As regards simultaneous binary forms, the system of two **quadratics**, and of any number of **quadratics**, is alluded to above and has long been known.

The system of two ternary **quadratics** consists of 20 forms; it has been investigated by Gordan (Clebsch-Lindemann's Vorlesungen i.

Ciamberlini has found a system of 127 forms appertaining to three ternary **quadratics** (Batt.

2 cos w xy+y 2 = X 2 +2 cos w'XY+Y2, from which it appears that the Boolian invariants of axe+2bxy-y2 are nothing more than the full invariants of the simultaneous **quadratics** ax2+2bxy+y2, x 2 +2 cos coxy+y2, the word invariant including here covariant.