38 C. V. L. CHARLIER, 
Using the values of r, given above, we obtain 
Ste VA, 
Bu = Ir Ups ESI — 0 a7e4 
Sip = + 01086 , Sp, — 0.0913 , 
Sig = — 281, 85 0:98207. 
It the coordinates x", y", 2" are denoted by x, 4., %, the 
frequency function now takes the form 
—dÁ 
e ium, 
F = — , 
0,0,0,Y(2n)S ^" 
where 
=== 
E 90:0 0 
The numerical values of «a, are 
Au = + 0.004622 , Ay = + 0.000767 
iy, = + 0.000297 , Gy; = — 0.000160 
As = — 0.002159 , — gy = + 0.001885 . 
The number — n — of stars within a parallelopipedon having 
the corners 
| I 
is now given by the formulæ 
n= NPFduydz;dm,. 
where N denotes the total number of stars. 
17. Direction of the principal axes. The direction of these axes 
is determined with the help of the JacoBrAN equation of the third degree 
JA) = l'air, Gens dsl. = 
An 5 Ag — A, A 
| dy + Aa, Aas — À 
| 
