278 
MR. GEORGE H. DARWIN ON THE INFLUENCE OF 
2. Inequalities independent of the Impressed Forces. 
First, then, suppose that L=M=0. 
Integrate the equations, and neglect compared with n, and we have 
*q=^(a— b+c) t cos (b — c) sinwif— ^(y+^^cos nt 
— ~ "t - F cos j ud — G sin qit, 
" 2 = x ( “ a + b + c) t sin nt + ~ (c — a) cos nt — ^ (V+x) sin nt 
+ ^/3 + ~^\ — F sin [Xit — G cos yst. 
The last two terms in t» L and oj 2 represent the complementary function ; and the values 
of F and G must be determined from the initial conditions. 
Now it will be shown later that a, (3, y are comparable with c ~ —A ’ C— -A ’ bence 
the terms in the second lines are much more important than those in the first. Thus 
in determining the values of F and G we may neglect the first lines. 
Now, initially, the instantaneous axis coincides with the axis of greatest moment of 
inertia; so that when t—0, co l =co 2 = 0, and therefore 
The terms in F and G represent an inequality of 306 days period. 
3. The Inequality of 306 -Bays Period *. 
I have worked out the value of and in two supposed cases of elevation, under 
certain suppositions as to the nature of the internal movements of the earth. In one of 
* I have thought it necessary to discuss this inequality fully, both on account of its intrinsic interest, and 
because it has been referred to by the Astronomer Royal and Sir William Thomson. 
The former says (‘ Athenaeum/ Sept. 22, 1860) : — “ Now, let us suppose the earth not absolutely rigid, hut 
that there is susceptibility to change of form, either from that degree of yielding or fracture to which most 
solid substances are liable, or from the hydrostatic pressure of internal fluid. This, as I conceive, puts an end 
to all supposition of change of axis. The first day’s whirl would again make the axis of rotation to be a prin- 
cipal axis, and the position of the axis would then be permanent.” 
But Sir Geoege Aiex is here speaking of the effect of the elevation of a mountain mass in about latitude 45°, 
by something like a gaseous explosion. This supposition is not at all in accordance with the belief of geologists, 
whereas a gradual elevation is so. 
Sir W. Thomson, on the other hand, says (Trans. Geol. Soc. Glasgow, 1874, vol. xiv. p. 312) : — ■“ In the 
present condition of the earth, any change in the axis of rotation could not be permanent, because the instan- 
taneous axis would travel round the principal axis of the solid in a period of 296 days In very early 
geologic ages, if we suppose the earth to have been plastic, the yielding of the surface might have made the uew 
axis a principal axis. But certain it is that the earth at present is so rigid that no such change is possible.” 
And he adds that practical rigidity has prevailed throughout geologic history. 
