478 MR. 8S. S. HOUGH ON THE OSCILLATIONS OF A 
Therefore, 
G-A_ CHAt+qy _mt+ae 
G ~ Cat+q+2%e)” 144 
very nearly. 
Therefore the period in which the latitude variations will take place is 

sidereal days = 
€ Dy crt f 
eee aT ee sidereal days ; 
when the Earth is supposed solid throughout, this period is 
ea sidereal days. 
We thus see that if the Earth consisted of a rigid shell containing a homogeneous 
fluid nucleus, the theoretical period of 305 days, calculated on the assumption of the 
Earth’s rigidity throughout, would be diminished in the ratio 1: 1 -+ qg, where gq is 
an essentially positive quantity, whose magnitude increases with the size of the 
nucleus. 
In order to form some idea of the magnitude of this effect, let us suppose that the 
fluid and the crust have the same density p, and that 7, 7, are the mean radii of the 
fluid nucleus, and of the Earth as a whole. 
We then have approximately 
p=v= ampre, and C = ap (7° — 7”). 


Therefore, 
pall iy havent AN 2 
Le €,C iH Tae 
7? 1 / » 5 
1 as ——— = —(—]), 
pu Tee I 0) : () 
and the period will be diminished by les i xX 305 days. 
») 
Taking the mean radius of the Earth as 4000 miles, we obtain the following table, 
where the first line gives the thickness of the crust in miles, and the second the 
diminution of the period in sidereal days :— 


Thickness of crust in miles . 2000 1000 500 250 | 100 


Diminution of period in days . 


