and the different Motions of the Earth's Axis.

3 * 1

(= x ~ X bd X versed sine z — {ac x versed sine 2 z) is

consequently the measure of the nutation, or the decrease of theinclination of the equator to the ecliptic, caused by the moon,from the time of the node’s coinciding with the equinoctialpoint Pf 5 , to its arrival at the position N.

Again, with regard to the precession of the equinox, the in-crease thereof being in proportion to the decrement of the in-clination, as the co-tangent of ppE to the fine of NppE (by

the Corollary to the precedent) or, in species, as —t— I (or

ad ~p bed 1 —ex

to a, its fluxion will therefore be had by mul-

tiplying that of the nutation, given above, into ———iand so is found to be

I abd x 1 ——————— j % *

-sr- X —7- X " 7- _ + bb — aax cdx — abc x */1 — xx >

1 abe v 1 — xx

whose fluent, which is

x ~ii 7 * abd x z-\-bb—aa x cdx — {abc 1 z — {abc 1 xs/ 1 — xx

(— x -d— x ~dd — {cc x abz -\-bb -aaxcdxf.z -; abcc x s. 2 z) >

must consequently be the precession itself.

But, at the end of half a revolution, when the node N ar-rives at the other equinoctial point £3, both this, and the ex-pression for the nutation, will become much more simple, xbeing then — o, and z = e y whence the nutation will be =

X ~ x 2 bd = x ; and the precession equal to— 7 p- x dd — {cc = xi — {cc (because cc -j- dd = 1),

COROLLARY I.

It appears from hence, that the mean precession of the equinox, arising from the action of the moon, is in propoi ionwhat it would otherwise be, if the moons 01 bit was to ooicide with the ecliptic, as 1 — {cc to-unity : whence the