1871.] 



of Electrical Resistance. 



249 



total resistance of the whole between ,1 and y, can be easily ascertained by 

 simple and well-known formulae . 



Fig. 1. 



cv 



7) . 



( % 



But let a leakage r, which we will suppose gives perfect earth, be 

 applied at some point in the shunt A B, the deflection previously produced 

 on G by a current arising in L will probably be considerably changed. I 

 say probably, because by sliding the leakage r along the whole length of 

 the shunt, we shall at last find a point Z at which the needle will return to 

 its original deflection ; the position of Z being ascertained, any resistance 

 varying from infinity to " dead earth " may be applied without causing 

 any change in the deflection of the needle. 



It is evident that, although the total resistance of the circuit between x 

 and y has been lessened by the insertion of the leakage, a proportionately 

 larger amount of current is diverted from the galvanometer by that part of 

 the shunt between L and the leakage at Z. 



Presuming the electromotive E in L to remain constant, and taking 

 r=0, we have the intensity of the current passing through G represented 

 by the equation 



E 



f— G.(A + B) 1 J G-RA+ET p 

 I + G + (A + B)^ J' 1 A + B j 

 but after r is connected, the equation becomes 



E 



A+G+ E + B 



A 



As the condition that the galvanometer deflection remains unchanged, the 

 first of these equations must be equal to the second, from which we obtain 

 the formula 



the resistance Gr being immaterial. It will therefore be seen that R 

 always bears the same proportion to L that B does to A, the latter 

 branches bearing some analogy to the proportion-coils of a Wheatstone 

 testing bridge. 



Under certain circumstances a test might be taken without any battery 



