ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 



677 



we see that their difference is identical with the previous difference. The result arrived 

 at thus is 



7) T 



^ = M 2 + K#AI - Ui^/sl. 



it being understood, of course, that M 2 here stands for a particular member of a triad of 

 quadrics, one of which has been so denoted. 



(17) If we do not discriminate as to form, the number of aggregates of multiples of 

 the original quadrics is infinite. Keeping, however, to the form which has turned up 

 repeatedly in what precedes we have only fifteen to reckon with, this being the number 

 of pairs of letters choosable from the six, a, b, c,f, g, h. The fifteen must, of course, 

 be separable into five triads, and it is best so to arrange them. They may therefore 

 be conveniently tabulated as follows : — 





X 2 



y 2 



2 2 



yz 



zx 



xy 



1 M A C 3 1 



[0] 







2[11] 



2[8] 



2[5] 



1 u \ C 2 a Z 1 





[0] 





2[6] 



2[12] 



2[9] 



1 M l«2 5 3 1 







[0] 



2[7] 



2[4] 



2[10] 



1 «1 Vs 1 



[7] 





-[11] 





-2[5'] 



-2[2] 



1 U l C -l9i 1 



-[12] 



[8] 





-2[3] 





-2[6'] 



1 M 1«2 A 3 i 





-[10] 



[9] 



-2[4'] 



-2[1] 





1 u A9z 1 



[4] 





-[8] 



2[5'] 





2[7'] 



1 «A*8 1 



-[91 



[5] 





2[8'] 



2[6'] 





1 "iVs 1 





"[7] 



[6] 





2[9'] 



2[4'] 



1 «i V l 3 1 



[10] 





-[51 



2[2] 



-2[7'] 





1 U l C Ji 1 



-[6] 



[11] 







2[3] 



-2[8'] 



1 "i^B 1 





-M 



[12] 



-2[9'] 





2[1] 



1 VWs 1 



[9'] 



-[5'] 



[3] 







2[0'] 



1 «10A 1 



[1] 



[7'] 



-[6'1 



2[0'] 







1 M A/s 1 



-m 



[2] 



[8'] 





2[0'] 





Unlike these, which cannot be taken along with Vi, u 2 , u 3 for purpose s 

 elimination, we have, as above pointed out, the single triad — 



