The distribution of the stars to the eleventh magnitude 



47 



We then get the expression 



For any other hmiting magnitude, wîj , we have: 



By combining these expressions we get 



1-P ■ 



1 - 



k 



This is in fact a suitable formula for the reduction of star densities from one 

 limiting magnitude to another. As the intension is to reduce the star densities to 

 tlie eleventh magnitude I calculate this reduction for 



= 11,0 



The equation for the reduction is accordingly: 



1 - 



or putting 







l-p 







^(11) = A{n>) . R(ni). 



In order to get a table for R{m) it is necessary to know the two parameters 

 iHq and /.-. These parameters have been discussed by prof. Charlier and is cal- 

 culated in Stellar Statistics I by help of the stars of Bonner Durchmusterung and 

 those of Cartes du Ciel. The following table is taken from this paper. 



Square 



c, 









a 









a, 



1: 



3,017 





3,175 



3,119 



2,832 



2,846 



3,103 



3,179 



2,705 





18,3i 



19,92 



18,93 



20,07 



17,51 



16,91 



17,59 



18,18 





