
we Sires 
Parr I] CONDITION OF THE EARTH'S INTERIOR. 51 
~ that, if the interior were a mass of sufficient viscosity, it might 
_behaye as if it were a solid, and thus the phenomenon of precession 
and nutation might not be affected. Sir William Thomson, who had 
already arrived at the conclusion that the interior of the globe must 
_ besolid, and acquiesced generally in Hopkins’s conclusions, pointed 
out that M. Delaunay had not worked out the problem mathe- 
matically, otherwise he could not have failed to see that the 
hypothesis of a viscous and quasi-rigid interior “ breaks down when 
tested by a simple calculation of the amount of tangential force 
_ required to give to any globular portion of the interior mass the 
precessional and nutational motions which, with other physical 
astronomers, he attributes to the earth as a whole.”? Sir William, 
in making this calculation, holds that it demonstrates the earth’s 
erust down to depths of hundreds of kilometres to be capable of 
resisting such a tangential stress (amounting to nearly ~;th of a 
gramme weight per square centimetre) as would with great rapidity 
draw out of shape any plastic substance which could properly be 
termed a viscous fluid. ‘An angular distortion of 8" is produced ina 
_ cube of glass by a distorting stress of about ten grammes weight per 
- square centimetre. .We may therefore safely conclude that the 
rigidity of the earth’s interior substance could not be less than 
a millionth of the rigidity of glass without very sensibly augmenting 
the lunar nineteen-yearly nutation.” ” 
In Hopkins’s hypothesis he assumed the crust to be infinitely rigid 
and unyielding, which is not true of any material substance. Sir 
William Thomson has recently returned to the problem, in the light 
- of his own researches in vortex-motion. He now finds that, while 
the argument against a thin crust and vast liquid interior is still 
invincible, the phenomena of precession and nutation do not 
decisively settle the question of internal fluidity, though the solar 
semi-annual and lunar fortnightly nutations absolutely disprove the 
existence of a thin rigid shell full of liquid. If the inner surface of 
the crust or shell were rigorously spherical, the interior mass of 
supposed liquid could experience no precessional or nutational 
influence, except in so far as, if heterogeneous in composition, it 
might suffer from external attraction due to non-sphericity of its 
‘surfaces of equal density. But “a very slight deviation of the mner 
surface of the shell from perfect sphericity would suffice, in virtue of 
the quasi-rigidity due to vortex-motion, to hold back the shell from 
taking sensibly more precession than it would give to the liquid, and 
to cause the liquid (homogeneous or heterogeneous) and the shell to 
haye sensibly the same precessional motion as if the whole constituted 
one rigid body.” 3 
The assumption of a comparatively thin crust requires that the 
erust shall have such perfect rigidity as is possessed by no known 
substance. The tide-producing force of the moon and sun exerts 
1 Nature, February 1, 1872. 2 Loe. cit. p. 258. 
’ Sir W. Thomson, Brit. Assoc. Rep. 1876, Sections, p. 5. 2 
E 
