i'os Lord Raylcigh. On the Bridge Method in its [Feb. 



The case that we have to deal with is when *i acts in /, and there 

 is no E.M.F. in e. We are at liberty, however, to suppose that two 

 opposite forces, each of magnitude Bi^/A, acts in e. One of these, 

 as we have seen, acting in conjunction with *, in /, gives no current 

 in e; so that, since electromotive forces act independently of one 

 another, the actual current in e, closed without internal E.M.F., ia 

 simply that due to the other component. The question is thus re- 

 duced to the determination of the current in e due to a given E.M.F. 

 in that branch. 



So far the argument is rigorous ; but we will now suppose that 

 we have to deal with an approximate balance. In this case an E.M.F. 

 in e gives rise to very little current in /, and in calculating the cur 

 rent in e we may suppose / to be broken. The total resistance to the 

 force in e is then given simply by C of equation (4'), and the approxl 

 mate value for ^- 2 is derived by dividing B*,/A by C, as we found 

 in (8). 



A continued application of the foregoing process gives W^i in the 

 form of an infinite geometric series : 



This is the rigorous solution already found; but the first term ol 

 the series suffices for practical purposes. 



The form of (8) enables us at once to compare the effects of inci 

 incuts of resistance and inductance in disturbing a balance. For 

 ad = be, and then change d to d + d 1 where d' = d\ + id' t . The valu 

 of Y^z/^i is proportional to d', and the amplitude of the vibratoi 

 current in the bridge is proportional to Mod d', that is, 

 \/(^V+dV). Thus d\ t d't are equally efficacious when numericallj 

 equal. 



The next application that we shall make of (8) is to the general- 

 ised form of Schwendler's problem. When all else is given, hoi 

 should the telephone, or other receiving instrument, be wound 

 order to get the greatest effect ? 



If by separation of real and imaginary parts we set 



the factor in the denominator of (6) with which we are concerned 

 becomes 



and the square of the modulus is given by 



Mod 2 = (ei + ri) l + (ej+r,)* (10). 



