Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/531

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t [67] fimiiar to the orbit, whoſe lon er axis it the double of the eccentricity; glue center of the vibratory motion, that is the place Where it is ſwifteſt, will be in the focus; the time of the lib ration, through the ſeveral f aces, is to be meaſured by feftors of? the ſaid ellipſis, ſimilar to thoſe deſcribed by the body round the focus of the orbit; and the period of the vibratory motion will be the ſame with the period .of the revolution. In any other law of gravity, the equant for the vibratory motion, will either be of a form different from the orbit, or if it be of the ſame form, it muſt not be ſimilarly divided. I may juſt mention, that the equant for the vibratory motion, in the caſe of the Moon, is a curve of the third kind, or whoſe equation is of four dimenſions; but is to be deſcribed by an ellipſis, the center of the lib ration not being in the focus. - From this method of revolving the motion, it will not be difficult to ſhew the general cauſes of the alteration of the eccentricity and inequality in the motion of the apogee. For when the line of apſides is moving towards the Sun, it may be eaſily fhevvn, that ſince the external force in the apſides, is then centri-2 E .2 fugal,