**Discriminants**.-The discriminant of a homogeneous polynomial in k variables is the resultant of the k polynomials formed by differentiations in regard to each of the variables.

The discriminant of the product of two forms is equal to the product of their **discriminants** multiplied by the square of their resultant.

The two quadratic forms f, 4); the two **discriminants** (f, f')2,(0,4')2, and the first and second transvectants of f upon 4, (f,, >) 1 and (f, 402, which may be written (aa)a x a x and (aa) 2 .