On Closed forms and Polar forms

In the paper ' On the Rank of the Double-binary Form' (Proceedings of the London Mathematical Society, Series 3, Vol..94, Part 2, p. 83), the rank of an (m. n) form

a_x^m b_yⁿ, was defined as the rank of the matrix of m + 1 rows and n + I columns, formed by its co-efficients.