364] 



General Theory 



319 



then the determinant on the right-hand of equation (299) is obtained from 

 D by striking out the lines and columns which contain the terms J5T 13 and 

 KM- Thus equation (299) may be written in the form 



8 2 D 



AIS + ^24 A 23 Z\ 14 j, -., . 



Again the determinant A given by 

 A 



-^223 -^23) 



^-n 1,1 > 



may be written in the form 



.(300) 



A = 



dD 



This is not of symmetrical form, for the point n enters unsymmetrically. 

 We can, however, easily shew that the value of A is symmetrical, although its 

 form is unsymmetrical. 



By application of relation (298), we can transform equation (300) into 



jr TT _ jr rr 



IT W TT ~K~ 



"Hi -^22> -^-23> 1) n 1 



-n 1,3> '> J *-ni t n\ 

 TT jr 



-"-23> > - CL 2,n 1 



1,2 



-711,711 



r 1 



-n,n i 



-2,n 







K 



n,n 



Thus A is the differential coefficient of D with respect to either jBT u or 

 ^n,, or of course with respect to any other one of the terms in the leading 

 diagonal of D. Thus, if K denote any term in the leading diagonal of D, 

 we have 



and this virtually expresses A in a symmetrical form. 



