362 
The Galactic System of Stars [ch. xiv 
to a single plane, namely the plane of the orbits of the outer planets, while in 
the neighbourhood of any one point, the motion of the asteroids is nearly 
confined to one direction in that plane, namely the direction at right angles 
to the direction of the sun. 
The question arises as to whether the motion of the stars is in any sense 
an ordered motion like that of the asteroids, or whether it is purely random 
like the motion of the molecules of a gas. Until 1904 most astronomers would 
probably have conjectured that the motion was of the latter type, but solely 
on the grounds that the motion had not so far been found to be anything but 
characterless. In 1904 the situation was abruptly changed by Kapteyn’s 
discovery of the phenomenon of “ star-streaming.” 
Kapteyn found that the motion of the stars in the neighbourhood of the 
sun shewed a distinct preference for one direction in space. The preference 
was not entirely like the preferential motion of the asteroids, since some stars 
moved forwards and some backwards along the same direction, but this dis 
tinction is one which can be removed by altering the frame of reference to 
which the motions are referred. The stars do not all move along this particular 
direction; indeed, the preference for this direction is not very highly marked, 
many stars moving absolutely athwart it. 
The direction of the preferential motion is found by Kapteyn and many 
others to be exactly in the galactic plane. Kapteyn attempted a dynamical 
explanation on the general lines that the direction of preferential motion was 
at right angles to the direction pointing towards the centre of the galactic 
system, the motion of the stars about the centre of the galactic system thus 
being supposed similar to that of the asteroids about the sun, except that 
Kapteyn imagined two swarms of “ asteroids ” intermingled with one another 
and moving in opposite directions. 
An alternative mathematical expression of the observed fact was suggested 
by Schwarzschild. The molecules of a gas obey Maxwells law of distribution, 
according to which the number whose components of velocity u, v, w lie within 
a small range dudvdw is'of the form 
J q e -A(M 2 +t) s +w 2 ) dudvdw. 
Schwarzschild proposed that the motions of the stars conformed to an 
“ ellipsoidal ” law of distribution of the type 
A-6~h ('“H-« 2 )-*«’ 8 dudvdw. 
If h is made equal to k in this formula, the motion reduces to the random 
motion specified by Maxwell’s law. If h is infinite in comparison with k, u and 
v must be zero for every star, so that the motion reduces to a pure to-and-fro 
motion along the axis of £. If h is larger than k , the motion shews a 
preference for the two directions along the axis of z, the amount of this pre 
ference being determined by the value of the ratio h/k. The observed degree 
of preferential motion is represented by assigning to h/k a value of about 2.