AND ON THE REMOTE HISTORY OF THE EARTH. 
533 
constant viscosity; but there is every reason to believe that the earth is a cooling 
body, and has stiffened as it cooled. We therefore have to deal with a spheroid whose 
viscosity diminishes as we look backwards. 
A second solution is accordingly given (Section 17) where the viscosity is variable; no 
definite law of diminution of viscosity is assumed, however, but it is merely supposed 
that the viscosity always remains small from a tidal point of view. This solution gives 
no indication of the time which may have elapsed, and differs chiefly from the preceding- 
one in the fact that the change in the obliquity is rather greater for a given amount of 
change in the moons distance. 
There is not much to say about it here, because the two solutions follow closely 
parallel lines as far as the place where the former one left off. 
The first solution was not carried further, because as the month approximates in 
length to the clay, the three semi-diurnal tides cease to be of nearly equal frequencies, 
and so likewise do the three diurnal tides; hence the assumption on which the solution 
was founded, as to their approximately equal speeds, ceases to be sufficiently accurate. 
In this second solution all the seven tides are throughout distinguished from one 
another. At about the stage where the previous solution stops the solar terms have 
become relatively unimportant, and are dropped out. It appears that (still looking 
backwards in time) the obliquity will only continue to diminish a little more beyond 
the point it had reached when the previous method had become inapplicable. For 
when the month has become equal to twice the day, there is no change of obliquity ; 
and for yet smaller values of the month the change is the other way. 
This shows that for small viscosity of the planet the position of zero obliquity is 
dynamically stable for values of the month which are less than twice the day, while 
for greater values it is unstable; and the same appears to be true for very large vis¬ 
cosity of the planet (see the foot-note on p. 500). 
If the integration be carried back as far as the critical point of relationship between 
the day and month, it appears that the whole change of obliquity since the beginning 
is 91°. 
The interesting question then arises—-Does the hypothesis of the earth’s viscosity 
afford a complete explanation of the obliquity of the ecliptic ? It does not seem at 
present possible to give any very conclusive answer to this question ; for the problem 
which has been solved differs in many respects from the true problem of the earth. 
The most important difference from the truth is in the neglect of the secular changes 
of the plane of the lunar orbit; and I now (September, 1879) see reason to believe 
that that neglect will make a material difference in the results given for the obliquity 
at the end of the third and fourth periods of integration in both solutions. It will 
not, therefore, be possible to discuss this point adequately at present; but it will be 
well to refer to some other points in which our hypothesis must differ from reality. 
I do not see that the heterogeneity of density and viscosity would make any very 
material difference in the solution, because both the change of obliquity and the tidal 
