For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two **cubics**, and then, by supposing the two **cubics** to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian.

This author questioned the possibility of solving **cubics** by pure algebra, and biquadratics by geometry.

Similarly as regards **cubics**, or curves of any other order: a cubic depends on 9 constants, and the elementary problems are to find the number of the **cubics** (9 p), (8p, 1l), &c., which pass through 9 points, pass through 8 points and touch 1 line, &c.; but it is in the investigation convenient to seek for the characteristics of the systems of **cubics** (8p), &c., which satisfy 8 instead of 9 conditions.

The elementary problems in regard to **cubics** are solved very completely by S.

He determines in every case the characteristics (µ, v) of the corresponding systems of **cubics** (4p), (3 p, il), &c. The same problems, or most of them, and also the elementary problems in regard to quartics are solved by Zeuthen, who in the elaborate memoir " Almindelige Egenskaber, &c.," Danish Academy, t.