The Distribution of Absolute Magnitudes among M Stars Brighter than the Sixth Apparent Magnitude as Determined from Parallactic and Peculiar Velocities

i. The distribution of absolute magnitudes among M st~rs brighter than the sixth apparent magnitude has been determined from the distributions of parallactic and pe~ culiar reduced proper motions and the distribution of radial velocities. The methods used are described in Mount Wilson Contributions Nos. 395 and 410. The number of proper-motion stars used is 247, and of radial-velocity stars292. 2. The distribution of absolute magnitudes shows two distinct groups: supergiants with a maximum frequency at absolute magnitude -4.5 and ordinary giants around magnitude zero. The groups are separated by a clear gap around absolute magnitude -3.0. The relative proportions of stars in the two groups are 9 and 91 per cent, re- spectively. 3. Numerical values are given which will enable one to compute the mean absolute magnitude from the mean apparent magnitude and the mean of the logarithms of the r- or u-components