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

 t [67] fimiiar to the orbit, whoe lon er axis it the double of the eccentricity; glue center of the vibratory motion, that is the place Where it is wiftet, will be in the focus; the time of the lib ration, through the everal f aces, is to be meaured by feftors of? the aid ellipis, imilar to thoe decribed by the body round the focus of the orbit; and the period of the vibratory motion will be the ame 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 ame form, it mut not be imilarly divided. I may jut mention, that the equant for the vibratory motion, in the cae of the Moon, is a curve of the third kind, or whoe equation is of four dimenions; but is to be decribed by an ellipis, the center of the lib ration not being in the focus. - From this method of revolving the motion, it will not be difficult to hew the general caues of the alteration of the eccentricity and inequality in the motion of the apogee. For when the line of apides is moving towards the Sun, it may be eaily fhevvn, that ince the external force in the apides, is then centri-2 E .2 fugal,