STABILITY OF A GP.AVITATING PLANET. 
I7'.» 
It is easy to see that enormous stresses would be set up in the interior of the earth 
after consolidation. An equilihrium configuration depends in general upon the 
compressibility of the material, and a configuration Avhich was one of equilibrium for 
the compressibility which obtained at the moment of solidification would not remain 
so after the incompressibility and rigidity of the material had increased by cooling. 
If we supjDOse the earth to cool in an unsymmetrical configuration the stresses set up 
will soon become very great. In fact, Professor Darwin has shown that the stresses 
which would he produced by the weights of our continents in an earth initially 
homogeneous {i.e., by an irregularity of less than a thousandth part of the radius) 
would be so great that the material would be near the breaking point.'" 
We must therefore suppose that as the earth cools and the elastic constants change 
there will be a series of I'uptures resulting from the stresses set up in the inteiior. 
The configuration will become approximately spherical (spheroidal if rotation is taken 
into account) as so(m as the point of bifurcation is passed. 
The fact that the ultimate configuration is reached oidy as the result of a long 
succession of ruptures puts the whole question outside the range of exact mathe¬ 
matical treatment. We can, however, see that the final configuration (disregarding 
rotation) will prohalfiy not be cpiite spherical, hut will retain traces of tlie initial 
unsymmetrical configuratioi i. 
§ 35. Before we can attem})t to decide whether or ]iot the earth shows traces of a, 
process suclr as that just described, it will be necessary to form some idea of the 
unsymmetrical configuration witli wliich the process must liave begun. We cannot 
accurately calculate the “ linear series” of unsymmetrical configurations except in the 
immediate neighbourhood of tlie point of liifurcation. Near to this point the 
configuration is spherical except for terms proportional to the first harmonic. The 
free surface will, therefore, be strictly spherical, and it will, of course, be an equl- 
potential. but its centre will not coincide with the centres of other surfaces of equal 
potential. If we suppose a fluid mass of tliis kind to solidify, and then to shriidv by 
cooling, the shrinking being accompanied by a series of ruptures of the kind already 
explained, we can easily imagine that the free surface would retain an approximately 
spherical form, but that when the final state is reached this surface would not be 
quite an equipotential, and the centre of gravity would not quite coincide with the 
centre of figure. If water is placed on the surface of a planet of this kind, it will 
form a circular sea, of which the centre will be on the axis of harmonics, while the 
dry land will form a spherical cap. 
Evidence from the 1)istrihution of Seas and Land: 
§ 36. Now this is not observed on the earth, and it could not be expected, since we 
have ignored all the agencies which have contriliuted to the figure of the earth, 
* ‘Phil. Trans.,’ vol. 173, 1882, p. 187. 
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