STUDIES IN STELLAR STATISTICS. II. 9 
and let D,, where X and / denote any one of the letters n, a, b, c, 
be the subdeterminant obtained from D through putting (kl) = 1 and 
giving to all other elements in the same horizontal or vertieal line as 
(kl) the value zero, so that 
In similar manner subdeterminants of the second or higher order 
may be indicated. 
We have then the solution of the normal equations in the form 
C1 UTE MAGN ! 
(7) Dee Ds D, Des 
The mean errors — ¢— in x, y, 2 are obtained from the formule! 
: eG) _ El) d) _ D 
( ) De aa Ds bb De ce ND, 
where N is the number of observations. 
For the numerical computation of the determinants I refer to 
Meddel. N:o 66. 
As a check? I have computed x, y and 2 from (6) in the usual 
manner — through successive elimination of the variables — and com- 
puted the mean errors with the help of the formula: 
(44) = (nn) — (na)x — (nb)y — (nc)2 
TR XP 
TS De D) DEAN: 
nn, cc 
e(x) _ (y) _ Ad) _ 
(9) ; 
“nn, aa 
6. Let us begin with the determination of U", V". W" from 
the radial velocities, h. e. from the equation 
Mr Ua Ye 
1 These equations are first given by GLAISHER. 
? The method of determinants is somewhat laborious when a great number of solu- 
tions are to be computed. I have therefore later usually made use of the method of succes- 
sive elimination of the variables. 
Nova Acta Reg. Soc. Se. Ups., Ser. 4, Vol. 4, N. 7. Impr. 18/6 1916. 2 
