Ig. I. 



[ 4 1 



The firft Lemma which Newton premifes to the iuTeftigation 

 of the preceffion is as follows : 



" If a P E p. reprefent the earth, of xmiform denfity, de- 



" fcribed with the centre C, poles P, /, and equator A E ; and 



" if with the centre C and radius P C, the fphere ^ ape he fup- 



" pofed to be defcribed ; and 0,R be a plane perpendicular to 



" the right line joining the centres of the fun and earth ; and 



" every particle of all the exterior earth P « / A P if, which is' 



" higher than the infcribed fphere, endeavour to recede on 



" either fide from the plane 0,R, and the effort of each particle 



«' be proportional to its diftance from the plane; I fay, firft, 



" that the whole force and efficacy of all the particles in the 



" circle of the equator A E difpofed uniformly without the 



" fphere, throughout the whole circumference, in the form of a 



" ring, to turn the earth round its centre, is to the whole force 



" and efficacy of as many particles placed at the point A of 



" the equator which -is moft remote from the plane 0,R, to 



" move the earth round its centre with a like circular motion, 



" as one to two. And that circular motion will be performed 



" round an axis lying in the common interfedion of the equator 



" and the plane Q,R.." 



The demonftration of this Lemma is given in the Principia, 

 and allowed t© be legitimate. 



His 



