Form of Trajectory

—Take that portion of the trajectory where the velocity is uniform. The weight of the rocket applied at its centre of gravity, and acting in a vertical direction, and the propelling force acting in the direction of its length, are two forces the oblique resultant of which moves the rocket parallel to itself; but the resistance of the air is oblique to this direction, and acting at the centre of figure, a point situated between the centre of gravity and extremity of the guide-stick, produces a rotation which raises the stick, and thereby changes the direction in which the gas acts. As these forces are constantly acting, it follows that each element of the trajectory has le inclination to the horizon than the element of an ordinary trajectory in which the velocity is equal. When the velocity is not uniform , the position of the centre of gravity has a certain influence on the form of the trajectory. To understand this, it is nece ary to consider that the component of the resistance of the air which acts on the head of the rocket is greater than that which acts on the side of the stick. It is also nece ary to consider that the pre ure of the inflamed gas acts in a direction opposite to the resistance of the air, that is to say, from the rear to the front, and that the centre of gravity is near the rear extremity of the case. At the beginning of the trajectory, when the motion of the rocket is accelerated, its inertia is opposed to motion, and being applied at the centre of gravity, which is in rear of the vent, the point of application of the moving force, it acts to prevent the rocket from turning over in its flight. But when the composition is consumed, the centre of gravity is thrown farther to the rear, and the velocity of the rocket is retarded, the inertia acts in the opposite direction, and the effect will be, if the centre of gravity or inertia is sufficiently far to the rear, to cause it to turn over in the direction of its length. If the rocket be directed toward the earth, this turning over will be counteracted by the acceleration of velocity due to the weight, and the form of the trajectory will be preserved.