Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/323

 to the plane of the orbit PAB) beides the perturbation of the motion jut now poken of as to longitude. introduces another perturbation alo as to latitude, attracting the body P out of the plane of its orbit. And this perturbation, in any given ituation of the bodies P and T to each other, will be as the generating force MN; and therefore becomes leat when the force MN is leat, that is, (as was jut now hewn) where the attraction 5N is not much greater nor much les than the attraction SK. Q. E. D.

. Hence it may be eaily collected, that if everal les bodies P, S, R, &c. revolve about a very great body T; the motion of the innermot revolving body P will be leat diturbed by the attractions of the others. when the great body is as well attracted and agitated by the ret (according to the ratio of the accelerative forces) as the ret are by each other mutually.

In a ytem of three bodies T, P, S, if the accelerative attractions of any two of them towards a third be to each other reciprocally as the quares of the ditances; the body P, by the radius PT; will decribe its area wifter near the conjunction A and the opposition B, than it will near the quadratures C and D. For every force with which the body P is acted on and the body T is not, and which does not act in the direction of the line PT; does either accelerate or retard the decription of the area, according as it is directed, whether in conequentia or in antecedentia. Such is the force NM. This force in the paage of the body P from C to A is directed in conequentia to its motion, and therefore accelerates it; then as far as D in antecedentia, and retards