AKD OjST THE REMOTE HISTORY OF THE EARTH. 
537 
initial configuration must have been slower, and the moon more distant from the earth. 
This slower revolution would correspond with a smaller ellipticity, and thus the system 
would probably be less nearly unstable. 
The following appears to me at least a possible cause of instability of the spheroid 
when rotating in about 5 hours. Sir William Thomson has shown that a fluid spheroid 
of the same mean density as the earth would perform a complete gravitational oscillation 
in 1 hour 34 minutes. The speed of oscillation varies as the square root of the density, 
hence it follows that a less dense spheroid would oscillate more slowly, and therefore a 
spheroid of the same mean density as the earth, but consisting of a denser nucleus and 
a rarer surface, would probably oscillate in a longer time than 1 hour 34 minutes. It 
seems to be quite possible that two complete gravitational oscillations of the earth in 
its primitive state might occupy 4 or 5 hours. But if this were the case, then the solar 
semi-diurnal tide would have very nearly the same period as the free oscillation of 
the spheroid, and accordingly the solar tides would be of enormous height. 
Does it not then seem possible that, if the rotation were fast enough to bring the 
spheroid into anything near the unstable condition, then the large solar tides might 
rupture the body into two or more parts ? In this case one would conjecture that it 
would not be a ring which would detach itself. 
It seems highly probable that the moon once did rotate more rapidly round her own 
axis than in her orbit, and if she was formed out of the fusion together of a ring of 
meteorites, this rotation would necessarily result. 
In Section 23 it is shown that the tidal friction due to the earth’s action on the 
moon must have been enormous, and it must necessarily have soon brought her to 
present the same face constantly to the earth. This explanation was, I believe, first 
given by Helmholtz. In the process, the inclination of her axis to the plane of her 
orbit must have rapidly increased, and then, as she rotated more and more slowly, 
must have slowly diminished again. Her present aspect is thus in strict accordance 
with the results of the purely theoretical investigation. 
It would perhaps be premature to undertake a complete review of the planetary 
system, so as to see how far the ideas here developed accord with it. Although many 
facts which could be adduced seem favourable to their acceptance, I wall only refer 
to two. The satellites of Mars appear to me a most remarkable confirmation of these 
views. Their extreme minuteness has prevented them from being subject to any per¬ 
ceptible tidal reaction, just as the minuteness of the earth compared with the sun has 
prevented the earth’s orbit from being perceptibly influenced (see Section 19); they thus 
remain as a standing memorial of the primitive periodic time of Mars round his axis. 
Mars, on the other hand, has been subjected to solar tidal friction. This case, however, 
deserves to be submitted to numerical calculation. 
The other case is that of Uranus, and this appears to be somewhat unfavourable to 
the theory ; for on account of the supposed adverse revolution of the satellites, and of 
the high inclinations of their orbits, it is not easy to believe that they could have 
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