42 
HEPOBT-1847* 
precession and nutation of the pole of the earth, and a corresponding small 
inequality in the motion of the moon. If the earth’s external surface and all 
the interior surfaces of equal density were spherical and concentric, the rau* 
tual attractions of the earth and moon tvould be equivalent to a single force 
passing through the spherical centre, or centre of gravity of the eartli, 
and would therefore not tend to impress on the earth a motion of rotation 
about any axis through its centre; nor, on the other hand, would this force 
have any tendency to draw the moon out of a fixed plane passing through 
that centre. But, the earth being oblate, it is easily seen tliat when the moon 
is out ot the plane of the equator, the resultant force of her attraction will 
not pass through the. earth’s centre, because her attraction on the portion of 
the equatorial protuberance nearest to her will be greater than that on the 
opposite and more remote portion. Consequently this attraction will tend to 
impress on the earth a rotatory motion about an axis through the earth's 
centre, ami perpendicular to a plane through the earth’s axis and the moou's 
centre. This angular motion, combined with that of tbo earth’s daily rota¬ 
tion, produces lunar precession and nutation. The solar prccewion and na- 
tation admit of an exactly similar explanation. Again, since the attraction 
or the earth on the moon is exactly cijual and uppo»ite to that of the moon 
on the earth, it must tend to draw the moon out of the conalant plane in 
which she would move if slm were acted on only by a force passing accu¬ 
rately through the emrth’s centre. The inequality in the moons motion duo 
to tim cause has been accurately detmuiueil by very numerous oUervations; 
lunar precession and nutation are also accurately determined by ' 
servatioii.^ caleulaiion of tliese niotimm according to the theory of; 
Ob' 
gra- 
rlkon tj,e ellipticity of the caiih'aiid Ui.rlaw”ofTt#'density 
<’lbptioity determined by observation, nnd the assumed 
it mus/noM,n«S? derived from the earth’s form, 
force wonh't certain eonUitioiis, centrifugal 
force wonlri “‘f- umier certain eonUiUoiis, centniug« 
spheroidal form nfn ti tmuss a form approximating to die 
thrd?mensi^^^^^^^^ a solid syhere of 
locity, the ceiitrifueal fined fotation witii the eartli's angular ve- 
equator, all mattpr\f:,>f» • ‘t to bulge out in some degree at its 
am not aware that auv sm/,V*^*f***^^ ^ some degree of cxteusihility. j 
and consequently the form w liicirtr*"*" problem has becu attempt^, 
any exactness. It ^ evi^dm h , ’'“r 
ellipticity wlik-h » ould be athiined bv’dfl“* 
provided the solid should be Lble tl under the same eoDditioift 
cohesive power to resist tlm i< i^tam for an indefinite lime any 
n.ass in d?rec"„ ” ^ feS, force to erteod <*« 
ab.,.„oe of such resTstL force Umt Sc ‘7"““" ' 
attained. It may perhaps also be stl h spheroid tf 
sive power, the defect ii! the’excess of^tbd ‘"i ‘J.*’®' 
as compared with that excess in H.n « - f over the polar radius, 
inai e.xc. ss n, the «uid spheroid, xvould be of the same 
theory of f Pi-vveMioti ami mitation according to ihe 
tame are «h- 
>'>»> o„.-fa„r,h 0? r..«n!r„"r'S Siw ° "" 
