54 GEOLOGY. 



reduced to zero, gravitation would draw a finite group of stars directly 

 together. When both factors are present, relative freedom from col- 

 lision and disruptive approach lies between the two extremes. A numer- 

 ical inquiry 1 leads to the interesting conclusion that most of the existing 

 velocities lie near that happy medium that gives fewest catastrophes, 

 from which the inference is drawn that a selective process has removed 

 most of the bodies of dangerously high and dangerously low velocities, and 

 has left those possessed of the relatively safe intermediate velocities. 2 



If all stellar motions are like the known motions, and if the known 

 stars constitute a system by themselves, a uniform velocity cannot 

 be maintained in all parts of the stars' courses, nor can like velocities 

 prevail in all portions of the system. The velocities must be highest, 

 on the average, when a star is traversing the interior of the group, and 

 the contingencies that attend high velocities must be there resident. 

 The mherited velocities must be presumed to be lowest on the outer 

 borders of the system, where the constituent bodies reach the limit of 

 their outward excursions and turn back, under the gravity of the system, 

 to again traverse it. This at least seems the most tenable conception 

 of the movements of the members of the stellar system, considered 

 as a finite group of bodies possessed of the known motions and con- 

 trolled by the known forces. The alternative conception of an infinite 

 extension of stars is beyond treatment here. On the outer borders, 

 therefore, mutual attraction is assumed to be relatively more potential 

 than in the central portions. But, as some residual motion derived from 

 previous excursions is even there retained, and as a part of this is almost 

 inevitably tangential, close approaches rather than collisions are the 

 disturbing contingencies indicated. 



In this outer portion also, the paths assigned the stars are more 

 nearly parallel, because all are approximately parallel to the surface of 

 the stellar sphere at their turning-points, and hence such inherited 

 energies as the bodies possess oppose less resistance to the approach of 

 the bodies to one another, for it is only when the motions are in opposite 

 or transverse directions that their kinetic energies resist gravitative 

 approach. 



1 Made by the senior author in cooperation with F. R. Moulton and C. E. Sieben- 

 thal. 



2 There are, however, a number of stars with great enough velocities to carry them 

 beyond the visible system, even after allowing liberally for dark bodies (Moulton). 



