(150 ) 
composed are such that the strain does not exceed the 
limits of perfect elasticity. Let C;, A, denote the principal 
moments of inertia of the strained spherical planet; 
C, A the moments ‘of inertia of the actual Earth; and 
A — À + (C; — A;). Then it may be proved that the 
equations of motionfof the elastic Earth have the same 
form as before, except that A’ replaces A. Hence the 
solution will be the same in form as that for the unyield- 
ing Earth, and we may henceforth revert to our original 
hypothesis. Ï may however remark that if the Eulerian 
nutation has its period augmented from 506 to 430 days, 
we must have A’ — 1.00094 A. 
From the third of the differential equations, we have 
r—n,a Constant; and from the first two, with appro- 
priate choice of the epoch, 
. C—A 
p = F sin 
C— A 
nt, q = — Fcos Far nl, 
where F is a constant. 
If k 1s the resultant moment of momentum of the 
system, the direction cosines of Z referred to ABC 
’ Ap Ag Cr. 
ANSE te ve hence 
Ap JR Aq | Cr 
TT — — Sin 6, SIN #5, Nr — — SIN 6, COS 50, a = COS 6. 
Since r — n, the last of these shows that 6, is a con- 
stant, Say 7. 
Therefore 
Cn ; Cn 
pe DEEE, Point APE LE 
