COMPARISON OF RESISTANCES. 325 



Let r Q be the resistance of the battery and of the galvanometer, 

 including the connecting wires, r and r^ the two resistances to 

 be compared, I the intensity of the current with the resistance r Q 

 alone, I and I' the intensities obtained when the resistances r and r^ 

 are successively introduced into the circuit. We have 



(7) I r = I( 



whence 



the ratio of the resistances only depends on the ratio of the in- 

 tensities, and it is sufficient to use a graduated galvanometer. The 

 corresponding variations dr and d\ of the resistance r and of the 

 current I, give, from equation (8), 



r I (I, -I) 



For the same absolute sensitiveness d\ of the galvanometer, the 

 relative error for the value of r is a minimum, when the product 

 I(I - I) is a maximum, that is when I = 2!, or r=r Q , which gives 



dr d\ 



the relative error for the resistance r is twice the relative sensitiveness 

 of the galvanometer. 



If the resistances r and r' are first connected end to end, then in 

 parallel, the corresponding intensities \ and 1. 2 of the current still 

 give the ratios 



Comparing with equations (7), we deduce 



so that the experiment gives several controls. 



