OF SECONDARY MINORS OF A PERSYMMETRIC DETERMINANT. 



533 



2 



B, 

 Pi 



A 2 

 A Q 



Bo B 3 B 4 



C 2 C 3 C 4 



D 2 D, D 



P% 



3 



= | A^CjD, | • (/? 3 -y 2 ), 



which vanishes when | j3 2 y 3 | is axisymmetric. 



(33) When p = r the array of zeros in A is square, and therefore also the comple- 

 mentary array. Thus, 



2 



which vanishes when j a x /3 2 y s S 4 | is axisymmetric. 



When p = n — 1 , q = n , r = n—l the theorem degenerates into that of § 27. # 



* The proof desired at the end of § 10 will be found in a paper sent to the Edinburgh Math. Soc. on 29th Jan. 

 1902, and at present being printed as part of Vol. xx. of the Proceedings of that Society, under the title " The 

 applicability of the Law of Extensible Minors to determinants of special form." 





• 



B, 



B, 



B 3 



B 4 







c, 



c 2 



c 3 



c 4 



A, 



*i 



a i 



ft 



7i 



«! 



A 2 



X 2 



a 2 



ys 2 



72 



8 2 



a; 



X 3 



a 3 



Pi 



7:i 



Sa 



A 4 



X i 



a 4 



A 



74 



*4 





1 A 2 B 3 C 4 | 



• [ * a ; «i & 73 h ] 



- 



1 A, B 3 C 4 1 



• [ * £ ; «i & 7s K ] 



+ 



1 A, B 2 C 4 | 



• [ x 7 ; a i A 7s 8 4 ] 



- 



A, B., C 8 | 



• [ X S ; a l & 73 8 4 ] 



(Issued separately September 26, 1902.) 



