



B(0 + D)-O ' & { B ' C + D >- C 4 

 This equation must hold for every value of t ; hence 

 1 D 



and 



From (A), 



From (B), 



r B(0 + D)-O' 



(A) 



C + D _ B(C + D) 



L ~Kr{B(C + D)-0}" ' " * W 



rD = B(0 + D)-Cr, 



r(C + D) = B(C + D); 



.'. r = B or 0=-D. 



L== E>{B(0 + D)-O} 

 B~ 



