284 
ME. GEOEGE H. DAEWIN ON THE INFLUENCE OF 
subsided, #=R f, y=R-, or the pole of figure will have taken up a position on one 
side of the meridian, along which it was initially propelled by the explosion. 
It thus seems probable that during the consolidation of the earth there was a great 
instability in the position of the principal axis, and therefore also of the axis of rota- 
tion which followed it. 
6. Secular alteration in the obliquity of the Ecliptic, resulting from terms independent 
of the Impressed Forces. 
To return to the main line of the inquiry : — If the values of u 1 and co 2 , found in sec. 2, 
be substituted in the geometrical equations for ^ and ^ sin 6 (see sec. 1), a number 
of periodic terms will arise, and these terms have diurnal and semidiurnal periods, but 
their amplitudes are so small that they have no practical interest. 
The only thing which concerns us is to inquire whether there can be any secular 
change in the obliquity of the ecliptic. 
Select, then, only terms in sinw£ in and in cos nt in a 2 , and substitute in the geo- 
S 
metrical equation ^=— sm. nt-\-a. 2 cos nt, and reject periodic terms. It will then be 
found that 
dQ 
dt 
7. Terms dependent on the Impressed Forces. 
It now remains to consider the effect of the impressed forces on the precession and 
obliquity of the ecliptic. 
The equations of motion are reduced to 
t" 1 
Q 
1 
> 
L 
di + A 
=J> 
doo 2 C-A 
M 
dt A 
U &l = A.’ 
dco 3 
N 
dt 
~ A 
If we write for L, M, N, L-f-SL, c)N, and indicate by L and M the couples 
caused by the attractions of the sun and moon on the protuberant parts of the earth 
before it has begun to change its shape, then L and M only cause the ordinary precession 
and nutations. For the present problem it is therefore only necessary to consider the 
effects of £L, SM, &N, which arise from the change of shape of the earth. 
It follows, from the same arguments that were used in sec. 1, that the change in the 
earth’s angular velocity of rotation due to will only have a very small effect on u x 
and u 2 ; so that, as far as is now important, u z may be put equal to — n in the first two 
