50 
REPORT—184 7 » 
different particles of the earth’s mass not passing through the centre of gra¬ 
vity of the earth. The consequence is, that the attractiou of the sun con* 
stantly tends to communicate to the eartli an angular motion about a diameter 
perpendicular to the plane passing through the axis of the earth and the 
sun’s centre; and an exactly similar proposition holds with respect to 
moon’s attraction. It is the composition of these two angular motions wtli 
that of the earth’s d-oily rotation which produces the lutii-Bolar precession 
and nutation. Now it will be manifest at once to those wl»» are familiar 
with physical investigations of this nature, that if tlie central portion of the 
earth be fluid, the direct effects of the attractions of the sun and moon 
in producing the angular motions above mentioned, must be very different 
from the effects which these altraetiona would produce if the central portion 
were solid. The latter, however, was the only hypothesis on which the pre* 
ccssional motion of tlio pole had been investigated. ’I’hc result thus obtained 
depends on the cllipticity of the earth and the law of its density, and is found 
to agree, to a very close approximation, with the observed amount of pre* 
cession and nutation, taking tlio same? value of the ellipticiiy and the same 
law of the earth's density as ar(; deduced from independent cotisidcralioni in 
the manner already explained (art. 10). This oxattt accordance seemed to 
render it improbable that an equal accordance sliould exist iKJtwcen the 
observed aiuouut of prooesstumil motion and the amount calculated oti the 
hypothesis ot the earth's iiitemal fluidity, ttiougli it was inipcissiblc to wy 
beJbrehand how far coinpensatioiis luight exist which would render the re¬ 
sulting motions very approximately the same, though the forci-s producing 
them acted under such diflbrent coudilions. Without the required accord¬ 
ance on the hypothesis of internal fluidity, wc should be under the necessity 
of recognising the earth’s entire solidity. 
In my first Memoir, published in 1‘urt 11. for 1859 of the TratiRactioiis of 
the Uoyal Society, I investigated the amount of luni-sulor preCesaiou and 
nutatioii, asBuming the earth to consist ofa solid spheroidal shell filled will' 
UK. lo solve the problem, in the first instance, in its most simple lonu. 
supposed the solid shell to he bounded interiorly by a detennmatc splie- 
roidal surface, of which the ellliiticity was equal to that of tlie external sur- 
taco, the transition from the solkliiy of the shell to the fluidity of the internal 
mass not being gradual but abrupt. The densities of the shell and fluid 
Thirfnr equal. The results arrived at, under 
this form of the problem, were the following ;~ 
thicknci of frT’n" «puld be the same, whatever might he the 
f9 ^ TK« ; ^ ' as it the whole earth were homogeneous and solid. 
»I)I.Soi,l nr “ f*'- ‘he homogeneous Wid 
approximation, that the different would be 
aphemi/ the homogeneow 
tS lTnil’ I ® thickneas of the shell should approximate very nearly 
which pa*Scular\a»i> *?‘.”****““* '-^8“ oiie-fourth of the earth's radius, in 
solid sp^heroid. *'«tatir»n might become much greater than for the 
neous^ position^oMhe'tni V'^ *^“^rdinatcs which determine the instanW- 
tlK.. resSlS iu^eivcn n. ^rnis of which 
the intenml fiuidhv n, 1 rt- '"‘erprctations. other terms which depend on 
The inUwprctatiof/ot^Ih Jentirely when the whole spheroid is solid, 
tnofiojis of precewiioii -ind '«■ that in addition to the above-mentioned 
circular motion, the radius nf tl**^'*’ * f 
, me ladius of the circle thus described being greatest when 
