Mariotte and Desaguliers have given two distinct theories of the motion of rockets. The latter ascribes their motion to the momentum of combustion, and the former to the elastic nature of the gaseous fluid, generated by the combustion, and the resistance of air. The observations of Desaguliers are the following: "Conceive the rocket to have no vent at the choke, and to be set on fire, the consequence will be, either that the rocket will burst in the weakest place, or if all the parts be equally strong, and be able to sustain the impulse of the flame, the rocket would burn out immoveable. Now, as the force of the flame is equable, suppose its action downwards, or that upwards, to lift 40 pounds; as these forces are equal, but their directions contrary, they will destroy each other's action. Imagine then the rocket opened at the choke; by this means, the action of the flame downwards is taken away, and there remains a force equal to forty pounds, acting upwards, to carry up the rocket and stick." This theory, however ingenious, is not altogether true; for it is asserted on the contrary, that the action of the flame or gas within the rocket, when closed, as supposed above, is conceived to arise wholly from the elastic nature of the gas, and the reaction it experiences against the ends and sides of the rocket-case; the whole of which ceases as soon as a free vent is given to the flame; and, therefore, if a rocket could be fixed in a vacuum, as the flame would, in that case, experience no resistance, there would be no reaction, and consequently, no motion would ensue. Some experiments, analogous to this position, have been made. We may merely add, with respect to Mariotte's theory, that he attributes the motion of the rocket to the resistance and reaction of the air, in consequence of which the propelling force will decrease as the velocity increases, owing to the partial vacuum left behind the rocket in its flight; so that the correct solution of the problem necessarily involves the integration of partial differences of the highest orders.