Table of contents. 



I. Distribution of linear velocities. Moments of the first order. Apex. 



§ 1. Introduction. 



§ 2 — 3. Formulée for computing the moments of the Hnear velocities from the 

 moments of the observed proper motions. 

 § 4. The observed proper motions. Tab. I. 



§ 5. Characteristics of the observed proper motions of the stars. Tab. IL 

 § 6. Discussion of the characteristics. Tab. III. 

 § 7. Characteristics of the linear velocities. Tab. IV and V. 

 § 8. Influence of different values of on the values of the characteristics. 

 Tab. VI. 



§ 9. Three different systems of coordinates; K^, and K^. Tab. VII. 

 § 10 — 11. Determination of the Apex. 

 § 12 — 13. Mean errors in this determination. 



§ 14. Mean distance and parallax of stars of the 5'^ magnitude. 



§ 15. Systetn of projection for graphical representation of Apex and Vertex. 

 § 16 — 17. The motion of the invariable plane. 



II. Moments of the second order. Ellipsoidal hypothesis. 



§ 18—22. General form of the frequency function of the linear velocities. 

 § 23 — 25. Simplification for an ellipsoid of revolution. Determination of vertex and 

 of the peculiar velocities of the stars. Tab. VIII and IX. 

 § 26. Apex, apparent vertex and true vertex in the same plane. 



III. Moments of higher orders. Star-streams. 



§ 27. The ellipsoidal hypothesis does not suffice for explaining the distribution 

 of the observed proper motions of the stars. Tab. X. 



§ 28. The higher characteristics of the frequency function of the linear velo- 

 cities is not here explicitly given. 



