1876.] 
The British Association 
559 
same precessional motion as if the whole constituted one rigid body. But 
although so much could be foreseen readily enough, he found it impossible to 
discover, without thorough mathematical investigation, what might be the 
characters and amounts of the deviations from a rigid body’s motion which 
the several cases of precession and nutation contemplated would present. 
The investigation, limited to the case of a homogeneous liquid enclosed in an 
ellipsoidal shell, had brought out results which had greatly surprised him. 
When the interior ellipticity of the shell is just too small, or the periodic 
speed of the disturbance just too great to allow the motion of the whole to be 
sensibly that of a rigid body, the deviation first sensible renders the preces- 
sional or nutational motion of the shell smaller by a small difference than if 
the whole were rigid, instead of greater, as he expedted. The amount of this 
difference bears the same proportion to the adtual precession or nutation as 
the fra&ion measuring the periodic speed of the disturbance (in terms of the 
period of rotation as unity) bears to the fraction measuring the interior 
ellipticity of the shell ; and it is remarkable that this result is independent of 
the thickness of the shell, assumed, however, to be small in proportion to the 
earth’s radius. The conclusions to which Sir William’s investigations led, he 
considered to be absolutely decisive against the geological hypothesis of a 
thin rigid shell full of liquid. But, he proceeded, interesting in a dynamical 
point of view as Hopkins’s problem is, it could not afford a decisive argument 
against the earth’s interior liquidity. It assumed the crust to be perfectly 
stiff and unyielding in its figure ; but if it consisted of continuous steel and 500 
kilometres thick, it would yield very nearly as much as if it were india-rubber, 
to the deforming influences of centrifugal force and of the sun’s and moon’s 
attractions. The state of the case was shortly this : — The hypothesis of a 
perfectly rigid crust containing liquid violates physics by assuming preter- 
naturally rigid matter and dynamical astronomy in the solar semi-annual and 
lunar fortnightly nutations ; but tidal theory has nothing to say against it. 
On the other hand the tide, decides against any crust flexible enough to per- 
form the nutations correCtly with a liquid interior, or as flexible as the crust 
must be unless of preternaturally rigid matter. 
But thrice to slay the slain ; suppose the earth this moment to be a thin 
crust of rock or metal resting on liquid matter. Its equilibrium would be un- 
stable. The upheavals and subsidences would be strikingly analogous to 
those of a ship which had been rammed ; one portion of crust up and another 
down, and then all down. Whatever might be the relative densities of rock 
solid and melted, at or about the temperature of liquefaction, it was, he 
thought, quite certain that cold solid rock was denser than hot melted rock; 
and no possible degree of rigidity in the crust could prevent it from breaking 
in pieces and sinking wholly below the liquid lava. Something like this 
probably went on for thousands of years after solidification commenced ; 
surface portions of the melted material losing heat, freezing, sinking imme- 
diately, or growing to thickness of a few metres when the surface would be 
cool and the whole solid dense enough to sink. “ This process must go on 
until the sunk portions of crust build up from the bottom a sufficiently close- 
ribbed skeleton or frame, to allow fresh incrustations to remain bridging 
across the now small areas of lava pools or lakes. In the honey-combed solid 
and liquid mass thus formed there must be a continual tendency for the 
liquid, in consequence of its less specific gravity, to work its way up, whether 
by masses of solid falling from the roofs of vesicles or tunnels, and causing 
earthquake shocks, or by the roof breaking quite through when very thin, so 
as to cause two such hollows to unite or the liquid of any of them to flow out 
freely over the outer surface of the earth ; or by gradual subsidence of the 
solid owing to thermodynamic melting, which portions of it under intense 
stress must experience according to his brother’s theory. The results which 
must follow from this tendency seem sufficiently great and various to account 
for all that we learn from geological investigation of earthquakes, of upheavals, 
and subsidences of solid, and of eruptions of melted rock.” 
Leaving altogether now the hypothesis of a hollow shell filled with liquid, 
we must still face the question, how much does the earth, solid throughout, 
