40 



Walter Gyllenberg 



Examination of the velocity distribution of stars of different spectral 

 classes in relation to the galactic system. 



37. The velocity distribution being known to be closely related to the plane 

 of the Milky Way, it may be convenient from many points of wiew directly to 

 determine the moments in the galactic system by a transformation of the coordinates. 

 To this end I have used a galactic system defined in the following way: The posi- 

 tive Z-axis is directed towards the pole of the Milky Way: a= 191°. 2, S = -f- 28°.o, 

 the positive 3-axis is directed towards a point: a — 274°6, S = — 12°. o, situated in 

 the Milky Way and approximatively coinciding with the principal vertex. The H- 

 axis lies in the plane of the Milky Way. 



For the relations between this system, denoted by G, and the other systems 

 I have used the following denominations and direction cosines 





G: 



H II Z 



X" 



Y" 



Z" 



X 



Pi. 



Pn 



Pat 





«h 



«21 



«31 



K,: Y 



P,i 



022 



Pes 



G: H 



«12 



«22 



«32 



Z 



Pia 



q 



P23 



Pas 



z 



«13 



«23 



«33 



The numerical values of the direction cosines I have published in another 

 paper '; here I only reprint the quantities, owing to some small misprints in 

 the paper mentioned: 



a n = 4- 0.0801, a n = + 0.4933, a n = — 0.8661, 

 a. n = — 0.9749, a 22 = — 0.1425, a 23 = — 0.1715, 



a 3] = — 0.2079, « 32 = 4- 0.8581, rt 33 = 4- 0.4695. 



38. Let the three velocity components of a single star in the system K 3 be 

 denoted by 



U, V, w, 



and let the velocity components of the same star in the system G be denoted by 



3, H, Z, 



then from the schemes above we get the following relations: 



C7 = ß 11 S4-ß 21 H + ß 31 Z, 

 (36) F=ß 12 E4-ß 22 H + ß 32 Z, 



W =*ß 13 E- r ß 28 H + ß 88 Z, 



* On the absolute motion of 160 parallax-stars by K. W. Gyllenberg. Meddelande fr. Lunds 

 Astr. Obs. No. 65. 



