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CARNEGIE INSTITUTION OF WASHINGTON. 



assume for the system a rotatory motion of some sort around the axis 

 toward the pole of the Milky Way. 



On this assumption the stars in the immediate neighborhood of the 

 rotation axis have no systematic motion, and observation shows that 

 the peculiar velocities are at least approximately distributed according 

 to Maxwell's law. These stars are, therefore, in much the same cir- 

 cumstance as the particles of air in our own atmosphere, with the total 

 attraction of the whole system in place of that of the earth. Further^ 

 the encounters of the separate stars must be relatively very scarce as 

 compared with those of the molecules of the air. 



Though such differences make it seem doubtful whether we are justi- 

 fied in applying to the stellar system the formula furnished by the 

 kinetic theory of gases for barometric determination of altitudes, 

 Professor Kapteyn has ventured to make such an application to the 

 stars lying along the rotation axis. In this way he has been led to a 

 determination of the following values of the average effective mass of a 

 star: 



Since the attractive force which enters into the formula includes the 

 attraction of any existing dark matter, and since the above masses 

 represent total mass divided by total number of luminous stars, they 

 have been called average effective masses. The good agreement of 

 their values with what has been found for the masses from binary stars 

 proves that the total dark mass in the system must be small as compared 

 with the luminous mass. 



In applying similar reasoning to the stars in the plane of the Milky 

 Way the centrifugal forces must be taken into account. These forces 

 have been determined in such a way that for regions of equal star- 

 density on the rotation axis and in the plane of the Milky Way we are 

 led to the same average effective mass. Once the centrifugal forces 

 are known, the radial and linear velocities can be determined. The- 

 results for the latter are as follows : 



Linear velocity in plane of Milky Way. 



