34 2 COMPARISON OF RESISTANCES. 



give also 



and all the opposite sides are conjugate in pairs. 



From what has been said above (943) the four summits will 

 form 'three distinct equations, and the closed circuits three other 

 equations that is to say, that the number of necessary conductors 

 is equal to three. We might take, for instance, the six equations, 



(20) 



aa + ri - a' a = E a + e - 

 bfi-b'fi -ri^^-^ 



It is useless to solve these equations in their greatest generality. 



In the case of a permanent regime it is sufficient to consider a 

 single electromotive force for the ordinary practical case. Moreover, 

 from the principle of the superposition of permanent states (202), 

 we shall get the strength of the current in any given side by simply 

 adding the currents relative to each of the electromotive forces 

 taken separately. 



The problem is more complicated for variable electromotive 

 forces, but we shall suppose then that two of the resistances, 

 r and R for instance, are conjugate. This case corresponds to 

 that which is carried out in practice in comparing coefficients of 

 induction. 



The general remarks (944) relative to the properties of a 

 complete network, enable us to find directly the common 

 denominator of the equations (20). The six resistances give 20 

 combinations 3 by 3, but as we must deduct the four combinations 

 of three conductors terminating at the same summit, there only 

 remain 16 terms in the denominator, and we may write it in the 

 form 



,,/ T z * T 

 + aabb ( -++-+ 



\a a b b' 



