One complicating factor is the asymmetry of high velocity stars, which has been discovered by J. H. Oort and G. Stromberg. According to Oort, stars with speed greater than about 6o km. per sec. are moving almost exclusively towards one hemisphere of the sky. It seems reasonable to interpret this critical speed as the "velocity of escape" from our local star-cloud. Stars with velocity below the velocity of escape are permanent members of the star-cloud, and describe orbits within it under its gravitational attraction ; on the average, therefore, they move as much in one direction as in the opposite. Stars with velocity above that of escape cannot be permanent members ; they pass once through the system and do not return; accordingly they may well show an asymmetry of motion, dropping into our star-cloud from a cluster or clusters on one side of it, passing through it, and not returning. The value of the velocity of escape is more or less what we should expect from our general knowledge of the extent of the star-cloud and the number of stars per unit volume.
About 18 stars are known within a sphere of 4 parsecs radius surrounding the sun, i.e., having parallaxes greater than o.25"; there may be a few additional faint stars yet to be detected. Many of these near neighbours are red dwarfs with masses one quarter or one-fifth that of the sun; on the other hand a con siderable proportion are double stars (here counted as one).
The total mass within the 4 parsecs sphere may be estimated at about 12 times the sun's mass. If this may be taken as the general average density of our star-cloud, it is possible to calcu late the orbital period of the stars moving within it under its gravitational attraction; for the periods of orbits in a sphere of uniform density are isochronous, and depend only on the dens ity and not on the size of the sphere. The period would be 200 million years. In addition to the mass of the lucid stars there may be other masses in the sphere, e.g., dark stars or scattered nebulous matter of great tenuity. These added masses would shorten the period ; but we cannot allow the period to be shortened very much, because then the stars in the largest orbits, hurrying to get from one side of the star-cloud to the other and back again in the prescribed period, would need to have greater veloci ties than we observe. Dark stars and nebulous material together cannot amount to many times the mass of the lucid stars. At the end of this article direct observational evidence will be given for the existence of a cloud of diffuse matter in interstellar space. This must be extremely rarefied ; one atom per cubic centimetre is the most we can possibly allow consistently with the dynamics of stellar motions.