534 MR. G. H. DARWIN ON THE PRECESSION OF A VISCOUS SPHEROID, 
friction would be affected pari passu, and therefore the change of obliquity for a given 
amount of change in the day would not be much altered. 
Although the effects of the contraction of the earth in cooling would be certainly 
such as to render the changes more rapid in time, yet as the tidal friction would be 
somewhat counteracted, the critical point where the month is equal to twice the day 
would be reached when the moon was further from the earth than in my problem. I 
think, however, that there is reason to believe that the whole amount of contraction 
of the earth, since the moon has existed, has not been large (Section 24). 
There is one thing which might exercise a considerable influence favourable to change 
of obliquity. We are in almost complete ignorance of the behaviour of semi-solids 
under very great pressures, such as must exist in the earth, and there is no reason to 
suppose that the amount of relative displacement is simply proportional to the stress 
and the time of its action. Suppose, then, that the displacement varied as some other 
function of the time, then clearly the relative importance of the several tides might be 
much altered. 
Now, the great obstacle to a large change of obliquity is the diurnal combined 
effect (see Table IV., Section 15); and so any change in the law of viscosity which allowed 
a relatively greater influence to the semi-diurnal tides would cause a greater change of 
obliquity, and this without much affecting the tidal friction and reaction. Such a law 
seems quite within the bounds of possibility. The special hypothesis, however, of 
elastico-viscosity, used in the previous paper, makes the other way, and allows greater 
influence to the tides of long period than to those of short. This was exemplified where 
it was shown that the tidal reaction might depend principally on the fortnightly tide. 
The whole investigation is based on a theory of tides in which the effects of inertia 
are neglected. Now it will be shown in Part III. of the next paper that the effect 
of inertia will be to make the crest of the tidal spheroid lag more for a given height 
of tide than results from the theory founded on the neglect of inertia. An analysis of 
the effect produced on the present results, by the modification of the theory of tides 
introduced by inertia, is given in the next paper. 
On the whole, we can only "say at present that it seems probable that a part of the 
obliquity of the ecliptic may be referred to the causes here considered; but a complete 
discussion of the subject must be deferred to a future occasion, when the secular 
changes in the plane of the lunar orbit will be treated. 
The question of the obliquity is now set on one side, and it is supposed that when 
the moon has reached the critical point (where the month is twice the day) the 
obliquity to the plane of the lunar orbit was zero. In the more remote past the 
obliquity had no tendency to alter, except under the influence of certain nutations, 
which are referred to at the end of Section 17. 
The manner in which the moon’s periodic time approximates to the day is an 
inducement to speculate as to the limiting or initial condition from which the earth 
and moon started their course of development. 
