182 Mr. 0. Heaviside on the 



" Practically, take 



R^Rs, and L 1 = L 2 ; . . . . (28c) 



that is, let branches 1 and 2 be of equal resistance and induct- 

 ance. Then the second and third conditions become identical; 

 and, to get perfect balance, we need only make 



R 3 = R 4 , and L 3 =L 4 (29c) 



" This is the method I have generally used, reducing the 

 three conditions to two, whilst preserving exactness. It is 

 also the simplest method. The mutual induction, if any, of 

 1 and 2, or of 3 and 4, does not influence the balance when 

 this ratio of equality Rx = R 2 is employed (whether L 1 = L 2 or 

 not) *. So branches 1 and 2 may consist of two similar wires 

 wound together on the same bobbin, to keep their tempera- 

 tures equal." t 



Of the eight quantities, four R's and four L's, only five 

 can be stated arbitrarily, of which not more than three may 

 be R's, and not more than three may be L's. We may state 

 the matter thus : — There must first be a resistance-balance. 

 Then, if we give definite values to two of the L's, the cor- 

 responding time-constants become fixed, and it is required 

 that the other two time-constants shall be equal to them ; 

 thus 



either x ± =x 3 and # 2 = ^ 4 , 



or else sc 1 =x 2 and # 3 =5# 4 . 

 Thus the remaining two L's become usually fixed. In fact, 

 eliminating R 4 and L 4 from (26c) by (25c) and (27c), the 

 second condition may be written 



Suppose R 1? R 2 , R 3 given, then R 4 is fixed by (25c). 

 Two of the inductances may then be given, fixing the 

 corresponding time-constants. If these inductances be L, 

 and L 2 , then we must have (unless m x = # 2 ) 



X\ = x§ , a? 2 = i# 4 . 

 But if Yi x and L 3 be given, then we require (unless x x — x$) 



These two cases present a remarkable difference in one 

 respect. The absence of current in 5 allowing us to remove 5 



* The words in the ( ) should be cancelled. The independence of M 12 

 and M 34 , which is exact when L^Lg, L 3 = L 4 , and sensibly true when 

 the inequalities are small, becomes sensibly untrue when the inequalities 

 L x — L 2 and L s —L 4 are great. 



t « Electrician/ April 30, 1886, p. 489. 



