STUDIES IN STELLAR Statistics. II. 39 
Each of the three roots of this equation determines the position 
of one of the principal axes. Let A denote any of the roots and let 
|l, m, n be the direction cosines of the corresponding principal axis 
then we have 
. (an — 4)Ld- dam + an = 0, 
dal + (Av — à)m + an = 0 , 
Gg 0 + day + (Ass — An =O. 
If 7, denotes the subdeterminants of the determinant 7/(4), we 
thus have 
MUI 
Rete ee 
Using the values of the coefficients «a, given above and obser- 
ij à 
ving that the developement of J(4) gives for J(4) the following form 
za) = X — (a, + Gas ta y) 
zi À (d, Ass T= diss ny Ar 031039 — (Ls a a ai») 
ies Tig DU I OO em did SUERTE 
we get for /(4) the expression 
= (a) — i = Toa M Ar 8.928 A, 9.027 
where 4, = 1000 4. 
Tabulating this function for different values of 4, we get the 
table 
Table 15. Values of — J(A). 
— — T = = — - = = = — — = = 
A, | — I(A) A, — I(A) À —I(A) A, ESTA 
| | 
Ron = 201229 0.50 0.256 1. | = 2.626 475 191022 
| ON O48 || 0073 2.0 | — 6.267 5.0 | — 15.237 
One) :205 (Qm 0002 2.5 | — 10.544 | Bi | ee 
0.2 | — 1.524 0.8 | — 0.028 3.0 | — 14.709 5.6 5.521 | 
(138051010777. 0.9 — 0.155 Ae | 2. on 5.7 3.274 
0.4 | — 0.556 1.0 — 0.373 4.0 | — 19.697 | 5.8 0.835 
DOME er 
6.0 + 4,683 
