MR. A. CAYLEY ON EQUATIONS OE THE FIETH ORDER. 
‘.^70 
30. The cubic function is therefore =<pxif—')Qf\ and dividing by Ave have 
O is thus a fractional covariantive function, the leadmg coefficient whereof is <p, and the 
equation for the determination of O is consequently that deduced from the equation for 
(p, by replacing therein the seminvariants by the corresponding covariants. The equa- 
tion is 
U«, ^ 
0 , 
-100 Tab. No. 14, 
0 , iy=o, 
-f 2000U^[6(Tab. No. 14)^- 4 Tab. No. 20], 
- 800 UV5\/disct.=Tab. No. 26, 
(^, 33, C, 2B, C, f, yf. 
w liere the Tables referred to are those of my Second Memoir on Quantics ; the coeffi- 
cients are in regard to [x, y) of the orders 30, — , 22, — , 14, 10, 6 respectively. The 
last coefficient, being of the degree 6 in the coefficients {a, b, c, d, is not given 
in the Tables ; it is therefore merely indicated by (0, 33, C, 13, (25, JT, yf, the 
leading coefficient 91 being of course the last coefficient in the equation for (p, to the 
standard form. 
1 refrain from at present entering into the consideration of the values of the expres- 
sions &c. 
