1. The study of the motion of the stars may be based either on the apparent 

 proper motions of the stars in right ascension and dechnation or on the observed 

 values of their velocities in the line of sight. For a complete solution of the problem 

 both of these sources must be taken into consideration, as shall be further developed 

 in the following, but certain questions may be independently studied with the help 

 of only one of these groups of observational data. In this memoir I shall consider 

 those questions, that may be investigated with he help of the observed proper motions 

 of the stars. 



As in N;o 8 ^ of these »IMeddelanden» I shall suppose the available data to be 

 distributed over 48 squares, all of the same area, according to the scheme given on 

 p. 25 of I. Each square is treated independent of the others. 



The investigation to be made may appropriately be subdivided into the follo- 

 wing three problems: 



A. Determine the char;icteristics for each square in the correlation surface 

 connecting the proper motions in a and S; 



B. Compute the corresponding characteristics in the correlation surface of the 

 linear velocities; 



C. Collecting and combining the results for the diffent squares we have to 

 consider the following points: 



a) direction of the motion of the sun; 



b) corrections to the adopted values of the precessional constants, together with, 

 eventually, a determination of the motion of the invariable plan of the solar system; 



c) discussion of the resulting frequency distribution in the motions of the stars, 

 whereby it is to be investigated, whether this distribution can be explained 



through the ellipsoidal hypothesis, 

 through star streams, or 

 whether another explanation must be sought for. 



2. Let u and v denote the observed values, for a certain star, of the proper 

 motions in a and S, and let U and V be the corresponding linear velocities projected 

 on two axes perpendicular to the line of sight. If the direction of these axes is 



^ In this memoir cited as I. 



Lunds Univ:s Årsskrift. N. P. Afd. 2. Bd. 8. 



1 



