Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/360

274 of the forces, the proportions remaining as before.

If pheres of this kind revolve about others at ret, each about each; and the ditances between the centres of the quiecent and revolving bodies are proportional to the diameters of the quiecent bodies; the periodic times will be equal.

And again, if the periodic times are equal, the ditances will be proportional to the diameters.

All thoe truths above demontrated, relating to the motions of bodies about the foci of conic ections, will take place, when an attracting phere, of any form and condition like that above decribed, is placed in the focus.

9. And alo when the revolving bodies are alo attracting pheres of any condition like that above decribed.

If to the everal points of pheres there tend centripetal forces proportional to the diŧances of the points from the attracted bodies; I ay that the compounded force with which two pheres attract each other mutually is or the diŧance between the centres of the pberes.

Let AEBF (Pl. 22. Fig. 2.) be a phere; S its centre; P a corpucle attracted; PASB the axis of the phere pulling through the centre of the corpucle; EF, ef two planes cutting the phere, and perpendicular to the axis, and