1126 



au, ai2, ... ai, 



Vjl\. 



The algebraic complement of üji we call Aji . 

 By the substitution 



1 



becomes 



H ^= :E bjj xf + 2 ^ bj]c xj x]c. 

 1 1 



Tlie functions x^,...x^ are given. We now dispose of the remaining 

 (.t;^i , . . . x^) in such a manner that the following relations are 

 satisfied : 



hjj, — for 7 = 1,2, ... (J ; A: == 9 + 1, . . . ö. 



In this waj we attain that the introduced rj — () auxiliary variables 

 occur only squared. 



Solving Vi from the equations of substitution we find 





(i=l,2...(7). 



Consequently we find for H 



2 [ 2: Aji.vj ) ^ (^1/^*1 + A, A-2 + . . . + A,,x^y 



H = ^' Vi' — 



i (^-1 .t'l + "IAmA-hxx x-i 4- • • • + A^iXr) 

 1=1 



.2 2 



^ ^Ïj- . x\ + 2 ^ AxiMi . xi xo -{-■■. + 2 A^i. x"^ 

 i=\ i=\ 1 



:e ^ Aji .1- • + 2 :^^ [2 AjiAki I xj xk 



j^l\jz.-.l J • j:=X,k^\\i=l 



or putting 



.^r .^ j'i 



= b 



2 AjiAj,, 



i—l 



JJ 



^ bjlc (= 6a:j) 



H =z 2 bjj Xj^ -\- 2 2 bjk Xj xk. 



