318 Steady Currents in Linear Conductors [OH. ix 



so that, on subtraction, 



TT- jr 



-"-25 > ) -^-2,711 



-A-225 -"-23 + -^24) 



A 13 - A 14 = 



From the relation 



it follows that the sum of all the terms in the first row of the above deter- 

 minant is equal to K 2jn , the sum of all the terms in the second row is equal 

 to K 3%n , and so on. Thus the equation may be replaced by 



XL 2 1> -"22) -*^-25) ) -^-2,711) -^-2,71 > 



V V V V V 



A 31) -ft-32> -ft-35> "> J^3,1ll) J^-3,n 



** I,li -"-n i,2> -"-7ii,5) ) "-ni,ni> J^-ni,n 



and similarly, 



A 23 - A 24 = (- If -i K n , K 12 , K u , . . . , K ltn . 



These two determinants differ only in their first row, so that on sub- 

 traction, 



(A 13 - A 14 ) - (A ffl - A 24 ) 



K K K K 



"'g n ' 'J'^_ "' K ' n ' (299), 



the last transformation being effected by the use of relation (298). 



The relation which has now been obtained is in a symmetrical shape. If 

 D is a symmetrical determinant given by 



K K K K 



j^ w v TT 



- /1 -21) -^22) --23> '> -^-2,n 



