V. On certain developable surfaces

Abstract

If U = 0 be the equation of a developable surface, or say a developable, then the hessian HU vanishes, not identically, but only by virtue of the equation U = 0 of the surface; that is, HU contains U as a factor, or we may write HU = U. PU. The function PU, which for the developable replaces, as it were, the hessian HU, is termed the prohessian; and since, if r be the order of U, the order of HU is 4 r —8, we have 3 r —8 for the order of the prohessian. If r =4, the order of the prohessian is also 4; and in fact, as is known, the prohessian is in this case = U.