180 



Prof. A. Schuster's Electrical Notes, 



We might substitute an ordinary galvanometer for the 

 differential one, but balance the current by an independent 

 battery, as we frequently do in the comparison of electro- 

 motive force. The arrangement is that 

 shown in fig. 3. A small change 8p of p 

 will show itself as a deflexion of the gal- 

 vanometer. The sensitiveness is the same 

 as before, with the exception that the 

 resistance q of the auxiliary battery is a 



Fig. 3. 



disadvantage. 



If b is large, we now have 

 hp _ By 



Fig. 4. 



p+q+9 i m 



If we can make q small, we come back to the original 

 equation ; and I have introduced this example merely to show 

 that however much we may vary the form of the experiment, 

 we always come back to the same limiting value. 



The method most usually adopted for a comparison of 

 resistances is the Wheatstone- bridge, which is generally 

 assumed without further discussion to be the most delicate 

 arrangement. 



It seems advisable, therefore, to discuss a little more fully 

 the conditions under which the best effects can be obtained. 

 If p is the resistance to be measured, we see at once that 

 if a change of resistance 8p produce a 

 current tBp/(p+g) in the galvanometer- 

 branch, the resistance s must be small and 

 q large compared to p and g. The arrange- 

 ment is therefore very different from that 

 we are usually told to adopt. To determine 

 the effect of a small electromotive force 

 i x Bp in the branch p, let i l9 i 2 , i 3 , i 4 , y be 

 the currents inp, q, r, s, and g respectively ; 

 then, in the usual way, we find in terms of the current in jo, 



T _ (pr-qs)^ 

 g{s + r) +s(q + r)' 



When the resistance p after being balanced is changed to 

 Bp, the current through the galvanometer will be 



S 7= — £5t = n& . . ( 5 ) 



g{s + r)+s{q + r) g(s + r) + r(p + s) 



In order that By should be as great as possible, s must be as 

 small as possible. If it can be neglected compared with jt?, we 

 should have 



rijip 



8y = 



g(s + r) + rp 



