MR. S. S. HOUGH ON THE ROTATION OF AN ELASTIC SPHEROID. 
343 
§ 9. Conclusions. 
The existence of the Eulerian nutation, and the fact that it would give rise to a 
variation in latitude, was first predicted theoretically on the assumption that the 
Earth could be regarded as a rigid body. Our present work, however, shows that 
the hypothesis of perfect rigidity, though affording a sufficiently close approximation 
to the circumstances presented by nature to specify the character of the oscillation, 
is totally inadequate to lead to a correct determination of the period unless the 
Earth possesses a very much higher degree of rigidity than is met with in substances 
which have been subjected to experiment. The only knowledge we have of the 
amount of the Earth’s rigidity arises from the very vague indications furnished by 
Tidal Theory, and we must therefore have recourse to observation to determine the 
period with accuracy. This has been effected by Dr. Chandler, who, as the result 
of a discussion of a very large number of observations, has assigued 427 days as the 
true period. This period is, as the present theory requires, considerably in excess of 
the Eulerian period of 305 days. 
In § 7 we have endeavoured to obtain a numerical estimate of the effective rigidity 
of the Earth which would be consistent with this observed period, and we have 
found it to be slightly greater than that of steel, a result which agrees sufficiently 
closely with the requirements of Tidal Theory. Various causes however combine to 
render this result liable to a considerable amount of uncertainty. In the first place, 
our present analysis applies only to a homogeneous spheroid composed of isotropic 
material, neither of which conditions are fully realized in the case of the Earth. In 
the second place, there are probably other causes in addition to the elastic deforma¬ 
tions of the solid parts of the Earth, which tend to modify the period. In particular 
we have completely neglected the effects of the mobility of the ocean. According to 
Newcomb these effects will be small compared with the effects of elastic deformation, 
but different writers have expressed widely different opinions on the subject. Thus 
Woodward* is of opinion that they alone would be sufficient to fully account for the 
observed extension of the period. Newcomb’s view is to some extent confirmed by 
the smallness of the tide having a 427-day period which has been made the subject of 
observation by BakhuysenI and A. S. Christie, \ and as it has appeared to me to 
be quite open to question in what manner the results would be affected, I have 
thought it best not to apply any correction on this account ; the results, then, must 
only be regarded as provisional, pending more complete mathematical investigations 
on the subject. 
In a previous paper § I have investigated the effects of an internal fluid nucleus, 
* ‘ Astron. Jour.,’ No. 345, vol. 15. 
f ‘Astron. Nach.,’ No. 3261. 
J ‘Astron. Jour.,’ No. 351. 
§ ‘ Phil. Trans.,’ A, J895. 
