The second transvectant of a form over itself is called the Hessian of the form.
This can be verified by equating to zero the five coefficients of the Hessian (ab) 2 axb2.
But if the given curve has a node, then not only the Hessian passes through the node, but it has there a node the two branches at which touch respectively the two branches of the curve; and the node thus counts as six intersections; so if the curve has a cusp, then the Hessian not only passes through the cusp, but it has there a cusp through which it again passes, that is, there is a cuspidal branch touching the cuspidal branch of the curve, and besides a simple branch passing through the cusp, and hence the cusp counts as eight intersections.
Bought in this state, the wool arrived in 150 Kg hessian wrapped bales (not very moveable ).
I worked the lid off and the ripping sound of hessian against hessian brought the old busybody bustling back down the stall.