30 



DR THOMAS MUIR ON THE 



Source. 



u Af:i I 



u l e i g. i | 



U \ a J l 3 

 T^Cgfig I 



U l''-2.f 3 I 



Ml a 2 <7 3 1 



V^/3 I 



&<# +/ 2 Z C 3 I * * 



c 2 z + tf 2 z a, | * y 

 a 2 a: + 7i 2 y & 3 1 — z 



c 2 </ 3 2 + a 3 z I + y 

 a 2 7i 3 :r + b 3 y I -r z 



a;' 2 



?/ 2 



Z 2 



yz 



zx 



xy 











n 



8 



5 











6 



12 



9 











7 



4 



To 



7 





-11 





-5' 



-2 



-12 



8 





-3 





-6' 





-10 



9 



-4' 



-1 





4 





-8 



5' 





r 



-9 



5 





8' 



6' 







-7 



6 





9' 



4' 



10 





-5 



2 



-7' 





-6 



11 







3 



-8' 





-4 



12 



-9' 





1 



9' 



-5' 



3 







0' 



1 



7' 



-6' 



0' 







-4' 



2 



8' 





0' 







5 



-3 



8 + 8' 



6 







-1 





6 







9 + 9' 



4 



4 



-2 





5 







7 + 7' 





- 2 



8 



5-5' 







7 



9 





-3 



8 



6-6' 







-1 



7 









9 



4-4' 



Temporary 

 Name. 



A 2 



A, 



B 2 



c. 



D 2 



E 2 

 E. 



F 2 

 F 3 



Oq 



(jr, 



and we find that there are seven of them which do not contain a term in x 2 . Of these, 

 however, B 3 , C 3 , D 3 are each derivable from A 2 and A 3 , the connecting equations being 



9A„ - 10 A 2 = OB,, 



6A, 



7 A, = 0C 3 , 



12A 3 - 4A 2 = 0D 3 . 



It is not possible, therefore, to use B 3 , C 3 , D 3 along with A 2 , A 3 in a process of dialytic 

 elimination, and we are thus left with only four available equations, viz., A 2 , A 3 , F l5 G r 

 On examining whether any pair of the remaining quadrics may be readily used to obtain 

 a quadric free of x 2 , we see that the possible pairs are 



Ci , F 3 > C 2 , Gr 2 ; 



E F ■ 



±J 2 ' 2 ' 



E 2 , G 3 ; F , , G- 3 



