By working directly from Newtonian equations of motion and representing accelerationẍas[(x,H), H], families of Hamiltonians may be constructed which are functions of the energy and which, while describing the same classical motions, are not connected by canonical transformations. One dimensional examples are given, and the formal rules of quantization executed whenHis(energy)12to show that the quantum motion does not come out right. The reason is that the commutation rule(x,p) = iħdoes not have universal standing; quantum theory in employing this rule is apparently requiring not merely thatHbe a generator of motion, but also that it be a very particular one, viz., the energy when the system is conservative.