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The meaning of the term multiple galaxies obviously can be clear only if we know what an individual galaxy is. Unfortunately it is not at the present time possible to give an exact definition of a galaxy as a physical stellar system which is in practice operationally useful. Theoretically one might postulate that any agglomeration of stars, gases and solid particles constitutes a galaxy if its various material components cannot escape directly from this agglomeration. A stellar system or galaxy is therefore a cohesive unit of stars, dust and gases within which only a fraction of its components possess velocities high enough to allow them to escape and to make their way to the vast intergalactic spaces. In reality we cannot of course use the criterion just formulated, since for a long time to come the data available on the velocities of the various members of stellar systems will be entirely insufficient. A more modest approach must therefore be chosen. One may for instance attempt to identify the individual galaxies from their structural features as well as from the surface brightness within a given area and from the decline of this brightness as he moves away from the central regions of the system. Using criteria of this somewhat indefinite character, mistakes are naturally inevitable in the sense that some nebulae will be classified as single systems although they may in reality be groups comprising several self contained dynamic units of the type described above. On the other hand, what appears to be a multiple galaxy may actually be a single dynamic unit when judged according to the proper criteria of dynamic statistical stability.

Another conceptual difficulty which begins to loom high on the horizon is related to the recent discovery of both dark and luminous intergalactic matter (1). Indeed, extrapolating the results obtained so far it is probable that most if not all galaxies extend indefinitely until their tenuous outskirts meet those of the neighboring galaxies. Stellar systems may therefore not be island universes as HERSCHEL called them and as most astronomers assumed until very recently but they are rather concentrations of stars, dust and gases within a tenuous but continuous distribution of matter distributed throughout the whole universe. Without awaiting the solution of these problems we may nevertheless deal fruitfully with certain simplified criteria defining single and multiple galaxies. Using this operational approach the following tentative classification will be adopted.

a) An extragalactic nebula will in general be considered to be a single galaxy if the average surface brightness within circles of ever increasing size and centered On the brightest nucleus decreases monotonely as it approaches the surface brightness of the sky background.

b) As a second more restrictive condition we demand that the appearance of the nebulae in question and of the spectra in its various parts be such that the nebula does not obviously represent two galaxies in a close encounter as is for instance the case of NGC 1275 which we shall discuss further on.

c) Multiple nebulae fall into two classes, namely, line of sight groups and physically related systems. The following criteria will often suffice to distinguish between the two classes. The members of a line of sight double nebula do not show any effects of mutual tidal actions and there will be no visible connection between them of the type to be discussed later in this article. Also, the redshifts in the spectra of the components should in general be different although, statistically there will be rare exceptions to this rule, as we shall see in the course of our study.

Physical double or multiple galaxies can be of several types. For instance, the components of a group may be clearly separated by areas whose brightness is not markedly superior to that of the night sky, and there may or may not be any clear evidence of mutually induced tidal actions and distortions. On the other hand the member galaxies of a group may be actually interconnected by luminous intergalactic filaments, bridge like structure and interwoven long spiral arms, or all of the galaxies may be imbedded in a luminous cloud of matter. For convenience we shall distinguish between close pairs and groups whose members are separated by less than two or three of their "classical" diameters on the one hand and physical associations of galaxies which are farther apart. Many of the close multiple galaxies probably are real dynamic units whose components cannot escape directly, while most of the widely separated galaxies are presumably in the process of departing from each other, in spite of the fact that they may be connected by long filaments.

It was originally thought that the single isolated galaxies are in the majority (2) and that only a few percent of the total number are members of large clusters. Work during the past two decades with the Schmidt telescopes on Palomar Mountain however, has led to the conclusion that this estimate is entirely incorrect and that most galaxies belong to clusters which may be virtually regarded as filling cosmic space completely. When discussing the subject of multiple galaxies in this study we shall arbitrarily make a distinction between small groups and large clusters. We shall not deal to any great extent with clusters here but concentrate our attention almost entirely on double galaxies and some small groups not containing more than half a dozen members.

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