CHAPTER IX. 



Characteristics of distribution for the linear motions. 



28. By the preceding investigations we have found that the parameter q 

 probably is of the order of magnitude 0.75. Adopting this value for q we find 

 from the results of § 18 for the axes of the velocity ellipsoid and its vertices the 

 following values 



^ a/ = 1.5606 + 0.0140 Vertex I a = 273°.9 S = — 18°.2 

 o 2 ' = 1 .0432 ± 0.0209 Vertex II a = 338°.8 3 = + 53°.6 

 ^a./ = 0.8580 ± 0.0242 Vertex III a = 194°.8 o = + 31°.o. 



The mean errors are computed as described in § 25 and the unit is here the 

 class-breadth w = 0".05, Wishing to have the axes expressed in km. per sec. we 

 have to put = 0.0529. Thus we find 



o/ = 29.60 ± 0.26 km. per sec. 

 a 2 ' = 19.72 + 0.40 km. per sec. 

 o 3 ' = 16 22 ± 0.46 km. per sec. 



These values are, however, as yet uncorrected for the probable variation of the 

 mean parallax with galactic latitude. We have in the preceding paragraph found 

 that variation to be of a magnitude to make the ratio of & 1 in the polar regions 

 to $ l in the galactic regions about 1.2. To correct the axes for the effect of such 

 a variation we have found that the above values shall be divided by respectively 

 ]/" 1.12, }/l- 12 an d ]/ 0.95. Hence we obtain as the best values to be found for the axes 



o 1 ' = 27.83 + 0.24 km. per sec. 

 o 2 ' = 18.60 ± 0.38 km. per sec. 

 o 3 ' = 16.73 ± 0.47 km. per sec. 



For the sake of completeness we remark that the mean error in the above value 

 of frj is about ± 0.0009, which corresponds to a simultaneous oscillation in the length 

 of the axes in the same direction of about 2 %. 



