524 Mr. milner on the 
<{ appears further,’- fays he, “ by perufing his thirty-ninth 
“ proportion, that he there affumes it as a principle, that 
“ if a ring encompaffing the earth at its equator, but de- 
“ tached therefrom, was to tend or begin to move about 
“ its diameter with the fame accelerative force or angular 
{i celerity as that whereby the earth itfelf tends to move 
“ about the fame diameter through the adtion of the 
“ Sun, that then the motion of the nodes of the ring and 
11 of the equator would be exadtly the fame.” 
The principle is certainly implied in newton’s proof, 
and is capable of the molt rigid demonftration, art. 1 6, 
17. 
§ 1 9. It will be afked then, where is the fault of new- 
ton’s reafoning? How comes his conclufion to be too lit- 
tle by above one half ? It is acknowledged on all hands 
that there is an error in his third lemma; but then the 
correction of that error makes only a very fmall altera- 
tion in the refult. 
It is impoflible for any one to form a complete judge- 
ment of his method without going through the whole of 
his calculations, which pre-fuppofes that the mean mo- 
tion of the lunar nodes is computed. This motion may 
be concifely determined and exactly enough for the pur- 
pofe from prop. 30. of the Principia, and from thence is 
inferred the motion of the nodes of a fatellite revolving 
m 
