COIL BRIDGE. 363 



There is no current in the galvanometer when the quantity 

 within brackets is null. We deduce 



U- + L*(l+L\, 



b a E a \b a] 



or 



b' a! e /i i\/ a\ f a' a + b 



It will be seen that the influence of the electromotive force e 

 may be considerable when the resistance R of the branch con- 

 taining the battery is large compared with a and b. Moreover, 

 the term of correction changes its sign with E. If we reverse the 

 battery current, and observe the values b' and b' v which establish 

 the balance, then, if 8 is the term of correction, 



b' a' b( a' 



= + 5, - = -- 6, 



b a b a 



or 



We shall take for the desired resistance, the mean of the values 

 corresponding to the two directions of the battery which give zero 

 current. 



If the balance is unchanged on reversing the current of the 

 battery, we conclude that the electromotive force e is null. This 

 would also be shown by closing the circuit of the galvanometer. 



When the condition ab = ab' is exactly satisfied, the electro- 

 motive force e of the galvanometer not being zero, the deflection 

 of the needle is independent of the battery. It does not change 

 when the current is reversed, or when the battery circuit is alter- 

 nately opened and closed. 



Hence, if we wish to get rid of all corrections, we should first 

 close the galvanometer circuit, observe the deflection of the needle, 

 and then adjust the resistance until the deflection does not change 

 when the battery is closed. This method, however, is not rigorous 

 unless the effects of induction are insensible. 



