EVOLUTION OF THE SOLAR SYSTEM. 
533 
contact with the earth, in a circular orbit coincident with the earth’s equator, and 
with a periodic time only slightly exceeding that of the earth’s rotation. 
Then it was proved that lunar and solar tidal friction would reduce the system from 
this primitive condition down to the state which now exists by causing a retardation 
of terrestrial rotation, an increase of lunar period, an increase of obliquity of ecliptic, 
an increase of eccentricity of lunar orbit, and a modification in the plane of the lunar 
orbit too complex to admit of being stated shortly. 
It was also found that the friction of the tides raised by the earth in the moon 
would explain the present motion of the moon about her axis, both as regards the 
identity of the axial and orbital revolutions, and as regards the direction of her polar 
axis. 
Thus the theory that tidal friction has been the ruling power in the evolution of 
the earth and moon completely coordinates the present motions of the two bodies, and 
leads us back to an initial state when the moon first had a separate existence as a 
satellite. 
This initial configuration of the two bodies is such that we are almost compelled to 
believe that the moon is a portion of the primitive earth detached by rapid rotation or 
other causes. 
There may be some reason to suppose that the earliest form in which the moon 
had a separate existence was in the shape of a ring, but this annular condition precedes 
the condition to which the dynamical investigation leads back. 
The present investigation shows, in confirmation of preceding ones/" that at this 
origin of the moon the earth had a period of revolution about the sun shorter than at 
present by perhaps only a minute or two, and it also shows that since the terrestrial 
planet itself first had a separate existence the length of the year can have increased 
but very little—almost certainly by not so much as an hour, and probably by not 
more than five minutes.t 
With regard to the 11° or 12° of obliquity which still remains when the moon and 
earth are in their primitive condition, it may undoubtedly be partly explained by the 
friction of the solar tides before the origin of the moon, and perhaps partly also by the 
simultaneous action of the ordinary precession and the contraction and change of 
ellipticity of the nebulous mass.| 
* “ Precession,” § 19. 
t If the change lias been as much as an hour the rotational momentum of the earth destroyed by solar 
tidal friction must have been 33 times the present total internal momentum of moon and earth. For the 
orbital momentum of a planet varies as the cube root of its periodic time, and if we differentiate logarith¬ 
mically we obtain the increment of periodic time in terms of the increment of orbital momentum. Then 
taking the numerical data from Tables I. and II. we see that this statement is proved by the fact that 
3 x 33 times [216-f-'01720 X 10 10 ] X 365‘25 x 24 is very nearly equal to unity, 
X See a paper “ On a Suggested Explanation of the Obliquity of Planets to their Orbits,” ‘ Phil. Mag.,’ 
March, 1877. See however § 21 “Precession.” 
3 z 2 
