Part II.— CRITICAL AND SUPPLEMENTARY. 



In the development of the theory in Part I, the attempt was made to 

 give explicit statement, though without critical setting, of the more impor- 

 tant of the secondary hypotheses which were used as auxihary to the gen- 

 eral hypothesis in order to give the theory a sufficiently definite form. But 

 since the main purpose is to seek such features of the geophysical phenom- 

 ena as seem to be essentially consequences of the general hypothesis, it is 

 necessary further to inquire how far the results are peculiar to the special 

 conditions adopted and how far they seem to persist under variations of 

 these secondary assumptions; and also to what extent these assumptions 

 are subject to obscurity or positive objection through the accessibility of a 

 direct or indirect test by observation or well-established theory. 



The Laplacian law of density has been assumed chiefly because of its 

 analytic convenience, though it seems doubtful whether any geophysical 

 theory is likely to be sufficiently trustworthy in detail to afford more than 

 a crude test of any assumption on this point. Nevertheless, by inspection 

 of some of its consequences, it is possible to surmise the probable character 

 of its departure from the true law of compressibility of the average earth- 

 substance. It appears that the modifications which seem to be needed 

 from the standpoint of the planetesimal hypothesis agree, at least in kind, 

 with those famihar from the indications of general geophysical theory. 



Column 7 of table 3 shows that in the earlier stages of the growth of the 

 planet the thickness of a stratum deposited is nearly all effective in enlarg- 

 ing the geometric radius of the mass, while toward the last not much more 

 than one-quarter of a new stratum remains above the former horizon; as 

 the mass grows larger the less significant becomes the actual increase of 

 dimensions produced by a new stratum of given thickness. Moreover, with 

 a strict interpretation of the law of compressibiUty assumed above, there ia 

 a definite limit to the possible radius of the planet, no matter how much 

 material might be laid down. For in equation (25) the factor g is a defi- 

 nite constant, depending solely on h, which is determined by the compressi- 

 bility as a physical constant of the material, independent of the dimensions 

 of the mass into which it may be aggregated; while if there are to be no 

 meaningless negative densities introduced, the angle /? can not surpass the 

 value TT, at which the density at the center becomes infinite. This means 

 that no amount of accretion could produce a mass with radius greater 



than — centimeters, or about 5,000 miles. 



Now, even independently of any supposition as to the actual origin of 

 the planets, there seems to be little reason for supposing that if deposits of 

 indefinite extent could be brought about at the surface of an existing planet 

 there would be such a limit of growth, at least of such comparatively meager 

 dimensions. This objection has not much force, for the reason that the law 

 might be practically accurate for the range of densities contemplated and 

 seriously in error for the higher densities; but its suggestion is that the true 



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