(111.) It is not alone by the direct fall of bodies that the gravitation of the earth is manifested. The curvilinear motion of bodies projected in directions different from the perpendicular, is a combination of the effects of the uniform velocity which has been given to the projectile by the impulse which it has received, and the accelerated velocity which it receives from the earth’s attraction. Suppose a body placed at any point P, _fig. 21._, above the surface of the earth, and let P C be the direction of the earth’s centre. If the body were allowed to move without receiving any impulse, it would descend to the earth in the direction P A, with an accelerated motion. But suppose that at the moment of its departure from P, it receives an impulse in the direction P B, which would carry it to B in the time the body would fall from P to A, then, by the composition of motion, the body must at the end of that time be found in the line B D, parallel to P A. If the motion in the direction of P A were uniform, the body P would in this case move in the straight line from P to D. But this is not the case. The velocity of the body in the direction P A is at first so small as to produce very little deflection of its motion from the line P B. As the velocity, however, increases, this deflection increases, so that it moves from P to D in a curve, which is convex, towards P B. The greater the velocity of the projectile in the direction P A, the greater sweep the curve will take. Thus it will successively take the forms P D, P E, P F, &c., and that velocity can be computed, which (setting aside the resistance of the air) would cause the projectile to go completely round the earth, and return to the point P from which it departed. In this case, the body P would continue to revolve round the earth like the moon. Hence it is obvious, that the phenomenon of the revolution of the moon round the earth, is nothing more than the combined effects of the earth’s attraction, and the impulse which it received when launched into space by the hand of its Creator. (112.) This is a great step in the analysis of the phenomenon of gravitation. We have thus reduced to the same class two effects apparently very dissimilar, the rectilinear descent of a heavy body, and the nearly circular revolution of the moon round the earth. Hence we are conducted to a generalisation still more extensive.