On the Masses of Nebulae and of Clusters of Nebulae

Present estimates of the masses of nebulae are based on observations of the lumi- nosities and internal rotations of nebulae. It is shown that both these methods are unreliable; that from the observed luminosities of extragalactic systems only lower limits for the values of their masses can be obtained (sec. i), and that from internal rotations alone no determination of the masses of nebulae is possible (sec. ii). The observed internal motions of nebulae can be understood on the basis of a simple me- chanical model, some properties of which are discussed. The essential feature is a central core whose internal viscosity due to the gravitational interactions of its component masses is so high as to cause it to rotate like a solid body. In sections iii, iv, and v three newmethods for the determination of nebular masses are discussed, each of which makes use of a different fundamental principle of physics. Method iii is based on the z~irial theorem of classical mechanics. The application of this theorem to the Coma cluster leads to a minimum value M = 4.5 X Io'°MO for the average mass of its member nebulae. Method iv calls for the observation among nebulae of certain graz~itational lens effects. Section v gives a generalization of the principles of ordinary statistical mechanics to the whole system of nebulae, which suggests a new and powerful method which ulti- mately should enable us to determine the masses of all types of nebulae. This method is very flexible and is capable of many modes of application. It is proposed, in par- ticular, to investigate the distribution of nebulae in individual great clusters. As a first step toward the realization of the proposed program, the Coma cluster of nebulae was photographed with the new i8-inch Schmidt telescope on Mount Palomar. Counts of nebulae brighter than about m= 16.7 given in section vi lead to the gratifying result that the distribution of nebulae in the Coma cluster is very similar to the dis- tribution of luminosity in globular nebulae, which, according to Hubble's investiga- tions, coincides closely with the theoretically determined distribution of matter in isothermal gravitational gas spheres. The high central condensation of the Coma cluster, the very gradual decrease of the number of nebulae per unit volume at great distances from its center, and the hitherto unexpected enormous extension of this cluster become here apparent for the first time. These results also suggest that the current classification of nebulae into relatively few cluster nebulae and a majority of 21