studies in Stellar Statistics 



55 



the Shattuck Observatorj' in Hannover U. S. A. and will be discussed by him. 

 The results regarding the brightness and the proper motions are preliminaryly 

 discussed in this memoir. 



The function a{m) I have determined for 12 of the »Squares» with the help 

 of BD and the French photographic charts. The determination was possible chiefly 

 with the help of the extensive photometric observations made in Harvard. An 

 essential point was the determination of the number — N — of stars within a 

 cone having one of the squares as base. The equation (66) for determining N 

 is of an easy use for 'numerical applications. Owing chiefly to the uncertainty in 

 the determination of the limiting magnitude of the Paris charts the value of N 

 can only be found within rather wide limits. In the square C^, in the Milky Way, 

 the number of stars lies between 30 000 000 and 250 000 000, whereas in C^, con- 

 taining the pole of the Milky Way, the corresponding limits are 600 000 and 

 2 000 000 stars. 



It has already been stated that the determination of the density, which nearly 

 depends on the determination of M^ir), is very uncertain, as far as the investigation 

 here is carried out. According as different values of the parameter Xj are used, 

 the limit of our stellar system, in the direction of the plane of the Milky Way, 

 may be put to some 600 or to 1 400 siriometers. These numbers are, however, as 

 yet not definitive, depending as the are on the value used for the limiting magni- 

 tude of the C. du C. 



Lund the 5th Dec. 1911. 



