62 GEOLOGY. 



The sizes of the nuclear masses. — If the present planets have grown 

 from these nebular nuclei, the greatness of their growth is measured 

 by the smallness of the primitive nuclear masses. The amount of 

 such accretion is a matter of geologic interest, for it is fundamentally 

 related to many dynamical questions of the earth's later history. 

 There are two considerations that bear upon the size of the original 

 nuclei. 



1. There is a certain inherent and necessary limitation to the size 

 of scattered or tenuous bodies in the presence of more massive bodies. 

 The principle involved is one of vital importance in the study of planet- 

 ary evolution. Within the field of the effective attraction of a domi- 

 nant body like the sun, or the ancestral nebular center, small bodies 

 exercise differential gravitative control over a limited sphere only, 

 known, technically, as the "sphere of activity." This sphere for the 

 earth, with its present mass, reaches out about 620,000 miles. 1 If 

 the earth has grown at all, its primitive sphere of control must have 

 been smaller than this. The earth nucleus could, therefore, only 

 have embraced such matter as lay within this limited sphere. If 

 the original knot could be supposed to have extended beyond this limit, 

 the outlying portion would have been drawn away by the solar mass 

 into independent planetesimals, and must have been gathered in, if 

 it became a part of the earth, by some other means than direct attrac- 

 tion. The moon controls, as against the attraction of the earth at its 

 present distance, a sphere whose radius is about 25,000 miles; and 

 considerably less than 25,000 miles as against the joint attraction of 

 the earth and sun. Its primitive nucleus, if it has grown at all, was 

 confined to smaller dimensions. Attenuated nuclei of indefinite size 

 cannot, therefore, be supposed to maintain themselves permanently 

 in the fields of attraction dominated by larger bodies. Bodies of gas, 

 subject to the dispersive effects of their own molecular velocities, in 

 addition to the competitive gravity of dominant bodies, have still 

 narrower limits, and below a certain mass are inevitably dispersed. 

 In such a system as ours, gases must, for the most part, either join 

 themselves to the dominant bodies or be scattered into molecular 

 planetesimals. None of the smaller knots of the solar nebula could 

 probably have been gaseous in any large measure. Gases were probably 

 attached to and occluded in the aggregated or solid planetesimals, and 



1 "The Spheres of Activity of the Planets," Moulton, Pop. Astro., No. 66, p. 4. 



