(1) There being n2 independent variables in a general n-line determinant, the Hessian of the determinant with respect to the said variables must be a determinant with n2 lines: and as a general n-line determinant has all its terms linear in the elements involved, it follows that each element of the Hessian being a second differential-quotient cannot be of a higher degree in the variables than the (n − 2)th, and that consequently the degree of the Hessian itself cannot exceed n2(n − 2). The object of the present short paper is to show that this degree is attained by the n(n − 2)th power of the given determinant being a factor of the Hessian.