14 C. V. L. CHARLIER, 
I have had occasion many times in my studies on stellar statis- 
ties to lay stress upon the difference between the mean value of a 
quantity x and the inverse value of the mean value of l/z. Especi- 
ally there is a great difference between 
a) 
and 1: M(r), where r denotes the distance of a star of, say, a cer- 
tain apparent magnitude. (Compare Meddel. N:o 68). 
The necessary condition for using the equation 
u) = 1: Me) 
is that the frequency distribution of the x-values does not contain such 
values of x, which are small, that moreover this frequency distribution 
is nearly normal of type A, and that the dispersion is small. 
These conditions are, evidently, nearly fulfilled for the values 
of R, at least as far as the stars of type B are concerned. Hence 
we are here entitled to put 
(+) =1:M(R)=1:R,. 
Inverting (14) we thus get! : 
(15) R, = 4.762 Siriometers 
h. e a star of type B placed at a distance of 4.762 Siriometers appears 
to an observer on the earth as a star of the apparent magnitude zero. 
The equation (2) gives for the «absolute magnitude (M) (= the 
apparent magnitude at a distance of one Siriometer) of a star of spec- 
tral type B the value 
(15*) = — 3,39 
somewhat brighter than was concluded in the more summary discus- 
sion of Meddel. N:o 68. 
! In the following I omit the index O to quantities deduced with the aid of the 
melhod of least squares. 
