662 Prof. Karl Pearson on a General 



Again from (x.) 



ma- P= n 



^ oa = "IT ^ (dp a(T P r ov) 



P = l 



ma P= n 

 ^/3=TT S ( d pP a P r op) 



,0=1 



ma- P= n 

 ^ov=-jy S (dpv<T P r oP ) 

 u P =l 



Multiply again by A s a, A s j3 y ..Asv respectively and add. 

 We find : 



S (yfr 0e As€)=m(T iT s r o8 (xii.) 



Equations (xi.) and (xii.) are true for every value o£ s 

 from 1 to n. 



Now multiply equations (iv.) by A s a, A s (3.... A s v and add 

 them : we find after dividing by a common factor : 



a- Q r 0s = A a J a5 + A /3 Jf3s + A 7 J ys + . . . + A v J vS . (xiii.) 

 where 



Jei= S (djj e &prsp)ID. 

 p=l 



There will be n such equations, if we take 5=1 to s = n. 

 Now consider the determinant 



R= 



1 



10; 



7*01 j ?\)>j 



1 r„. 



^20, ?" 21 , 





?'«0J '*»Ij ? '^2i • • • 1 



where the r's are defined by equations (ii.) and (iii.) above. 

 Let E o0 be the determinant found by striking out the first row 

 and column, and let p t t< be the minor of R 00 corresponding to 

 the constituent r u > in R or . Further let R-cs be the minor of R 

 corresponding to the constituent r 0S) then it may be shown 

 that 



S ( ? W>«') = — IV 



(xiv.) 



Write out the equations like (xiii) for s — 1 to s = n, mul- 

 tiply them respectively by p lflf p 2t !>-Pnt' anc ^ ac ^- 



