[ 5 ] 



His fecond Lemma is as follows : 



" The fame things being fuppofed, I fay, fecondly, that the 

 " whole force and efficacy of all the particles without the fphere 

 " to turn the earth round its axis, is to the whole force of as 

 " many particles difpofed uniformly in the form of a ring, in 

 " the circumference of the circle A E of the equator, to move 

 " the earth, with a like circular motion, as two to five." 



The demonftration of this Lemma is alfo given in the 

 Principles, and is likewife received as unexceptionable. 



Lemma 3. 



" The fame things being fuppofed, I fay, thirdly, that the 

 " motion of the earth round the axis already defcribed, com- 

 " pounded of the motion of all its particles, will be to the 

 " motion of the aforefaid ring round the fame axis in a ratio, 

 " which is compounded of the ratio of the quantity of matter 

 " in the earth to the quantity of matter in the ring, and of the 

 *' ratio of three fquares of the arch of a quadrant of a circle 

 " to two fquares of the diameter ; that is, in a ratio of matter 

 " to matter, and of the number 925275 to the number 

 " 1 000000." 



This Lemma I fhall firft demonftrate in Newton's fenie, and 

 then corred the conclufion on the principles propofed by Simpfon 

 and Frifi. 



By 



