496 T. C. CHAMBERLIN 



be outward; the reacting molecule or granule therefore rebounds 

 inward. The very process of dispersion was therefore mated with a 

 concentrating process and the two divided their results between the 

 forming of nuclei on the one hand and of planetesimals on the other. 

 On the residual side of the twin process the ultimate result was 

 the formation of a cloud of precipitated granules from which all 

 free molecules had escaped. The cloud of course had less mass than 

 the previous mixed nucleus, but there was a proportionately larger 

 reduction of dispersive activity. 



In the light of this we need next to consider further the holding 

 power represented by the spheres of control. The spheres of 

 control in Table II are computed for the earth's distance from 

 the sun. They would be relatively larger farther out and smaller 

 farther in. By reference to the table it«will be seen that the fields 

 under control are by no means insignificant even for the smallest 

 bodies represented. At the same time, reference to the adjoining 

 columns of the table will show that the strength of control is distinctly 

 limited. It is also to be noted that the velocities of retention and 

 escape are given for the surfaces of the concentrated bodies as 

 these now are, and that the velocities that can be controlled 

 decline rapidly for points farther from the center. 



Now expansion does not affect the simple static holding power 

 so much as it does the velocity that can be controlled. Within the 

 limits of the sphere of control, and with some other qualifications, 

 simple expansion or contraction does not affect the extent of the 

 sphere of control. It is a principle of celestial mechanics that if a 

 body is spherical and if its substance is distributed either uni- 

 formly or in homogeneous concentric layers its gravitative effect 

 on bodies outside it is as though the whole matter were concen- 

 trated at the center, and hence, of course, expansion or contraction 

 is immaterial so far as relates to bodies on the borders and outside 

 the body itself. If the body is not strictly spherical or homogeneous 

 in concentric layers, the deduction will not strictly hold, but any 

 departure will in general be measurably in proportion to the de- 

 parture from sphericity or homogeneity, so that the principle may 

 be used without radical error in respect to normal spheroids of 

 revolution. Applying this deduction to the range of bodies rep- 



