PreceJJlon of the Equinoxes . 
509 
ax aex f + bxbex s xa e arM j fpace defcribed by c is 
aXae‘+b xbe‘+cx ce‘ 
a x ae x s + bxbb x i x cb _ g ee ar ticle the I ^th, 
A X AE 1 +B X BE^ + C X CE* 
§ 3. The preceding article being well underftood, 
whatever doubts may remain concerning the motion of 
a ring of matter conndered as detached from the earth, 
we may be certain that the motion of the nodes of the 
equator can never be the fame, whether we fuppofe the 
ring at the equator to be fluid and to reft upon the fur- 
face of the earth, partaking of the diurnal motion, or 
whether we fuppofe it hard and compact, and by its co- 
hefion communicating a proportional degree of motion 
to the different parts of the earth. In fait, the problem 
of the preceflion of the equinoxes, which has hitherto 
been confidered as extremely difficult, and in its folution 
drawn out by authors to an immeafurable length, re- 
quires no principles but the received dodtrine of motion, 
and the application of the lever, which have been made 
ufe of in the laft article. In that article we fuppofed the 
bodies a and b to be impelled by different forces in pa- 
rallel lines, and we eftimated the real fpace, which either 
a or c in any fmall time would defcribe in confequence 
of thofe impulfive forces and their mutual connedtion 
by an inflexible lever. Now this is precifely what is re- 
Vo l. LXIX. X x x quired 
