CHAPTER VII 



The characteristics referred to a galactic system 

 of coordinates. 



21. For many obvious reasons it is preferable to have the characteristics of 

 the motion referred to a system of coordinates having one axis directed toward 

 the galactic pole. Accordingly we will perform the transformation of all the cha- 

 racteristics to the system III defined in § 8. The transformation is obtained alge- 

 braically by the equations (57) and permutations for the second moments, and by (41) 

 or (43) for the higher characteristics, exchanging the direction cosines ftj against a#. 

 The reason why the characteristics where not at once transformed to the system 

 III from each square, obviously lies in the advantage gained on account of the 

 symmetry to the equator. Thus the way via the system II is really a short cut, 

 besides giving the vertices in equatoreal coordinates. 



As the principal vertex (vertex of the longest axis) 'lies in the Milky Way we 

 naturally take the ?7 (s) axis in that direction. Originally it was my intention to take 

 the vertex system for q = 0.8 as the system III*. By a calamity this vertex-system 

 was slightly miscalculated and consequently the system III does not coincide with 

 the vertices of q = 0.8. As this was not discovered before the transformations of the 

 characteristics were nearly completed I did not think it worth while to alter the system. 

 Besides the difference is very small, any of the axes lying within 4° of the vertices 

 mentioned and the W® axis lying within 2°. 5 of the galactic pole of Kobold. 



The system III is now defined as follows 



System III: Direction of the U^-axis a = 270°.o S = — 15°.o 

 FW-axis a = 335°.7 8= 4- 56°.9 

 TFW-axis « = 188°.B S = + 28°.7 



* Unfortunately I was not aware at the time of the fact that Gyllenberg had already 

 made use of a similar system. His system could as well have been used, and it is to deplore 

 that there is a difference, though very small. 



