Table of contents. 



CHAPTER I. 



The frequency function of the A -type for three variables 8 



CHAPTER II. 



The frequency function of the linear motions 17 



CHAPTER III. 



The method of Chaklier to express the moments of the linear cross motions through the mo- 

 ments of the proper motions 21 



CHAPTER IV. 



The determination of the frequency distribution of the velocities in space from the proper 



motions 27 



CHAPTER V. 



The observational data ... 38 



CHAPTER VI. 



The normal equations and the characteristics as referred to the system of the equator 43 



CHAPTER VII. 



The characteristics referred to a galactic system of coordinates 51 



CHAPTER VIII. 



The mean errors and the effert of a varying & t on the position of the vertices and the values 



of the characteristics 59 



CHAPTER IX. 



Characteristics of distribution for the linear motions '. 72 



Printing finished April 13, 1915. 



