338 MR. S. S. HOUGH OH THE ROTATION OF AH ELASTIC SPHEROID. 
whence 
and finally 
€ 
1 + e'je 
I 
335 
We conclude that for a homogeneous spheroid of the same size and mean density 
as the Earth, the period would be extended from 232 days to 335 days in consequence 
of elastic distortions, if we suppose the rigidity to be that of steel. 
If we take into account the variations in the density of the Earth’s strata the 
problem presented becomes much more complicated. We must replace e by the 
Precessional Constant, which will no longer be equal to the surface ellipticity. Its 
value may however be accurately determined by means of data furnished by the 
Theory of Precession ; this value is known to be 1/305. Hence the effective value of 
e is diminished in the ratio 232 : 305. 
As regards the effect of heterogeneity on the value of e, we are, at present, only in 
a position to make speculations. Professor New t comb points out that in calculating 
the mean density, greater weight should be given to the density of the superficial 
layers oil account of their greater effective inertia, and hence e should also be 
diminished. A reasonable hypothesis seems to be that it is diminished in the same 
ratio as e. If we make this hypothesis, we find that if the effective rigidity of the 
Earth were as great as that of steel, the period of the Eulerian nutation would 
become 
305 x 
335 
daj’s = 410 days. 
This period is slightly in excess of Chandler’s observed period of 427 dajos. TV e 
therefore conclude that the effective rigidity of the Earth is slightly greater than 
that of steel. 
If we make the same hypothesis as above, with regard to the effects of the 
variations of density, we may easily calculate what degree of rigidity would be 
consistent with Chandler’s observed period. We find for the period of a homo¬ 
geneous spheroid of the same degree of rigidity 
427 x 23' 
305 
days = 326 days. 
Putting X/cu = e = - 2 ^ in (31) we obtain 
1 + e'/e = || 
6 . 
3 2 
e = 
_ J4 
2 3 2 c — 572> 
