876 
MR, G. H. DARWIN ON THE SECULAR CHANGES IN 
we shall be more nearly correct in supposing that the terrestrial nucleus possessed a 
high degree of stiffness in the earliest times, and that it will be best to apply the 
hypothesis of small viscosity to the more modern stages of the evolution, and that of 
large viscosity to the more ancient. 
At any rate this appears to be a not improbable theory, and one which accords very 
well with the present values of the obliquity of the ecliptic, and of the inclination of 
the lunar orbit. 
§ 33. On the initial condition of the earth and moon. 
It was remarked above that the equation of conservation of moment of momentum, 
as modified by the effects of solar tidal friction, could only be regarded as practically 
independent of the degree of viscosity of the earth, so long as the moon’s sidereal 
period was not nearly equal to the day; and that if this relationship were nearly 
satisfied, the equation which we have used throughout might be considerably in error. 
Now in the paper on “Precession” the system was traced backwards, in much the 
same way as has been done here, until the moon’s tide-generating influence was very 
large compared with that of the sun ; the solar influence was then entirely neglected, 
and the equation of conservation of moment of momentum was used for determining 
that initial condition, where the month and day were identical, from which the system 
started its course of development.* The period of revolution of the system in its 
initial configuration was found to be about hours. I now however see reason to 
believe that the solar tidal friction will make the numerical value assigned to this 
period of revolution considerably in error, whilst the general principle remains almost 
unaffected. This subject is considered in § 22. 
The necessity of correction arises from the assumption that because the moon is 
retrospectively getting nearer and nearer to the earth, therefore the effects of lunar 
tidal friction must more and more preponderate over those of solar tidal friction, so 
that if the solar tidal friction were once negligeable it would always remain so. 
But tidal friction depends on two elements, viz. : the magnitude of the tide-gen¬ 
erating influence, and the relative motion of the two bodies. Now whilst the tide¬ 
generating influence of the moon does become larger and larger, as we approach the 
critical state, yet the relative motion of the moon and earth becomes smaller and 
smaller; on the other hand the tide-generating influence of the sun remains sensibly 
constant, whilst the relative motion of the earth and sun slightly increases.! 
From this it follows that the solar tidal friction must ultimately become actually 
more important than the lunar, notwithstanding the close proximity of the moon to 
the earth. 
* See also a paper on “The Determination of the Secular Effects of Tidal Friction by a Graphical 
Method,” Proc. Roy. Soc., No. 197, 1879. 
f In the paper on “ Precession ” it was stated in § 18 that this must he the case, but I did not at that 
time perceive the importance of this consideration 
