64 Mr. 0. Heaviside on the 



steady current in either of the to-be conjugate conductors due 

 to impressed force in the other, a true resistance-balance was 

 still wanted to ensure conjugacy, when the currents vary. I am 

 unable to maintain this hasty generalization. In the example 

 I gave, equations (59c) to (61c), in which each side of the 

 quadrilateral consists of a condenser and a coil in sequence, so 

 that there can be no steady current in the bridge-wire, it is true 

 that the obvious simple way of getting conjugacy is to have a 

 true resistance-balance. The conditions may then be written 



E, 1 E 4 = R 2 B'3j S 1 S 4 =S 2 S 3 , L 1 L 4 =L 2 L 3 ; . . (Id) 

 and either 



x \ =x ^ anc [ yi—y^ 

 %3=%±, y*=y±\ 



or else 



(2d) 



*=** and y^y^ 



where R stands for the resistance and L for the inductance of 

 a coil, S for the capacity of the corresponding condenser, x for 

 the coil time- constant L/R, and y for the condenser time- 

 constant RS ; that is, we require either vertical or else hori- 

 zontal equality of time-constants, electrostatic and electro- 

 magnetic, subject to certain exceptional peculiarities similar 

 to those mentioned in connexion with the self-induction 

 balance. It is also the case that on first testing the power of 

 evanescence of the other factor on the right of equation (61c), 

 it seemed to always require negative values to be given to 

 some of the necessarily positive quantities concerned. But a 

 closer examination shows that this is not necessary. As an 

 example, choose 



R! = l, R 2 = 2, R 3 = 3, R 4 =10, -\ 



1^=12, L 2 =5, U=h% U=i, J- . '(3d) 



It will be found that these values satisfy the whole of equa- 

 tions (61c), and yet the resistance-balance is not established. 

 No doubt simpler illustrations can be found. We must there- 

 fore remove the requirement of a resistance-balance when 

 there can be no steady current, although the condition of a 

 resistance-balance, when fulfilled, leads to the simple way of 

 satisfying all the conditions. 



(2) Similar Systems. — If Y = Z l C be the characteristic 

 equation of one system and V = Z 2 C that of a second, Y being 

 the potential difference and C the current at the terminals, 



