

Axisymmetric Determinants. 

 connected with the determinant 



457 



d e 



« 3 



f h 



9 I 



h m 



i n 



f 

 k 



o 



V 

 9 



T 



a 



9 

 I 



V 



s 



t 



b 



c 



h 



i 



m 



n 



9 



r 



t 



u 



V 



ID 



w 



' X 



2 3 4 



2 3 4 



vanishes. From 



let us see what happens when the minor 



§10 we learn that on that supposition S, V, X are expressible as 

 squares, and consequently can have their roots extracted. We thus 

 have from §11 



aJS+b VV + c VX 



"I 



b 



9 



c 



r 



• 



d 



e 



e 

 3 



2 



b c 

 m n 



• 



d 

 f 



f 







' 2 + 



b 

 h 



c 



i 



• 



d 



k 



k 







'I 



-M 



a c 

 p r 



• 



d e 



1 



a c 

 I n 



• 



d 

 f 



f 







1 

 2 



+ 



a 

 9 



c\ \d k 



i\ ' \k o 



i 



H 



a b 

 P 9 



• 



d e 

 z 3 



— 



a b 



I m 





d 

 f 



f 







• la 

 \9 



b 

 h 



• 



d k 

 k o 



'i 



a b c 





d e 



■'• — 



a b c 



. \d 



f 



- + a 



b c 





d k 



a b c 





e 3 





a b c 



1/ 







a 



b c 





k o 



V 9 



r 











\i 



m n 











9 



h 



i 









= 0. 



And this vanishing expression being one of the eight whose product 

 constitutes the norm, the norm itself must vanish. 



Capetown, S.A. 

 Dec. 22, 1906. 



