Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/28

Rh of the Earth, as the quare of the emi-diameter of the Earth to the quare of the emi-diameter of the orbit. But by what was hewn before the very ame ratio holds between the centripetal force of the Moon revolving in its orbit, and the centripetal force of the Moon near the urface of the Earth. Therefore the centripetal force near the urface of the Earth is equal to the force of gravity. Therefore thee are not two different forces, but one and the ame; for if they were different, thee forces united would caue bodies to decend to the Earth with twice the velocity they would fall with by the force of gravity alone. Therefore it is plain that the centripetal force, by which the Moon is perpetually, either impelled or attracted out of the tangent and retained in its orbit, is the very force of terretrial gravity reaching up to the Moon. And it is very reaonable to believe that virtue hould extend it elf to vat ditances, ince upon the tops of the highet mountains we find no enible diminution of it. Therefore the Moon gravitates towards the Earth; but on the other hand, the Earth by a mutual action equally gravitates towards the Moon; which is alo abundantly confirmed in this philoophy, where the Tides in the Sea and the Præceon of the Æquinoxes are treated of; which arie from the action both of the Moon and of the Sun upon the Earth. Hence latly, we dicover by what law the force of gravity decreaes at great ditances from the Earth. For ince gravity is no ways different from the Moon's centripetal force, and this is reciprocally proportional to the quare of the ditance; it follows that it is in that ratio that the force of gravity decreaes. Rh