68 



THE UNIVERSITY SCIENCE BULLETIN. 



fir = o,j^ = j^[j-U'], 





W) 



K-\{I'y-2r,-^{J -IP) + 



ax 



Ari^(J-]P) 



K'i = 



i^'y 





(38) 



^ 



'^1^-^^^'^n-^^^^ 



AJ-\P)- 



Ix - 



(I'/ 



47(J-iP)i +15V^/-(J-17'0 - 

 ' dx 



20v^(J- ID j, 



-21 -^{J- \P)+^P{J -\P) 

 ox' 



-hrA±[K- \{ry] - 2i4-{J-\P)i 



( ax ax ) 



+ bry\^(J-\P)-AI{J-\P)l 



' dx^ ) 



+ 15r,2 \K-\_{i'y 



+ 25r/(J- IP) 



25r,^-i (J-i P) 



dx 



V 



The system (D) is left in the canonical form by the trans- 

 formation (20) provided that ."- = 0. We shall now seek those 

 functions of the seminvariants in their semi-canonical form which 

 are left unchanged in value by the transformation (20) subject 

 to the condition ," = 0. 



From (34) or by direct substitution we find that (20) with 

 p- = converts Qik into 



(39) Qik = jjyQ.^, {i, k = l, 2), 



