202 AISTNUAL EEPORT SMITHSONIAN INSTITUTION", 193 3 



erential direction being nearly in the direction to the center of 

 the galaxy, is also explainable though not so directly as a result of 

 galactic rotation. While Lindblad's theory thus successfully ac- 

 counted for these previously unexplained systematic motions, it did 

 not point the way to any observational means of testing the rota- 

 tion. A method was developed by J. H. Oort, of Leyden, in a 

 masterly paper about a year later, but before discussing Oort's 

 work, it will be well to consider the general consequences of a rota- 

 tion and to see what possibility there is of detecting any rotation 

 from our position within the galaxy where the sun and stars are 

 rotating together. 



The rotation of a system of stars implies a central attracting force, 

 obviously provided by the matter of the stars themselves, directed 

 toward the center of gravity of the system. The law of force and 

 the manner of rotation will depend upon the distribution of the 

 stars within the system, and two particular cases may be considered, 

 that of uniform distribution and that of a concentration toward 

 the center. 



In the case of uniform distribution of the stars or matter through- 

 out the system, it is an elementary principle of dynamics that for 

 stars within the system the attractive force will be directly propor- 

 tional to the distance from the center, and that all the bodies within 

 the system will revolve around the center in the same time ; in other 

 words, such a stellar system will rotate like a solid disk or wheel. 

 For uniform distribution of the stars throughout a system, there 

 will hence be no relative motion between the sun and stars and no 

 possibility of detecting a rotation from observations of the radial 

 velocities or proper motions of neighboring stars. Just as a fly on 

 the spoke of a rapidly rotating wheel could not tell by observing 

 other flies on the rim, hub, or spokes whether the wheel was sta- 

 tionary or spinning. 



Although it is impossible to detect a rotation of the galaxy from 

 internal evidence, when the stars are uniformly distributed through 

 the system, the position is more hopeful if there is a concentration 

 of the stars or matter toward the center. Analogy with the spirals, 

 which all show central condensation, makes it highly probable that 

 the stars are more concentrated toward the center of the galaxy. 

 In the extreme theoretical case, with all the matter concentrated at 

 the center, practically true of the solar system, the attracting force 

 is inversel}?^ as the square of the distance, and the bodies or stars 

 nearer the center revolve faster, both linearly and angularly, than 

 those farther out. An example is the solar system, where the inner 

 planets move much faster than the out«r, and if we were to measure 

 the radial velocities of the planets we could prove that they were 



