880 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
an axis inclined at about 11° or 12° to the normal to the ecliptic,* * * § with a period of 
from 2 to 4 hours,! and is revolving about the sun with a period not very much 
shorter than our present year.! 
The rapidity of the planet’s rotation causes so great a compression of its figure that 
it cannot continue to exist in an ellipsoidal form§ with stability ; or else it is so nearly 
unstable that complete instability is induced by the solar tides. [| 
The planet then separates into two masses, the larger being the earth and the 
smaller the moon. I do not attempt to define the mode of separation, or to say 
whether the moon was initially more or less annular. At any rate it must be assumed 
that the smaller mass became more or less conglomerated, and finally fused into a 
spheroid—perhaps in consequence of impacts between its constituent meteorites, which 
were once part of the primeval planet. Up to this point the history is largely specu¬ 
lative, for although the limiting ellipticity of form of a rotating mass of fluid is known, 
yet the conditions of its stability, and a fortiori of its rupture, have not as yet been 
investigated. 
o 
We now have the earth and the moon nearly in contact with one another, and 
rotating nearly as though they were parts of one rigid body. 
This is the system which has been made the subject of the present dynamical 
investigation. 
As the two masses are not rigid, the attraction of each distorts the other ; and if 
they do not move rigorously with the same periodic time, each raises a tide in the 
other. Also the sun raises tides in both. 
In consequence of the frictional resistance to these tidal motions, such a system is 
dynamically unstable^ If the moon had moved orbitally a little faster than the earth 
rotates she must have fallen back into the earth ; thus the existence of the moon 
compels us to believe that the equilibrium broke down by the moon revolving orbit- 
ally a little slower than the earth rotates. Perhaps the actual rupture into two 
masses was the cause of this slower motion ; for if the detached mass retained the 
same moment of momentum as it had initially, when it formed a part of the primeval 
planet, this would, I think, necessarily be the case. 
In consequence of the tidal friction the periodic time of the moon (or the month) 
increases in length, and that of the earth’s rotation (or the day) also increases ; but 
the month increases in length at a much greater rate than the day. 
* This at least appears to be the obliquity at tbe earliest stage to which the system bas been traced 
back in detail, but the effect of solar tidal friction would make the obliquity primevally less than this, to 
an uncertain and perhaps considerable amount, 
f “ Precession,” § 18, and Part IV., § 22. 
j “ Precession,” § 19. 
§ “ Precession,” § 18, and Part IV., § 22. 
|| Summary of “ Precession.” 
“1 “Secular Effects,” Ac., Proc. Roy. Soc., 197, 1879; and “Precession.” § 18. 
