40 



C. V. L. Oharlier 



The squares C^, Cg, Cg, Oj, Cg, Cg and Cg have been treated by my auditors 

 according to the same scheme as C^ and C^ above. The numbers of stars of 

 different magnitudes in BD for the squares to Cj^ are given in tab. 25 at the 

 end of the memoir. The numbers of stars in the G. du C. for the same regions 

 are given in tab. 13 to 24. Finally the comparison between BD and HR is found 

 from tab. 26 and 27. The resulting values of JV, h and are shown from the 

 following table: 



Tab. 8. 



Square 



N 



k 



nio 



Com putor 





1 985 000 



+ 3.017 



+ 18™.34 



Poor 





3 430 000 



4- 3.363 



+ 19 .92 



IWicksell 





4 8«5 000 



+ 3.175 



+ 18 .93 



(Gyllenberg 





30 000 000 



-i- 3.119 



+ 20 .07 



Charlier 



c. 



1 950 000 



+ 2.832 



+ 17 .51 



Stadler 





600 000 



+ 2.846 



+ 16 .91 



Jung 





630 000 



4- 3.108 



+ 17 .59 



Charlier 





1 010 000 



+ 3.179 



+ 18 .18 



Jönsson 





1 550 000 



+ 2.705 



+ 16 .88 



Åkesson 



Mean 





+ 3.038 





It is found that the value of Jc is nearly the same in all the squares. 1 

 shall in the following use the mean value 



Jc = 3.038 



as the value of 7c.. 



At the pole of the Milky Way (in C,) we have only some 600 000 stars in 

 the cone determined hj a square, whereas in the Milky Way this number rises to 

 the 50-fold (= 30 000 000). As to it is in general allied to N. In the Milky 

 May (in C^) we must go to the 20th magnitude, before the maximum value of the 

 number of stars (belonging to one magnitude) is reached, whereas in Cg this 

 maximum is attained already at the 17th magnitude. It is evidently within the 

 scope of modern photography to check the accuracy of these results. This check 

 is especially easily performed at the pole of our Milky Way. 



20. The parallaxes of the stars. We have proposed in the 13th § to 

 determine the parallaxes of the stars from their proper motions. Supposing the 

 mean value of the stars of the magnitude m to be represented by the formula 



(69) M„r{p) = ^.e"^*"' 



we have indeed 



(69*) M,l^) ^ K.e"'^'*'. 



Against the use of the proper motions as measure of the parallax there have 

 been given certain objections by Kapteyn (A. N. 3487) and others, even by myself 



