The Theoretical Frequency Distribution Of Photographic Meteors

34. ASTRONOMY: P. M. MILLMAN PROC. N. A. S. throughout the same region as that occupied by the globular clusters; and these clusters appear more clearly than ever to outline our galaxy, as the globular clusters recently discussed by HubbleW and by Shapley and Mohr,6 outline Messier 31 and the Large Magellanic Cloud, Along the galactic plane our direct measures are troubled by absorption, and we can only surmise, from the distribution of the globular clusters and cluster type Cepheids in galactic latitudes 200 to 400, that the dimensions in this direction are much greater than shown here for the directions perpendicular to the plane. The faintest variables in fields 209, 211 and 212 would project on to the galactic plane at a distance of more than 20,000 light years from the sun. The extension of the search to fainter magnitudes in these fields and in fields of somewhat lower latitudes will be an important step in measuring the extent of the Milky Way in its plane. 1 E.g., in H. Mon., 2, 22 (1930). H. B. 874 (1930). Paper read at Ann Arbor meeting of the National Academy of Sciences, November, 1932. 4 H. B. 890 (1932). 6 Ap. J., 76, 44 (1932). 6 H. B. 889 (1932). 2 3 THE THEORETICAL FREQUENCY DISTRIBUTION OF PHOTOGRAPHIC METEORS By. PETER M. MILLMAN* HARvARD COLLEGE OBSERVATORY Commuiicated December 8, 1932 In considering the frequency distribution of meteors we must first make some simplifying assumptions before the subject can be satisfactorily treated. Let us then assume that: 1. The lutninous part of the paths for all meteors is at an average height of;lb1Jkilometers above the surface of the earth. 2. All meteors are moving with the same constant linear velocity with respect to the earth. 3. If we regard a meteor as a moving point of light, then it radiates a constant quantity of light per second. 4. If the absolute magnitude of a meteor is determined by the light radiated per unit of path when viewed perpendicular to the path at some unit distance, then there is a definite absolute magnitude distribution for meteors entering the atmosphere at the same angle. VOL. 19, 1933 ASTRONOMY: P. M. MILLMAN 35 5. All meteors from the same radiant are moving in parallel paths and are distributed with constant density over a cross-section perpendicular to the direction of motion. Furthermore, some law of absolute magnitude distribution must be assumed. Let Nm be the number of meteors brighter than absolute magnitude m. Opik' used the distribution Nm+ i/Nm = 4 for meteors apparently brighter than the third magnitude. In the derivation of the curves which accompany this paper the three distributions Nm+ I/Nm = 3, 4 and 5, have been used. The apparent brightness of any meteor will depend on its distance from the point of observation, the angle its path makes with the line of sight, and the amount of atmospheric absorption present. The curvature of the earth must be taken into account; this was done by first computing frequencies on the assumption that the earth's surface is a plane and then deriving a correction for curvature which was applied to the results. On the assumption of a plane surface the distance of the meteor will vary as sec z, where z is the zenith distance. The brightness will decrease with distance as sec2 z but the angular velocity will decrease as sec z. We may assume that the photographic effect varies inversely as the angular velocity, and hence we have the photographic brightness decreasing as sec z owing to increase of distance from the observer. The angular velocity will also vary as sin i, where i is the angular distance from the radiant. The luminosity of the meteor therefore varies as cosec i. Absorption of the air cuts down the magnitude in proportion to the length of the air path. The photographic absorption coeff