40 Jlpasurements of Small Resistances. 



When c = 0, 



nex 



[ii-^a)^-. 



qnex 



[lis J" ~1 



[n-\-a)h — neA 



Let resistances be written instead of conductances. /. e. let 



=x, ^ 



Then 



^ = X, - =M, ic. Ako let /.=A,X. 



ke 



(1) 



This is the complete formula. 

 I£ ^ = E, it takes the simple form 



_ ^E 1 



^-1 + /, 'A + X + Oil + A-) ^"^^ 



It can be seen from (1) that since h is ahvays positive, G 

 has always more relative influence than X. 



When the galvanometer resistance has not been fixed, if 

 we make the usual assumption mentioned above, then the 

 sensiti^^ty is proportional to a \/G. and can be calculated for 

 any case. The following table shows the result in two. pos- 

 sibly extreme, cases (when E = ^). 



T.'LBLE. 



k. 



G. 



A. 



X. 



(T 



varies as 



o-Vg 



varies as 



0-1 



100 



0-01 



100 



1 



L>iUU 



1 

 21U 



0-1 



1 



0-01 



0-1 



1 



1 

 12-1 



The values of a \/G show that for measuring a potential- 

 drop on a resistance of 0*01 ohm (with the battery voltao-e 

 eleven times the voltage measured) a potentiometer of O'l ohm 

 and galvanometer of 1 ohm give nearly twenty times greater 

 sensiti^-ity than a potentiometer and galvanometer of 100 ohms 

 each. 



