, or A say. 



Primary Minors of an Axlsymmetric Determinant. 511 

 fourth order 



a Y a. 2 «;. « 4 

 a 2 A, 6 3 6 4 



«3 &3 <?3 C 4 



« 4 b i C 4 tf 4 



the Jacobian 



a(A lf B 2 , C 3 , D 4 , C 4 , B 4 , B 3 , A 4 , A 3 , A 2 ) 



d(«u 6 2 , c 3 , d 4 , c 4 , b±, fr 3 , fl 4 , a 3 , ^2) 



(where the order of the independent variables deserves notice) 

 is equal to 



Cod± — c± b 2 d± — b 4 2 



CYh — Ci • a^U — a^ 2 



b^ — b^ a^J^ — a^ . ... 2(a 4 6 4 — a. 2 d±) 



•c 3 d 4 





• 



a J } 4T~ fl 2^4 



Multiplying this by A i3 



in the form 





9 9 



«r « 2 ~ 



« 3 2 





Wo 2 b 2 2 



6 3 2 



Go/'.? 



2a 1 a 2 2# 2 ?> 2 2« 3 & 3 a^^ + a^i 



we obtain 



a 1 A 1 . /'oB 2 . c 3 C : i 2« 3 A 3 . 2« 2 A 2 



1- 



a x A } 



b,B, 



I 



1- 



2a 2 A 2 



so that we have 



JA'^A 10 - 1 ' 1 - a i A i + ^ B 2 + - • . + 2a 2 A 2 I t 



