204. KANSAS UNIVERSITY QUARTERLY. 
The following are first coefficients of covariants of the sextic in 
which ¢ and ¢ are made zero. 
a=Cy,4 the sextic 
ae gbad=Co 4 
a? d-+-369=Cy.19 
r6abd* —2ab*f=Cy io 
(Notated according to E. B. Elliott in Algebra of Quantics.) 
Forming the covariant C,, the coefficient of whose first term 
vanishes when ¢ and ¢ are zero, we have: 
Cy==12C8 ie Cu 46 48C? ae ad BC? 
Cog Cr 6 
3° 
-8Cy g Ge lh 2agGe 
H Cad 2.4 
This covariant is of order 7 in the coefficients and 22 in the vari- 
ables. 
Theorem 3: Zhe non-singular sextic may be brought by linear trans- 
Jormation to the canonical form (a,6,0,a,0,f,2)(ay)® in eleven different 
ways. 
The covariant upon which the ground points are taken in order 
to drop the second, and next to the last terms of the- 
cubic is of order 2 in coefficients, degree 2 in variables; 
quartic is of order 3 in coefficients, degree 6 in variables; 
quintic is of order 4 in coefficients, degree 12 in variables; 
sextic is of order 5 in coefficients, degree 20 in variables; 
mic is of order (w—1) in coefficients, degree (n—1)(n 2) in 
variables. 
From the consideration of the above relation between the order 
and degree of the covariant and that of the quantic itself, we may 
conclude that, in all probability the order of the covariant is given 
in general by (n—r) and the degree by (n—-1)(n-—2), where 7 is the 
degree of the quantic whose canonical form is required. 
