516 MR. G. H. DARWIN ON THE PRECESSION OF A VISCOUS SPHEROID. 
S 21. On certain other small tei 
$ 
mis. 
It will be well to advert to certain terms, the neglect of which might be suspected 
of vitiating my results. 
According to the hypothesis of the plastic nature of the earth’s mass, that body 
must have been a figure of equilibrium at every time throughout the series of 
changes which are to be followed out. In consequence of tidal friction the earth’s 
rotation is diminishing, and therefore its ellipticity (which by the ordinary theory is 
-f—j is also diminishing; this change of figure might be supposed to exercise a 
material influence on the results, but I wall now show that in one respect at least its 
effects are unimportant. 
Q _ 
In a previous paper" I showed that, neglecting —— compared with unity, when 
A 
the earth’s figure changed symmetrically with respect to the axis of rotation, 
cli 
dt'' 
T + T. . . . d , 
■ - sin i cos i—(C — A) 
C n~ at J 
Now if e be the ellipticity of figure 
So that 
and therefore 
C—A=fM« 2 e 
1 d . ~ . ,_ de _ 5 na dn _ n 
^ ' dt 2 g dt g C 
dl T + T, . . . JE 
— — - -sin i cos i —- 
dt g-/i C 
C dV 
Now numerical calculation shows that at present 7 ” and since IP sm i cos i is 
r a, 10' 
C?i 
of the same order of magnitude as ~ (on which the changes of obliquity have been 
KjII 
shown to depend), it follows that this term is fairly negligeable compared with those 
already included in the equations. As far as it goes, however, this term tends in the 
direction of increasing the obliquity with the time.t 
* “ On the Influence of Geological Changes,” &c., Phil. Trans, Vol. 167, Part I., page 272, Section 8. 
The notation is changed, and the equation presented in a form suitable for the present purpose. 
f In a paper in the ‘ Phil. Mag.,’ March, 1877, I suggested that the obliquity might possibly be due to 
the contraction of the terrestrial nebula in cooling'; I there neglected tidal friction and assumed the con- 
servation of moment of momentum to hold good for the earth by itself, so that the ellipticity was con¬ 
tinually increasing with the time. I did not at that time perceive that this increase of ellipticity was 
antagonistic to the effects of contraction. Though the work of that paper is correct, as I believe, yet the 
fundamental assumption is incorrect, and therefore the results are not worthy of attention. 
