STRUCTURE OF THE GALAXY PLASKETT 205 



reliable parallaxes are available. If the stars were all of the same 

 intrinsic brightness, they could be arranged according to distance 

 by the apparent magnitudes, but this criterion is imperfect on ac- 

 count of the considerable range in total brightness. The criterion 

 eventually used depends on the properties of the diffuse gaseous 

 matter pervading the system which has already been mentioned, 

 whose presence is revealed and its motions determined by the dark 

 absorption lines H and K of calcium in the spectra of these stars. 

 The more distant the star, the greater depth of the diffuse gas the 

 starlight passes through, the greater the absorption, and the stronger 

 the H and K lines. Some 250 of these stars in which the H and K 

 lines are well defined were arranged into three groups of weak, 

 medium, and strong lines, and consequently into groups of stars, as 

 eventually appeared at average distances of 2,000, 3,000, and 5,500 

 light-years. 



As the rotational effect depends also upon the angle between the 

 star and the direction to the center of the galaxy, each of these dis- 

 tance groups was arranged into some 10 subgroups in longitude. 

 This had the further advantage, by combining a number of stars in 

 each subgroup, of diminishing the disturbing effects of random 

 motions. These different groups were then solved by Oort's equa- 

 tion, using the method of least-squares, a mathematical process of 

 getting the most probable values of the unknown quantities. The re- 

 sults of this solution are exhibited in table 2, in which the second and 

 third columns contain the number of stars and the average longitude 

 of each subgroup. The fourth column gives the average observed 

 residual velocity, corrected for the solar motion, of the stars in each 

 subgroup. The fifth column gives the computed velocity that would 

 be produced by the galactic rotation for the mean longitude of each 

 group. 



The eye needs only to glance down the pair of columns to be 

 struck by the remarkable agreement between the observed velocities 

 and those that would be produced by a rotation of the galaxy. The 

 coincidence seems even more striking when it is remembered that 

 there are unavoidable errors of observation present in the velocities 

 and that the stars have random motions on the average of about 10 

 kilometers per gecond. Considering the small numbers of stars in 

 many of the groups and the disturbing effects of such random mo- 

 tions, the agreement is extraordinary and can certainly not be acci- 

 dental. If the double wave swing of the residual velocities, from 

 positive to negative and back again to positive, so distinctly shown 

 in every group, is not due to a rotation of the galaxy, it must arise 

 from some cause which gives a distribution of the residual velocities 

 almost exactly similar to that produced by the galactic rotation. 



