158 SEE— DYNAMICAL THEORY [April 19, 



Other conditions being equal, the maximum moment of momen- 

 tum would therefore be attained by the separation of two stars to a 

 great distance, yet a pair of such passing stars would have to have 

 peculiar directions and velocities to enable them under mutual gravi- 

 tation to form a system. If the motions of two stars were directed 

 towards the same point in space, and with velocities which would 

 enable one to overtake the other, before or after the point was 

 reached, one might revolve about the other ; and with proper relative 

 velocity — to be gotten either by altering the directions of motion, or 

 by adjusting the velocities in the converging lines of motion — the 

 two stars might form a binary system. 



This dynamical condition of formation is so difficult to realize in 

 practice that we may be sure that it is quite rare in nature ; and that 

 the vast m.ajority of double stars have developed from nebulae, by 

 the appropriate division of the elements between two leading centers 

 of condensation. But it is now recognized that the nebulae them- 

 selves have developed from dust expelled from the fixed stars and 

 were originally of vast extent; and hence even if the bodies into 

 which they condense gradually approach the center of gravity of the 

 system, as the stars increase in mass and revolve against the nebular 

 resisting medium and their orbits grow smaller and smaller and 

 rounder and rounder, it will yet follow that many double stars have 

 components so far apart that their systems have large moments of 

 momentum of orbital motion. 



The difficulty of explaining the large orbital moments of momen- 

 tum of double stars first arose in completing certain calculations for 

 my inaugural dissertation at the University of Berlin just twenty 

 years ago. At that time I saw that a wide separation of the compo- 

 nents of a system gave large moment of momentum, and that in 

 order to account for the orbital moment of momentum by the hypoth- 

 esis of tidal friction first developed by Sir George Darwin and after- 

 wards extended by me to binary systems, it was necessary to endow 

 the stars with very rapid axial rotation. Otherwise the mean dis- 

 tance of the components would not be greatly increased by the ex- 

 haustipn of the moments of momentum of axial rotation under the 

 secular action of tidal friction. 



