370 
The Galactic System of Stars [oh. xiy 
Kapteyn’s adjusted figure of 0 - 77 times the mass of the sun is probably 
nearer to the mass of the average star than my figure of T08 times this mass. 
The majority of stars are either dwarfs of types K and M, or else perhaps white 
dwarfs, and an average of T08 times the sun’s mass seems impossibly high. 
From a statistical study of their orbits, Jackson and Furner* estimated the 
mean total mass of the two components of visual binaries to be 1*60 times the 
mass of the sun, giving 0'80 times the sun’s mass for each component. We 
have seen that visual binaries as a class have not been formed by fission, so ■ 
that 0'80 times the sun’s mass would represent the average mass of a single 
star. This is very near to Kapteyn’s value. On the other hand Kapteyn’s 
value leaves no margin for the gravitational field of dark stars, of stars still 
undiscovered in excess of ten to the cubic parsec, of diffuse or nebular matter 
in space, or of aggregations or star-clouds such as are known to exist within 
distances less than those with which we are now concerned (§ 15). When 
these factors are taken into account a distribution of matter equal to T08 
times the sun’s mass for each visible star is probably fairly near to the truth. 
From either investigation, and even more so from the two jointly, we 
seem entitled to conclude that the gravitational field of known stars is just 
about adequate to account for the observed velocities of stellar motions and 
of star-streaming. It is, perhaps, rather remarkable that if there had been 
neither planets nor binary systems to reveal the masses of the stars, the 
phenomena of stellar motions would have enabled us to estimate the average 
stellar mass to within a few per cent, of the truth. 
My investigation gave 1090 parsecs as the distance of the sun from the 
centre of the system. The observations summarised in § 15 indicate that the 
system has no true centre, the stars surrounding the sun belonging in part to 
a small local system and in part to the much larger general galactic system. 
When Seares and van Rhijnf treated these stars as all belonging to a single 
system, they estimated its centre to be 1200 parsecs distant from the sun. 
Final State. 
343. We have seen that a law of distribution of velocities of the type 
f(E u m t ) (3431) 
will give steady motion except for the disturbing effects of encounters of near 
stars. Further, this formula has been found to include all possible cases of 
stable steady motion. 
The effect of near encounters will be slowly to change the character of the 
motion, and after a sufficiently long time, of the order of magnitude of the 
times considered in Chapter xn, the system of stars will tend to a steady 
state in which even close encounters do not disturb the statistical specifica 
tion of motion. 
M.N. lxxxi (1920), p. 4. 
t Astrophys. Journ. lxii. (1925), p. 320.