ASTRONOMY: H. RAYMOND 
487 
I. The stars are evenly distributed over the sky. 
II. The distribution in distance is the same in different parts of the 
sky. 
III. The motions of the stars are distributed in the same way in all 
accessible parts of space. 
These hypotheses are of course not rigorously true. Ill is open to 
objection, but if it is not at least approximately true we have no general 
problem, merely a number of local problems. After the mean square 
velocities in the three principal directions are known, failure of II, so 
far as effect of different mean square parallax in different parts of the 
sky is concerned, may be taken care of and a new approximation made. 
The theoretical value of [xiXi] + bi^i] + [sizj can be computed for each 
region of the sky and compared with the observed values. A difference 
may be considered as due to the stars being nearer or farther than 
the average and factors applied accordingly. These approximations 
converge very rapidly; in fact, the error from the source considered is 
small, even in the first solution. Errors due to the spread or range 
of the stars in distance are not corrected by this process, but must 
usually be negligible. Hypothesis I can be made valid by simply 
weighting the material proportionally to the area of the sky covered, 
instead of proportionally to the number of stars. 
The material used was the 5943 proper-motions less than 8C per 
century from Boss's Preliminary General Catalogue. Of these, 5384 
were less than 20'' per century (allowing for solar motion^) and were 
called '^S"; the remaining 559 stars of larger proper-motion were called 
'X." Group S was subdivided according to type of spectrum as fol- 
lows: B, types Oe5 to B 5, 492 stars; A, B 8 to A 4, 1647; F, A 5 through 
F, 656; G, 446 stars; K, 1227; M, 223; X, including stars of unknown 
type — mostly faint — and some of types N, O, and P, 693 stars. 
The numerical results appear in the accompanying tables. Table 1 
gives, in column 1, the designation of the group; in 2 and 3 the Right 
Ascension and Declination respectively of the direction in which {pp\ 
is a maximum — the vertex of preferential motion; in 4 and 5, the same 
for direction of least motion. The third direction, in which [pp] is a 
minimax, is necessarily at right angles to each of these, hence is not given. 
The last three columns give the value of [pp\ for these three directions. 
Unit of motion, \" per century. 
Table 2 gives the solar motion derived at the same time. A and D 
are the Right Ascension and DecKnation of the Apex, M the amount 
of solar motion. The last three columns are given as a means of com- 
paring the various groups. If the means without regard to sign of the 
J 
