202 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



compressibility most probably diminishes, as the density increases, more 

 rapidly than is postulated by the Laplacian law. This would allow a larger 

 part of the compression to take place during the earlier stages, giving to the 

 nucleus, when it reaches a given radius, a larger mass than is assigned it 

 above. 



In the light of the planetesimal hypothesis a similar conclusion can be 

 reached in another way. For in view of the like origin predicated of the 

 earth and other bodies of the solar system from the primitive planetesimals, 

 composed of more or less similar materials of definite compressibility, it may 

 be expected that at the successive stages when the earth-nucleus reached 

 dimensions equal to those of various planets at the present time its mass 

 should show some agreement with the observed masses of those planets. 

 The supposition of the small upper limit of diameter just mentioned is of 

 course negatived by the existence of the planets of the Jovian group. But 

 such comparison is futile, partly because of the uncertainty as to their 

 true dimensions, brought about by their extensive atmospheres, partly 

 because of the wide difference in physical condition as compared with the 

 earth, illustrated in particular by mean densities smaller than even the 

 surface-density assumed for the earth. Moreover, it is conceivable that 

 the discrepancies of an assumed pressure-density law might become serious 

 only outside of the range met with in smaller bodies like the earth. But a 

 comparison with the other planets of the terrestrial group should prove 

 instructive. Table 8 gives their observed radii and masses as compared 

 with the earth, and the hypothetical masses computed by interpolation 

 from columns 2 and 4 of table 3. 



Table 8. 



To interpret this table it is necessary to observe that if the masses cor- 

 responding to assigned dimensions be computed according to two different 

 laws of compressibility, using the mean and surface-densities of the present 

 earth as given constants, then those masses must approach agreement, on 

 the one hand for small bodies where the compression is sUght and the aver- 

 age density therefore not very different from the assigned surface-density, 

 on the other hand for bodies approximating the earth in size, the average 

 density then approaching the assigned mean density. Thus it appears that 

 the divergence of result between two such assumptions would be likely to be 

 most marked for bodies of intermediate size, like Mars, Mercury, and the 

 moon, while the agreement should be close for Venus on the one hand and the 

 asteroids on the other — as, for instance, if the masses resulting from the 

 Laplacian law be compared as above with the observed masses, supposing the 

 latter to correspond to a definite, though unknown, law of compressibility. 



