344 Address of Sir Wm. Thomson at the Glasgow Meeting. 
closed in an ellipsoidal shell, has brought out results which I 
confess have greatly surprised me. W hen the interior ellipticity 
of the shell is just too small, or the periodic speed of the dis- 
turbance just too great to allow the motion of the whole to be 
sensibly that of a rigid body, the deviation first sensible ren- 
ders the precessional or nutational motion of the shell smaller 
than if the whole were rigid, instead of greater, as I expecte 
The amount of this difference bears the same proportion to the 
actual precession or nutation as the fraction measuring the pert- 
odie speed of the disturbance (in terms of the period of rota- 
tion as unity) bears to the fraction measuring the interior ellip- 
ticity of the shell; and it is remarkable that this result is inde- 
pendent of the thickness of the shell, assumed however to be 
small in proportion to the earth’s radius. Thus in the case of 
precession the effect of interior liquidity would be to diminish 
the periodic speed of the precession in the proportion stated ; 
in other words, it would add to the precessional period a num- 
ber of days equal to the multiple of the rotational period 
equal to the number whose reciprocal measures the ellipticity. 
Thus in the actual case of the earth if we still take gj, as the 
ellipticity of the inner boundary of the supposed rigid shell, 
the effect would be to augment by 300 days the precessional 
period of 2,600 years, or to diminish by about ;';” the annual 
precession of about 51’’—an effect which I need not say would 
be wholly insensible. But on the lunar nutation of 18°6 years 
period the effect of interior liquidity would be quite sensible ; 
18°6 years being 23 times 300 days, the effect would be to 
diminish the axes of the ellipse which the earth’s pole describes 
in this period each by ;'; of its own amount. The semi-axes 
of this ellipse calculated on the theory of perfect rigidity from 
the very accurately known amount of precession and the fairly 
accurate knowledge which we have of the ratio of the lunar t 
the solar part of the precessional motive are 9/22 and 6 $6, 
with an uncertainty not amounting to one-half per cent on a& 
count of want of perfect accuracy in the latter part of data. 
If the true values were less each by 3; of its own amount, the 
discrepance might have escaped detection, or might not have es 
caped detection; but certainly could be found if looked fe 
So far nothing can be considered as absolutely proved wit 
reference to the interior solidity of the earth from preecesy 
and nutation; but now think of the solar semi-annual and M 
lunar fortnightly nutations. The period of each of these 
less than 800 days. Now the hydrodynamical theory shows 
