is a tendency in the planet to go off again when it has come nearest to the sun; but whether it will absolutely go off again depends upon another circumstance: it depends upon the amount of force when the planet is nearest to the sun; as, though the speed be great, it may happen that the force is very great also, and it may happen that the force is so great, that after all we cannot, merely upon general considerations, answer for its coming back again. I wish to point out the general explanation, but it is quite impossible here to enter fully into these particular details, and to show to you whether, when the planet is coming near to the sun, the force will not be too great to allow it to recede again; or whether when it is going away from the sun, the force will be great enough to bridle it in or not. That is a thing for which you must trust me for a moment. If, as we assume in the law of gravitation, when the distance of the planet from the sun is doubled or trebled, the force of the sun is reduced te one-fourth or to one-ninth, and so on; if that be the law of force, then the velocity of the planet, on coming near to the sun, is so increased that the tendency to recede increases in a greater proportion than the force, and it is certain that the body will begin to recede. But this would not be the case with all laws of force; if we supposed that when the distance was doubled the force was one-sixteenth instead of one-fourth, this law of alternate recess and approach would not be true. Mathematical investigations are made to ascertain whether certain conditions are fulfilled. A planet is invariably moving quickest at that part of its orbit where it is nearest to the sun, and in consequence of that increased velocity of motion, it is able to overcome a degree of attractive force which it would not
