Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/272

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force ſubducted as cA, and therefore the remaining force as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikisource.org/v1/":): {\displaystyle \textstyle \frac {}{}} ; then (by the third exam.) 6 will be equal to 1, m equal to 1, and n equal to 4; and therefore the angle of revolution between the apſides is equal to deg. Suppoſe that foreign force to be 357.45 parts leſs than the other force with which the body revolves in the ellipſis; that is c to be or T being equal to 1, and then will be 1 or 180.7623, that is, 180 deg. 45 min. 44 ſec. Therefore the body parting from the upper apſis, will arrive at the lower apſis with an angular motion of 180 deg. 45 min. 44 ſec. and this angular motion being repeated will return to the upper apſis; and therefore the upper apſis in each revolution will go forward 1 deg. 31 m. 28 ſec. The apſis of the Moon is about twice as ſwift.

So much for the motion of bodies in orbits whoſe planes paſs through the centre of force. It now remains to determine thoſe motions in eccentrical planes. For thoſe authors who treat of the motion of heavy bodies uſe to conſider the aſcent and deſcent of ſuch bodies, not only in a perpendicular direction, but at all degrees obliquity upon any given planes; and for the ſame reaſon we are to conſider in this place the motions of bodies tending to centres by means of any forces whatſoever. when thoſe bodies move in eccentrical planes. Theſe planes are ſuppoſed to be perfectly ſmooth and poliſhed ſo as not to retard the motion of the bodies in the leaſt. Moreover in theſ demonſtrations