1 7(j ME. J. H. JEANS ON THE VIBRATIONS AND 
sniallness of the planet, hut the figure in the fourth column -would seem to suggest 
tluit rotational instability must have played a large part in tlie creation of the 
Martian satellites. 
If, on the other hand, we begin by regarding the planets not as a fortuitous 
collection of bodies, but as a series of satellites all ejected from the same primary, the 
case is different. For here we should expect the smaller planets to have cooled more 
than the heavier ones, and therefore to be at a lower temperature. Against this 
must he set the fact that the heavier planets will jDrobably have the greatest 
concentration of density about the centre, and the greatest mean- pressure. The first 
consideration tends to increase the value which we should expect for the mean 
density of the smallei' planets as compared with that of the greater ones; the second 
consideration tends in the opposite direction. We can hardly profess to estimate the 
I'elative weights of these two considerations with any approach to accuracy; perhaps 
it is best to revert to the argument given in the last paragraph, while bearing in 
mind that the approximate equality of our numbers may become considerably less 
significant as soon as the question of relative temperature is taken into account. 
§ 29. We now consider the evidence afibixled by the absolute value of our figures. 
After allowing for the exceptional cases, it a^Dpears that the value of Xq for the earth 
and for most of the planets is about 4 X lO^h In other words, if we suppose these 
planets suddenly to resume the molten state, while retaining their present mass and 
radius, the spherical form will be stable or unstable according as the mean value of 
\ 2jjL is greater or less than 4 X lO^f In the molten state we may take fx = 0, 
aud the value X = 4 X corresponds to a value equal to about half of that of 
steel, for which X = 8'3 X lldf If, however, we attempt to trace the history of a 
}danet backwaixl in time, we cannot suppose the mass and radius kept constant: the 
mass may be constant, but the radius will increase. Ujider these conditions we find 
that the critical value of X,, will be inversely proportional to the fourth power of the 
radius, and will, therefore, be somewhat less than the value X = 4 X lO^h It would 
be extremely difficult to form a reliable estimate of what this corrected value for X 
ought to I)e, and equally difficult to estimate A\'hat would l)e the actual value of X for 
molten material similar to that of Avhich our planets must have been composed Allien 
in the urjlten state. Our argument is that the two A'alues of X are at least of the 
same order (_)f magnitude, and probably equal, except for inaccuracies in our calcu¬ 
lations. 
Comparison oj the Ixotational and CI'avdtational Ilypotlicses. 
§ 30. We may conclude this j^art of our Avork l)y comparing tA\o extreme 
hypotheses: the first referiiug the phenomena of planetaiy eAmlution solely to 
rotational, and the second solely to graAntational instability. 
Given the approximate values of X and p for a planet, and the fact that this 
