361-364] General Theory 317 



The current which flows from A to B when an electromotive force E is 

 introduced into the arm CD of the network, is equal to the current which flows 

 from C to D when the same electromotive force is introduced into the 

 arm AB. 



Conjugate Conductors. 



363. The same expression occurs as a factor in the right-hand members 

 of each of the equations (292), (293), (294), and (295), namely, 



A P1 + A Q2 - A Q1 - A P2 (297). 



If this expression vanishes, the two conductors 12 and PQ are said to be 

 " conjugate." 



By examining the form assumed by equations (293) to (296), when ex- 

 pression (297) vanishes, we obtain the following theorems. 



THEOREM I. If the conductors AB and CD are conjugate, a current 

 entering at A and leaving at B will produce no current in CD. Similarly, 

 a current entering at C and leaving at D will produce no current in AB. 



THEOREM II. A battery introduced into the arm AB produces no current 

 in CD. Similarly, a battery introduced into the arm CD produces no current 

 in AB. 



As an illustration of two conductors which are conjugate, it may be 

 noticed that when the Wheatstone's Bridge ( 352) is in adjustment, the 

 conductors AD and BC are conjugate. 



Equations expressed in Symmetrical Form. 



364. The determinant A is not in form a symmetric function of the 

 n points 1, 2, ..., n, so that equations and conditions which must necessarily 

 involve these n points symmetrically have not yet been expressed in sym- 

 metrical form. 



We have, for instance, 



in which the points which enter unsym metrically are not only 1 and 3, but 

 also n. Similarly, we have 



i t \> -"- 



n i, 



**-n 1,5> > -**- 



