From multiple stars the transition is natural to star clusters although the gap between these types of stellar objects is very broad. The familiar group of the winter sky known as the Pleiades is a loose cluster, showing relatively very few stars even in telescopes or on photographic plates. The "Beehive," or cluster known as Praesepe in Cancer, and a double group in the sword-handle of Perseus, both just visible to the naked eye, are excellent examples of star clusters of the average type. When the moon is absent, they are easily recognized without a telescope as little patches of nebulous light; but every increase of optical power adds to their magnificence.
Then we come in regular succession to the truly marvelous globular clusters, that for instance in Hercules. Messier 13, a recent photograph of which, taken by Ritchey with the 60-inch reflector on Mount Wilson, reveals an aggregation of more than 50,000 stars. But the finest specimens are in the southern hemisphere. Sir John Herschel spent much time investigating them nearly a century ago at the Cape of Good Hope. His description of the cluster in the constellation of Centaurus is as follows: "The noble globular cluster Omega Centauri is beyond all comparison the richest and largest object of the kind in the heavens. The stars are literally innumerable, and as their total light when received by the naked eye affects it hardly more than a star of the fifth or fourth to fifth magnitude, the minuteness of each star may be imagined."
Others of these clusters are so remote that the separate stars are not distinguishable, especially at the center, and their distances are entirely beyond our present powers of direct measurement, although methods of estimating them are in process of development. If gravitation is regnant among the uncounted components of stellar clusters, as doubtless it is, these stars must be in rapid motion, although our photographs of measurements have been made too recently for us to detect even the slightest motion in any of the component stars of a cluster. The only variations are changes of apparent magnitude, of a type first detected in a large number of stars in Omega Centauri, by Bailey of Harvard, who by comparison of photographs of the globular clusters was the first to find variable stars quite numerous in these objects. Their unexplained variations of magnitude take place with great rapidity, often within a few hours.
There are about a hundred of these globular clusters, and the radial velocities of ten of them have been measured by Slipher and found to range from a recession of 410 to an approach of 225 kilometers per second. These excessive velocities are comparable with those found for the spiral nebulæ. Shapley has estimated the distances of many of these bodies, which contain a large number of variable stars of the Cepheid type. By assuming their absolute magnitudes equal to those of similar Cepheids at known distances, he finds their distance represented by the inconceivably minute parallax of 0".00012, corresponding to 30,000 light-years. This research also  places the globular clusters far outside and independent of our Galactic system of stars. The distribution of the globular clusters has also been investigated, and these interesting objects are found almost exclusively in but one hemisphere of the sky. Its center lies in the rich star clouds of Scorpio and Sagittarius. Success in finding the distances of these objects has made it possible to form a general idea of their distribution in three-dimensional space.
The numerous variable stars in any one cluster are remarkable for their uniformity. Accepting variables of this type as a constant standard of absolute brightness, and assuming that the differences of average magnitude of the variables in different clusters are entirely due to differences of distance, the relative distances of many clusters were ascertained with considerable accuracy. Then it was found that the average absolute magnitude of the twenty-five brightest stars in a cluster is also a uniform standard, or about 1.3 magnitudes brighter than the mean magnitude of the variables. This new standard was employed in ascertaining the distances of other clusters not containing many variables.
Shapley further shows that the linear dimensions of the clusters are nearly uniform, and the proper relative positions in space are charted for sixty-nine of these objects. We can determine the scale of the charts, if we know the absolute brightness of our primary standard—the variable stars; and this is deduced from a knowledge of the distances of variables of the same type in our immediate stellar system.
The most striking of all the globular clusters, Omega Centauri, comes out the nearest; nevertheless it is distant 6.5 kiloparsecs. A kiloparsec is a thousand parsecs, and is the equivalent of 3,256 light-years. At the inconceivable distance of sixty-seven kiloparsecs, or more than 200,000 light-years, is the most remote of the globular clusters, known to astronomers as N.G.C. 7006, from its number in the catalogue which records its position in the sky, the New General Catalogue of nebulæ by Dreyer of Armagh.
The clusters are widely scattered, and their center of diffusion is about twenty kiloparsecs on the Galactic plane toward the region of Scorpio-Sagittarius. Marked symmetry with reference to this plane makes it evident that the entire system of globular clusters is associated with the Galaxy itself. But to conceive of this it is necessary to extend our ideas of the actual dimensions of the Galactic system. Almost on the circumference of the great system of globular clusters our local stellar system is found, and it contains probably all the naked-eye stars, with millions of fainter ones. Its size seems almost diminutive, only about one kiloparsec in diameter. The relative location of our local stellar system shows why the globular clusters appear to be crowded into one hemisphere only.
Shapley suggests that globular clusters can exist only in empty space, and that when they enter the regions of space tenanted by stars, they dissolve into the well-known loose clusters and the star clouds of the Milky Way. Strangely the radial velocities of the clusters already observed show that most of them are traveling toward this region, and that some will enter the stellar regions within a period of the order of a hundred million years.
