studies in Stellar Statistics 



25 









C 





C 















0' 



-JO' 



colour spectra. I shall give further below the details of the treatment as well as 

 the results obtained. To day I shall elucidate a special point in the treatment 

 of the given material. 



The two principal characters of the 

 stars that are of use in the statistical research 

 are the brightness (magnitude) and the 

 proper motions. Moreover I think that the 

 double stars will give very important con- 

 tributions to the problem but I hope that 

 Mr Poor (one of my auditors) will carry out 

 the investigation on this point, and 1 shall, 

 generally, leave it here out of consideration. 



Respecting the magnitudes we shall 

 treat today the following problem. Each 

 estimation of the magnitude of a star is 

 subject to an uncertainty. Consequently tlie 

 number of stars, having a certain magnitude m, does not, generally, coincide with 

 the number of stars that, according to the observations, have this magnitude. We 

 will now deduce the true from the observed number. Let 



|JL = the observed magnitude, 

 m = the true » 

 Suppose the secular difference between [jl and m to be eliminated, so that <j. 

 and in do coincide in the mean. Then the frequency function of the observed 

 magnitudes may be assumed to have the form 



(fx — nif 



1 



a. being the mean error in the determination of the magnitude of a star. 



Then the number of stars having a true magnitude m ± ^/s dm and an pbser 

 ved magnitude = [j- ± V2 given by 



(p. — mf {m —m^Y 



(55) ' ^ ^ 1 



a{m) dm X 



dii where a(m) = — ^= e 

 ^ ■ ' k[/2n 



2¥ 



a]/2n 



Integrating this expression between m = — go and m = -\- ao we obtain the 

 whole number of stars having an observed magnitude (j. + V2 d\i. Applying the 

 formula (51) we thus have: 



([X — nioY 



as expression for the number of stars having an observed magnitude ± ^/z d\).. 

 Hence the theorem: Suppose ive have got from the observations that the number of 

 stars of the observed magnitude [j. ± d[x is given by 



Lunds Univ:s Årsskrift. N. F. Afd. 2. Bd. 8. 4 



