2. THESE powers or forces are by Sir ~ISAAC NEWTON~ called centripetal; and their first effect is to cause the body, on which they act, to quit the straight course, wherein it would proceed if undisturbed, and to describe an incurvated line, which shall always be bent towards the center of the force. It is not necessary, that such a power should cause the body to approach that center. The body may continue to recede from the center of the power, notwithstanding its being drawn by the power; but this property must always belong to its motion, that the line, in which it moves, will continually be concave towards the center, to which the power is directed. Suppose A (in fig. 72.) to be the center of a force. Let a body in B be moving in the direction of the straight line B C, in which line it would continue to move, if undisturbed; but being attracted by the centripetal force towards A, the body must necessarily depart from this line B C, and being drawn into the curve line B D, must pass between the lines A B and B C. It is evident therefore, that the body in B being gradually turned off from the straight line B C, it will at first be convex toward the line B C, and consequently concave towards the point A: for these centripetal powers are supposed to be in strength proportional to the power of gravity, and, like that, not to be able after the manner of an impulse to turn the body sensibly out of its course into a different one in an instant, but to take up some space of time in producing a visible effect. That the curve will always continue to have its concavity towards A may thus appear. In the line B C near to B take any point as E, from which the line E F G may be so drawn, as to touch the curve line B D in some point as F. Now when the body is come to F, if the centripetal power were immediately to be suspended, the body would no longer continue to move in a curve line, but being left to it self would forthwith reassume a straight course; and that straight course would be in the line F G: for that line is in the direction of the body’s motion at the point F. But the centripetal force continuing its energy, the body will be gradually drawn from this line F G so as to keep in the line F D, and make that line near the point F to be convex toward F G, and concave toward A. After the same manner the body may be followed on in its course through the line B D, and every part of that line be shewn to be concave toward the point A.