STUDIES IN STELLAR STATISTICS. II. 51 
(where x, y, z are reckoned from the centre of the Galaxy and are 
referred to the three galactic axes defined in § 18) is given through 
the formula 
(19) l= == dn 'dxdydz : 
0,0, ase, V (22)* m 
As to the numerical values of the three dispersions a,, a, and 
a,, they are easily deduced from the results of § 17. The three roots 
of the equation I(A) = 0 are, indeed, according to an well known theo- 
rem in the theory of quadratic forms, equal to the reciprocal values 
of the squares of the dispersions along the three fundamental axes. 
Let 4”, 2°, 4? be the three roots of the Jacobean equation, we thus 
have 
1:0 = A? = + 0.000721 , 
1:03 = 1° = + (000721 , 
1:05 = A? = + 0.005833. , 
so that 
€; = &, = 37.24 ; a, = 13.09 Sir. 
As a check to the computation we observe that 
0,0,0, = 0,0,0, Y S. 
Substituting these values into (19) we get 
(19*) n = Ü,000003496 Ne : 5 drdyde - 
For the B-stars we have N = 751 and hence 
(000003496 N = 0.002625 
Considering a parallelipipedon in the centre (h. e. x =y= z- 0), 
and having the length of the sides equal to one Siriometer we get 
n = 0.002625 , 
