John Machin

“ For the very same reason, the Moon's motion ought to be resolved into a third motion of revolution, since there remains a third force to be satisfied, and that is the force arising from the altes ration of the Moon's gravity to the Sun. And this when considered, will require a motion in a small ellipsis, in the manner here described. T H E circle ADFH represents t.he Fig; orbit of the Moon about the Earth in the center if, as it would be at a mean distance, ' supposing the Moon had n'o gravity to any, other body but the Earth. ”

“ The figure PQLK is an Ellipsis, whose cen-f ICI ll 1° nr is carried round the Earth in the orbit ABDEFIL hav' its longer axis PL in length double Gfm§ lC shortcr aXi8 215, and lying always parallel to TD, the line joining the centers of the Earth and Sun. Whllit the said figure is carried fromd to B, the Moon revolves the contrary Way from Qtr: N, so as to describe equal areas in equal times about the centre of it; and to perform its revolution in the same time as the center of the said Elliptic epicycle (if it may be so called,) performs its revolution ”

“ 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, 1 [ § 3'] fugal, it will contribute to lengthen the f ace and time of the lib ration; by lengthening the space, it increases ' the eccentricity; and by lengthening the time of the lib ration, it prmlracts the time of the revolution to the apsis, and causes what is improperly called a motion of the apsis forward. ”

“ For altho' it be of lit? tie or no use in Astronomy to know the rules for ascertaining the mean motions of the Node or Apogee, since the faéi is all that is wanting, and that is othere wife known by comparing the observations of former ages with those of the present; yet in matter of peculation, this is the chief and rnofl nece£ fary thing required: since there is no other way to know that the cause is rightly assigned, but by 'showing that the motions are so much and no more than what they ought to be. ”

“ Acconnmc to Sir Mac Newton, the mean eccentricity is o.o 550 5, hall the difference of the greatest and lean is o.or 173; which numbers are in proportion nearly as 13513; to 28%, each of which proportions is very near that above assigned. ”