Systems such as the local Supergalaxy should occupy an intermediate position in this respect. The constituent parts of the Supergalaxy are receding from each other (for instance, the Virgo cluster and the group associated with M81 are receding from the Local Group of galaxies).
What we have said about the sign of the total internal energy of galactic clusters applies to multiple systems of galaxies as well. Apparently, some multiple systems have a positive total energy, indicating that their components must be rather young (of the order of years old).
However, regardless of the sign of the total energy, another feature of the aggregate of multiple galaxies (triple, quadruple, etc.) is significant. Most mu multi p le s t a r s are known to have configurations of the "ordinary" type, whereas configurations of the "Trapezium of Orion" type occur in only a small percentage of cases (— 10%). Approximately half of the multiple galaxies , on the other hand, have configurations of the Trapezium type. Inasmuch as systems of the Trapezium type are usually unstable, the time which has elapsed since these multiple groups were formed cannot be much longer than several periods of revolution of such a multiple system (one period lasts for to 5 • years).
Finally, since the assumption that all binary galaxies have a negative total energy occasionally yields improbably high values for the mass of the components, it is likely that some binary galaxies have positive total energies.
For superclose systems such as the radio galaxies, considerable differences in the velocities of the components are observed. In radio galaxy Perseus A, for instance, this difference is as high as 3000 km/sec. Consequently, such galactic pairs also have positive energies. In our opinion, what is observed in this case is the formation of a galaxy pair from a single galaxy.
When further data are compiled on the radial velocities of galaxies, it will be possible to answer many of the remaining questions concerning their kinematics and dynamics. Some of the problems still awaiting solution are the following: a) More precise determination of the constant in the red-shift law. this, the scale of extragalactic distances must be specified more accurately.
b) Determination of the red shift as a function of distance for very great distances. Departure from the linear dependence should undoubtedly be observed. A knowledge of the sign of this nonlinearity, and a determi nation of whether its value is independent of direction, is very important for the solution of fundamental cosmological problems.
c) It is very important to determine the peculiar velocities of the centers of gravity of individual galactic clusters (that is, the discrepancies between their observed velocities and Hubble's law). Solution of this problem is essential in order to determine whether there is a genetic relation between neighboring clusters. However, in order to determine these discrepancies, some way must be found to measure the distances of distant clusters more accurately, without using Hubble's law.
d) The solution of many problems concerning the dynamics of galactic clusters and multiple galaxies requires the determination of their masses. Unfortunately, if the galaxies in these systems are far away, their masses are determined statistically, proceeding from the assumption that the energy is negative and that the virial theorem is applicable. However, the masses of galaxies, even if only of the galaxies contained in the nearest clusters, must be calculated independently of this. In addition, methods must be found for estimating at least the upper limit of the inter galactic masses possible in each system (cluster or group).
e) Marked disagreements have sometimes been found between the mass of a system determined according to the virial theorem and the mass calculated according to the luminosities of individual members of the system. This has been observed for several diffuse clusters and galactic groups (the clusters in Virgo and Hercules, the galactic groups in Sculptor and Leo, etc.). Moreover, according to Zwicky, the large globular clusters do not show any signs of expansion. Recently, however, Agekyan came to the opposite conclusion concerning the globular cluster in Coma Berenices.
In order to settle this question finally, as many radial velocities as possible in several of the nearest large globular clusters will have to be determined.