RECENT ADVANCES IN SCIENCE 621 



A third paper has appeared by Prof. A. S. Eddington 

 (M.N., R.A.S., lxxvi. 191 5, p. 37) in continuation of his 

 important researches in stellar dynamics. In this paper some 

 of the restrictions imposed in previous papers have been 

 removed, and more general systems discussed. The restriction 

 of spherical symmetry is removed, and in order to allow 

 for a possible influence of matter distributed throughout inter- 

 stellar space, as mentioned above, it is supposed that the system 

 moves under any potential of force instead of merely under 

 its own attraction. Many of the results obtained hold also 

 whether the system has attained a steady state or not. 

 Assuming the velocity distribution to be according to Schwarz- 

 schild's law, the velocity ellipsoids define three orthogonal 

 systems of curves which are called the principal velocity surfaces. 

 It is found that, even if a steady state has not been reached, 

 these surfaces must be confocal quadrics. For a system 

 moving under its own attraction, the only possible solution is 

 one of spherical symmetry. 



j. H. Jeans, M.N., R.A.S., lxxvi. 1915, p. 70, in a paper 

 on the theory of star-streaming and the structure of the 

 universe has obtained some important results of a very general 

 nature. If the law of star-streaming possesses no symmetry, 

 then to satisfy the kinematical conditions of the system, the 

 universe must be spherical ; if it possesses one degree of 

 symmetry, so that it is represented by a figure of revolution 

 about an axis, then the universe must also be a figure of revo- 

 lution. If the law has two degrees of symmetry, or is spherical, 

 then the universe can have any shape. Further restrictions 

 are, however, imposed by the dynamical conditions of the 

 system, and an examination of these indicates that with a 

 spherical law of star-streaming the universe must also be 

 spherical. With the conditions prevailing in our own universe, 

 the conclusion is reached that a steady state is impossible 

 and that star-streaming does not represent a steady state. As 

 was pointed out, however, by Prof. Eddington when this paper 

 was read (Observatory, xxxix. 1916, p. 41), there are strong 

 arguments for believing that a steady state gives a good 

 approximation to what is going on in our own universe, and a 

 consideration of steady systems may throw considerable light 

 on what is actually happening. 



Displacement of Solar Spectrum Lines. — The accurate 



