STUDIES IN STELLAR STATISTICS. Il. 39 
16. Determination of the fundamental axes of the B-stars. For 
solving this problem we have first to determine the form of the fre- 
queney surface referred to the equatorial axes. That is a problem 
from the mathematical statistics regarding which I refer to Meddelan- 
den N:ris 58 and 66. 
The solution is most easily obtained with the help of the values 
: I 
of the moments of the second (and first) order of the observed fre- 
es . . . 11 Hn 7 » 3 > 
quency distribution in x", y” and z". I first computed, for each star 
the products 
eet LT PT A nml CNE 
| es 
and summed these values for every subclass. The values of these 
sums are give in the following table: 
Table 11. Moments of the second order of the reduced 
direction cosines. 
[E] — Gu SE] rl [el ty 
Bo + 16111 — 3292 + 18168 + 53508 + 2869 + 47638 
Bi + 444 + 153 + talg 193 + 141 e MG 
B2 + 987 — 438 i MER + 2790 — 782 + 23 
B 3 + 7044 — 2651 x 9737 + 18217 — 5168 4 19685 
B5 + 4821 — 898 + 4415 + 8280 — 1569 + 10215 
I give also for the same stars the moments of the first order. 
Table 12. Moments of the first order of the reduced 
direction cosines. 
15] UM [5] 
Bo — 552.55 + 754.92 — 1709.11 
Bi — 23.95 + 52.13 — 101.38 
Be + 22.68 + 149.82 = 10.47 
Bs — 416.05 + 658.95 — 977.30 
B 5 — 38.94 269.00 — 517.03 
Multiplying the values by ZA we get the first moments of the 
rectangular coordinates. Using the values of À given in table 4 ob- 
tained from all stars brighter than the sixth magnitude, we get the 
following table. 
