MR. S. S. HOUGH OH THE ROTATION OF AN ELASTIC SPHEROID. 
337 
Hence neglecting terms of order co G only (A being regarded as of order &/') the 
equations (30) reduce to 
— iKoj . TMcrfb -j- por9 l . y- 5 -— = 0, 
5 ‘ 115 1 + e'/e 
-f- fA&) . -j- por0. 2 . i 8 5 -7rft 5 
1 + d/e 
= 0. 
These equations will be consistent if 6 1 = i0. 2 
-forpcPa? j —- 
x_ ^ -r e /e ___ _e 
— *M<A» ~ “ 1 + e'/e 
( 31 ). 
This gives the value of A with errors of the order a> 5 . 
© 
§ 7. Numerical Values. 
If we suppose the rigidity of our body to become perfect we should obtain e — 0, 
and therefore A/<u = e. 
This is the value we should arrive at if we started by neglecting the elastic distor¬ 
tions. We see now that it is too large and that consequently the effect of elastic 
deformation is to diminish the frequency or to prolong the period. 
The expressions for e, e are 
_ 15a) 3 , _ 5a) 3 ff 3 
I67 rp ’ o8?i 
Taking the sidereal day as 86164 mean solar seconds and using Boys’s values* for 
the mean density of the Earth and the constant of gravitation, viz. : 5‘5270 and 
6 ‘6576 X 10~ 8 we find from the above formula that for a spheroid of the same mean 
density as the Earth, rotating in a sidereal day, 
1 
Again taking the Earth’s mean radius as 6’37l X 10 8 centimetres and 
tl= 8T9 X 10 n ,+ which is the rigidity of steel, we find 
n= n/p = 1-482 X 10 n , 
* ‘ Proc. Roy. Soc.,’ 1894, p. 132. 
t Eyep.ett, ‘Units and Physical Constants,’ pp. 61, 65. 
2 X 
MDCCCXCVI.—A. 
