PreceJJlon of the Equinoxes. 513 
and,laftly, the fpace defcribed by a particle at the greateft 
diftance from the axis is equal to 4 ^ P x FK x *1211 . 
§ 5. In fig. 4. let pia/>dk reprefent the earth ortho- 
graphically projected on the plane of the folftitial co- 
lure, v,p, the poles, ik a lefler circle parallel to the equa- 
tor, and p ape a fphere defcribed with the polar radius 
pt: then, fince the particles without the globe only are 
concerned in changing the pofition of the axis of rota- 
tion, let l reprefent fuch a particle fituated in the cir- 
cumference of the circle ik, and by the preceding article 
its effect will be 45^lmxmtx^ and by the fame way of 
l6 A X ST 2 X I — 2 p 
reafoning, when two equal particles l, /, are fuppofed to 
be difturbed by the Sun’s attraction, the fpace defcribed by 
that point of the equator, which is at the greateft: diftance 
from the axis of rotation or the common interfedlion of 
the plane cd and the equator a, will be equal to 
— , ana the lame argument holds for 
16 ST X A X I — 2 p 0 
every other particle without the fphere. 
The fum of all the lx lmxmt+&c. mull now be 
found; and for this purpofe Sir isaac newton’s con- 
ftru&ion is, perhaps, as convenient as any that has hi- 
therto appeared. In the fame figure n# is parallel, and 
wy perpendicular, to cd ; take L x=x l, and let m, n, repre- 
fent 
