Measuring the Coefficient of Self-induction. 57 



and since BL = Kr 2 D, 



2KrSD 

 ?~*B(C + D)+G(B + C)' 

 If p be the fractional error in r, 8=pr; 

 __ 2Kr 2 Dp 



•'• ^~^B(C + D) + G(B + Cy 



Now E C 



(A + D)(B + C) C + D 



= E 



p+ A + B + O + D 



C 



since AC = BD ; and Kr 2 D = BL ; 



2EL^BC 



•* * ) P (0 + D) + D(B + 0)}{B(C + D) + G(B + C)} 

 2EIp 



-^U.g) t D(.*gj}{0 + D t8 (l + g)}- 



If we wish to make q as large as possible for a given value 

 of p, we must make C small and consequently B also small. 

 Of course B cannot be less than r, and will generally be a 

 given resistance, depending on the apparatus we are employing. 

 If B is given, differentiating the expression for q with respect 

 to 0, and equating to zero, we obtain 



_ / BD(G + U)(p + B)- 

 V (G + Ji)( p + D) ' 



If p is small compared to the other resistances, this gives 



' a+D 



G+B* 



This method can be made much more sensitive by adopting 

 the principle employed by Professors Ayr ton and Perry in 

 their admirable instrument the Secohmmeter. A commutator 

 is introduced into the battery and galvanometer-circuits, which 

 by its revolution puts on the battery, the galvanometer-circuit 

 being closed, breaks the latter, or short-circuits the galvano- 

 meter and then breaks the battery-circuit, afterwards closing 

 the galvanometer-circuit, repeating this cycle of operations 

 during each revolution. In this method neither the speed of 

 the commutator nor the fraction of the cycle during which 



V; 



