204 ANNUAL REPORT SMITHSONIAN INSTITUTION, 193 3 



Oort's great contribution to the problem of the rotation of the 

 galaxy was to translate the foregoing general principles into simple 

 mathematical language and test the resulting expressions from the 

 known motions of the stars. Expressed most simply, this states that 

 the residual velocity of any star, the velocity after the effect of the 

 solar motion has been removed, the actual velocity of the star in the 

 system, is directly proportional to its distance from the sun, provided 

 only that this distance is small compared to the distance of the center, 

 and to the sine of twice the angle between the star and the direction 

 to the center of the galaxy, or 



p = rA sin 2 (Z — Q 



Oort showed conclusively from an analysis of the then known 

 radial velocities of all the more distant celestial objects such as the 

 0-, B-, and N-type stars, the Cepheids and the " c " stars, the plane- 

 tary nebulae and the calcium clouds, that the observed velocities of 

 all these objects followed closely those predicted by the galactic rota- 

 tion. If the observed distribution of the velocities of all these objects 

 is not due to a rotation of the galaxy, the producing cause gives re- 

 sults very similar to galactic rotation. 



There are certain limitations and difficulties in conclusively dem- 

 onstrating the rotation which should be noted. It has been shown 

 that the rotation produces a change in velocity of 1 kilometer per 

 second for stars at a distance of 200 light-years. Since, owing to 

 the effect of the random motions and of errors of observation, a rota- 

 tional effect of 5 kilometers is the minimum for definite results, this 

 requires a knowledge of the velocities of stars 1,000 light-years dis- 

 tant. Only a very small proportion of the stars at that distance ar€ 

 bright enough for velocity determinations, and the numbers for analy- 

 sis are hence very small, too small to overcome the disturbing effect 

 of the random motions which only become harmless when averaged 

 out over several stars. Consequently Oort's tests of the galactic 

 rotation were limited by the small number of radial velocities of 

 distant stars available at that time. 



Fortunately, at Victoria there were available as a result of about 

 6 years' work by Dr. Pearce and me, the radial velocities of some 

 500 O- and B-type stars, the hottest, most massive, most luminous 

 stars in the sky, and hence the most distant that can be spectro- 

 scopically observed. As they also have the smallest random motions 

 of any class of stars they are especially suitable for testing the 

 rotation of the galaxy and indeed have provided the most convincing 

 evidence of its reality. It is necessary, however, as the rotational 

 effect is directly proportional to the distance, to arrange these stars 

 into groups at different distances. This is a difficult task, as no 



