212 Lord Rayleigh. On the Bridge Method in its [Feb. 10, 



The next remark tbat has to be made is that, even when the con- 

 ductors, b and </, to be compared are endowed with sensible in- 

 ductances (positive or negative), the problem may still, theoretically, 

 be brought under the above head. Suppose, for example, that 6, d 

 represent nearly equal electromagnets. Their inductances may be 

 compensated by the introduction (in series) of suitable equal con* 

 densers into these branches, so that b and d are reduced to 6, and d 1 . 

 If then we assume a to be a simple resistance (a 2 = 0), the solution is 

 as before. Two objections may here be raised. First, on the 

 theoretical side it has not been proved to be advantageous to assume 

 ./.. = <>; and, secondly, the introduction of extraneous condensers,* 

 even with interchange, into the branches to be accurately compar 

 may be a complication unfavourable to success. 



We will now resume the consideration of (19), supposing that 



---- (28), 



(29), 



e e!+e 2 = n tr 2 , srj + tj = , 



- r,, *i, * 2 being given by (20), (21). Thus, 



16 



and the question before us is how to make the modulus of the second 

 fraction on the right a maximum by variation of a. In the de- 

 nominator of this fraction r, and *i are real, and the modulus of 

 b is v/(&i 2 + &2 2 ). For the numerator we have 



2(*, i'go) 



a b 



so that 



PI 



i I , 



~ ' " 



Also from the definition of 



so that 



Thus 



and this is to be made a minimum by variation of 01, a^. 



IT (30), 



* The use of condensers or electromagnet! in the branches e and f stands, 

 course, upon a different footing. 



