Mr. Moore of the Royal Military Academy, Great Britain, (Treatise on the motion and flight of rockets,) who seems to have adopted the hypothesis of Dr. Desaguliers, respecting the momentum of the ignited composition, has given a variety of problems relative to the motion and flight of rockets in non-resisting mediums, some of which we purpose to notice.
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.
We may remark also, from the premises already established, that the first motion of the rocket, like all other motions not produced by a great momentary impulse, is slow; and before the stick is clear of the flame, gravity has been acting upon the rocket, and depressed it below its natural position, while the stick is prevented from being equally depressed, by the top of the frame; so that the angle of projection is in fact considerably less than the angle of the frame, or slope of the rocket's first position. In consequence of this, the rocket has the appearance of falling the moment after projection; and, for this reason also, the angle for producing the greatest range of a rocket exceeds very considerably that which gives the extreme range of a shell projected from a mortar. There are various propositions given by Mr. Moore respecting rockets, but to give the calculus, &c. would take up more room than we could appropriate to this abstract question. The nature of these propositions, however, may be given in a few words, viz: The strength or force of the gas from the inflamed composition of a rocket being given, as also the weight and quantity of the composition, the time of its burning, and the weight and dimensions of the case and stick, to find the height to which it will ascend, when projected perpendicularly upwards. After making the necessary calculation, he concludes by observing, that, having determined the height of the rocket, and its velocity, when the composition is just consumed, it follows that its whole height may be determined in the usual manner by the known formula, for the ascent and descent of heavy bodies. Another proposition is that of determining the path of a rocket near the earth's surface, neglecting the resistance of the air; and among others, for finding the horizontal range of a rocket, the angle of elevation, and the time the composition is on fire, being given.
The observations of Mr. Peyre, (Le Mouvement Igné,) are confined principally to the effects of gunpowder; and although applied to the use of gunpowder, and the theory of its explosive effects, yet there is nothing in immediate relation with this subject. The generation of gaseous fluid, and its impelling power, and the consequent recoil of pieces, predicated in fact on the ingenious experiments and conclusions of Mr. Robins, may furnish some data on this head. But the principles of accelerated motion, on which the effective power of war-rockets depends, this accelerated motion being no other than the acquired velocity of their recoil, necessarily involves a question of a different kind from that of common projectiles.
The caduceus rocket has not much more than half the power of ascension as the single rockets; because, being composed of two rockets placed at an angle of 90 degrees, with the usual counterpoise, (the stick), it forms in its flight a serpentine motion resembling two spiral lines, or double worm; and although by reason of the stick it ascends vertically, yet the great resistance it meets with from the air, in consequence of this motion, causes its flight to be considerably retarded.
On the contrary, when rockets are fixed one on the top of another, called towering rockets, their effect is not at all diminished; for they experience no additional resistance, as the small rocket is placed in the head of the large one; and when the latter arrives at the maximum of elevation, it communicates fire to the former, which then rises as far beyond the first, if not higher, in consequence of the pressure of the atmosphere being less, as it would, if discharged by itself on the ground. Sky rockets, however, which are merely placed on one stick, do not, unless so required, act in this manner. Although two, three, or more, may be so arranged, yet the intention is nothing more than to combine their effect, so that their tails may appear as one stream of fire. Nevertheless, they may be so arranged, as that when one is consumed, another may take its place, and produce a new volume of fire, and, in this case, they would mount to a great height.
Tourbillons, usually called the common or table tourbillons, which receive their name from the whirling motion they take in their flight, produce also, by the arrangement of their cases, and the cross stick which serves as a balance, a horizontal and rotary motion; and while one part of the fire serves to elevate them, another part, issuing in a horizontal direction, but at opposite sides and extremities, gives to the tourbillon a wheeling motion. The mosaic tourbillons are of a different kind, and intended for another effect. Tourbillons of this kind preserve a regular and constant motion.
The mosaic candle owes its effect, in a great measure, to the rocket composition. Using alternately, composition, meal-powder, and a star, ramming the composition sufficiently, but not so as to break the stars, a case