The actual dimensions of globular clusters are not easy to determine, because the outer stars are much scattered. To a typical cluster, Messier 3, Shapley assigns a diameter of 150 parsecs, which makes it comparable with the size of the stellar cluster to which the sun belongs. Also on certain likely assumptions, he finds that the diameter of the great cluster in Hercules, the finest one in our northern sky, is about 350 parsecs, and its distance no less than 30,000 parsecs; in other words, the staggering distance that light would require 9,750,000 years to travel over. While these distances can never be verified by direct measurement, it lends great weight to the three methods of indirect measurement, or estimation, (1) from the diameter of the image of the clusters, (2) from the mean magnitude of the twenty-five brightest stars, and (3) from the mean magnitude of the short period variables, that they are in excellent agreement.
Recent researches on the proper motions of stars have brought to light many groups of stars whose individual members have equal and parallel velocities. Eddington calls these moving clusters. The component stars are not exceptionally near to each other, and it often happens that other stars not belonging to the group are actually interspersed among them. They may be likened to double stars which are permanent neighbors, with some orbital motion, though exceedingly slow.
The connection is rather one of origin; occurring in the same region of space, perhaps, from a single nebula. They set out with the same motion, and have "shared all the accidents of the journey together." Their equality of motion is intact because any possible deflections by the gravitative pull of the stellar system is the same for both. Mutual attraction may tend to keep the stars together, but their community of motion persists chiefly because no forces tend to interfere with it. In this way physically connected pairs may be separated by very great distances.
So with the moving clusters: their component stars may be widely separate on the celestial sphere, but equality of their motions affords a clue to their association in groups. The Hyades, a loose cluster in Taurus, is a group of thirty-nine stars, within an area of about 15 degrees square, which has been pretty fully investigated, especially by the late Professor Lewis Boss; and no doubt many fainter stars in the same region will ultimately be found to belong to the same group.
If we draw arrows on a chart representing the amount and direction of the proper motions of these stars, these arrows must all converge toward a point. This shows that their motions are parallel in space. It is a relatively compact group, and the close convergence shows that their individual velocities must agree within a small fraction of a kilometer per second. Radial velocity measures of six of the component stars are in very satisfactory accord, giving 45.6 kilometers per second for the entire group.
We can get the transverse velocity, and therefrom the distances of the stars, which are among the best known in the heavens, because the proper motions are very accurately known. The mean parallax of the group by this indirect method comes out 0".025, agreeing almost exactly with the direct determination by photography, 0".023, by Kapteyn, De Sitter, and others.
Eddington concludes that this Taurus group is a globular cluster with a slight central condensation. Its entire diameter is about ten parsecs, and its known motion enables us to trace its past and future history. It was nearest the sun 800,000 years ago, when it was at about half its present distance. Boss calculated that in 65 million years, if the present motion is maintained, this group will have receded so far as to appear like an ordinary globular cluster 20' in diameter, its stars ranging from the ninth to the twelfth apparent magnitude. We may infer that the motion will likely continue undisturbed, because there are interspersed among the group many stars not belonging to it, and these have neither scattered its members nor sensibly interfered with the parallelism of their motion.
Another moving cluster, the similarity of proper motion of whose component stars was first pointed out by Proctor, is known as the Ursa Major system, which embraces primarily Beta, Gamma, Delta, Epsilon, and Zeta Ursæ Majoris, or five of the seven stars that mark the familiar Dipper. But as many as eight other stars widely scattered are thought to belong to the same system, including Sirius and Alpha Coronæ Borealis. The absolute motion amounts to 28.8 kilometers per second, and is approximately parallel to the Galaxy. Turner has made a model of the cluster, which has the form of a flat disk.
Among stars of the Orion type of spectrum are several examples of moving clusters. The Pleiades together with many fainter stars form another moving cluster; as also do the brighter stars of Orion, together with the faint cloudlike extensions of the great nebula in Orion, whose radial velocity agrees with that of the stars in the constellation. Still another very remarkable moving cluster is in Perseus, first detected by Eddington, and embracing eighteen stars, the brightest of which is Alpha Persei.
The further discovery of moving clusters is most important in the future development of stellar astronomy, because with their aid we can find out the relative distribution, luminosity, and distance of very remote stars. So far the stars found associated in groups are of early types of spectrum; but the Taurus cluster embraces several members equally advanced in evolution with the sun, and in the more scattered system of Ursæ Major there are three stars of Type F.
"Some of these systems," Eddington concludes, "would thus appear to have existed for a time comparable with the lifetime of an average star. They are wandering through a part of space in which are scattered stars not belonging to their system—interlopers penetrating right among the cluster stars. Nevertheless, the equality of motion has not been seriously disturbed. It is scarcely possible to avoid the conclusion that the chance attractions of stars passing in the vicinity have no appreciable effect on stellar motions; and that if the motions change in course of time (as it appears they must do) this change is due, not to the passage of individual stars, but to the central attraction of the whole stellar universe, which is sensibly constant over the volume of space occupied by a moving cluster."