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MR. S. S. HOUGH ON THE ROTATION OF AN ELASTIC SPHEROID. 
and found that if the central solid portions of a rigid spheroid were replaced by 
liquid, the theoretical estimate of the period of oscillation would be diminished. It 
might appear then that our estimate of the Earth’s rigidity would be diminished if 
we suppose there to be a central fluid nucleus. That this is not so, I think the 
following considerations will show. 
In accordance with the results of the above-mentioned paper the effect of internal 
fluidity would be to increase the effective value of the quantity we have denoted bye. 
When the external crust is of considerable thickness, the increase in this quantity is, 
however, very slight; thus for a crust of about 2,000 miles in thickness we find e is 
increased in the ratio 305 : 300. Now it seems that if the central solid portions of 
the Earth were replaced by fluid the increase in the value of e', which denotes the 
ellipticity due to rotation, would be much more rapid, and that consequently X'co 
would rapidly diminish. We conclude then that the increased effects of the elastic 
deformations would more than counteract the influence of the reduced effective 
inertia due to internal fluidity, and thar with a given degree of rigidity the period of 
oscillation would be still further prolonged. The degree of rigidity of the crust 
necessary to account for a given period would also have to be increased, and as the 
estimate we have already found is high, the evidence furnished by the latitude- 
variation still seems opposed to the existence of an internal fluid nucleus. 
Finally we may consider the effects of the Earth’s viscosity. Unless this be so 
great that the present work is inapplicable, a circumstance which seems to be quite 
precluded from the close agreement of our results with observation, the chief effect of 
internal friction will be to cause the oscillation in question to gradually die out 
without producing any material change in the period. The dissipative forces arise 
entirely from the distortion of the parts of the system, and consequently no such 
forces will occur if the system be absolutely rigid throughout. Now we have seen 
that the motion consists very approximately of a rotation as a rigid body, and that 
the elastic distortions are exceedingly minute. Hence we conclude that a very small 
amount of dissipative force will be called into play, and thus if the motion is once set 
up, there appears to be no difficulty in accounting for its continuance for a very con¬ 
siderable period, possibly extending over several centuries. 
