237-240] General Stellar Dynamics 235 



directions in space. If a velocity diagram be drawn at any point x, y, z, 

 formed of lines representing the velocities of the stars near this point in mag- 

 nitude and direction, this velocity diagram will not be spherically symmetrical ; 

 it will be a figure of revolution having the radius through the point as an 

 axis of symmetry. 



In the particular case in which this figure of revolution is very elongated 

 in the direction of the radius, the majority of the stars would appear to be 

 moving in directions only slightly inclined to the radius, and the motion might 

 be interpreted as that of two streams of stars intermingled, each moving in a 

 radial direction, but one moving inwards and the other outwards. 



This brings to mind a suggestion made by H. H. Turner* to explain 

 the observed " star-streaming " in our own universe. Turner supposed that 

 the " star-streaming " might originate in the backwards and forwards motion 

 of stars describing orbits of high eccentricity (nearly parabolic) about the 

 centre of gravity of the universe. The question of the possibility of some 

 such motion was investigated theoretically by Eddingtonf, who found, by a 

 method different from ours, that steady states of types included in formula ' 

 (573) were possible. Eddington, however, did not notice that such motions 

 were possible only in a strictly spherical universe. Our universe is almost 

 certainly not spherical, being a lenticular or biscuit-shaped structure, and the 

 star-streaming is almost certainly not along radii but in directions nearly 

 tangential to radii. Thus it appears fairly certain that a formula such as 

 (573) cannot express the observed stellar motions in our own universe. 



Before leaving this formula, let us notice that the angular momentum of 

 the whole system of stars about the axis of z 



I Illl \f^zdudvdwdxdydz 0. 



Since the angular momentum of a system moving solely under its own 

 gravitational forces must remain constant, it follows at once that a system 

 specified by formula (573) cannot possibly have originated out of a rotating 

 nebula or out of any other system in which the angular momentum was not 

 zero. 



240. We pass now to the consideration of the type of motion expressed 

 by formula (572). In this the total angular momenta about the axes of x and 

 y are easily seen to be zero, but the angular momentum about the axis of z 

 is not zero. The plane of xy is accordingly the invariable plane of the system, 

 and the system can have originated out of a system in rotation, the axis of 

 rotation having been parallel to the axis of z. 



* Monthly Notices R.A.S. 72 (1912), pp. 387 and 474. 



t Monthly Notices R.A.S. 74 (1914), p. 5, 75 (1915), p. 366, and 76 (1916), p. 37. 



