occurring with a remarkable regularity. The variation may be compared to that of a revolving light in a light house on the sea coast, in which there is the same rapid brightening, followed by a short and brilliant maximum, and finally by a steady fading away.

Now it appears that when the periods of different variables of this class are nearly equal, the physical conditions and luminosities of the different stars must be exactly the same also. Thus in the cluster Messier 3 there are no less than 150 of these variables, whose periods of variation are in each case almost exactly half a day; and the light curves of 110 of these have been carefully investigated. The average apparent magnitude of all these stars is 15.50 and the average deviation of the brightness of the individual stars from this mean is but 0.08 magnitude. Similarly, in the cluster Messier 5, there are 61 of these variables, the average brightness being 15.26 magnitude and the individual variations being but 0.07 magnitude. It cannot be doubted that there is a wonderful uniformity in the actual brightness of these stars and that the apparent differences in brightness of the stars of different clusters are due to the different distances of the clusters from us.

In the cluster, Omega Centauri, the brightest and apparently the nearest of all the globular clusters, there are 76 Cepheid variables whose average magnitude is 13.57. These actually thus appear 64 times as bright as the variables in the two clusters mentioned but their greater apparent brightness is certainly due to the fact that these two fainter clusters are 21⁄2 times as far away as the brighter cluster.

In some of the clusters these variables do not occur; the distances must then be determined by an assumption regarding the true, absolute brightness of the stars found in them. Apparently the most certain results are found by an examination of the stars called of the B-type, in the classification of all stars according to their spectra. The stars of this type are characterized by a very high temperature, and it is believed that no star can attain to this high temperature unless its mass is not too small. In fact, all of the nearer stars of this type whose

distances from us have been determined show a remarkable uniformity in their intrinsic brightness.

If, therefore, we assume a minimum absolute brightness for stars of this type, the excessive faintness of the B-stars found in the globular clusters must be due to the great distances of the clusters from us. The distances so obtained may then be compared with the distances found for those clusters which contain Cepheid variables and the agreement of results obtained by two such very different methods may be noted. In the same way, but with somewhat less certainty, the brightness of stars of other spectral types may be measured and their apparent brightness in the cluster compared with the known intrinsic brightness of such stars of each type as happen to be near us. The resulting distances obtained by these various methods are in remarkably close agreement. They all show that these spherical clouds of stars are not immersed in our Milky Way cloud, but that they are either on its boundaries or at a considerable distance wholly outside of it. If we assume that our own great cloud is slowly shrinking in size, these smaller clouds, which were probably originally of a very irregular shape, have been left behind to go through their development as isolated systems.

Mr. Howard Shapley, of the Mount Wilson Solar Observatory, has published within the past month the results of his investigation of 69 of these objects, all of the clusters which can at present be assigned to the globular class. The nearest of all is the magnificent and well-known Omega Centauri, whose distance from us is but 20,000 light years, the average distance of all the clusters being about 60,000 light years. It is found that the size of these globular clusters remains remarkably constant, and that they are but a few hundred light years in diameter. Thus the diameter of the typical globular cluster, Messier 3, is found to be 470 light years and its total mass is in the neighborhood of 160,000 times the mass of the sun. The crowding of the suns in these clusters is very remarkable. It is found, for example, that within a certain distance from the center of Messier 3, at least 15,000 suns, each brighter than our

own sun, can be counted, while within the same distance from our sun as a center there are less than twenty stars known which are as bright as the sun.

Thus it is seen that these objects are very small compared with our Milky Way universe of stars and that their structure is very different. But notwithstanding these present differences, it is very probable that they present to us an image of what our own, immeasurably larger, universe, will become after the passage of aeons of time so great that even our longest durations of hundreds of millions of years, heretofore considered, become almost as nothing in comparison. Truly, the life of man upon our little world is but short, but from the processes which he views, as it were, in but a flash of time, he can picture to himself what has happened in the remote past, and he can learn something of the New Heavens which shall come to be in the remotest ages of the future.

We now come to a very interesting feature of the globular clusters, which may throw some light on an even more farreaching problem. It is evident that they are connected with our Milky Way universe, for their distribution in space is by no means at random, but, on the contrary, their numbers increase rapidly as the plane of the Milky Way is approached from either side. But when a distance of 5,000 light years above or below the plane is reached, the occurrence of globular clusters very abruptly ceases. Of all the globular clusters in the heavens, there is but one so near the plane as this, and this single cluster is very near the boundary. Evidently, in the words of Shapley, "This mid-galactic region, which is peculiarly rich in all types of stars, planetary nebulas, and open clusters, is unquestionably a region unoccupied by globular clusters."

When we ask why this should be so, an answer is at once suggested by the great distances which, as we have seen, separate us from these objects. Though evidently associated with our universe, they lie upon or beyond its borders. It is reasonable to suppose that they actually are to be found in the greatest numbers in the direction of the plane of our greatly flattened cloud, but that the presence of opaque matter pre

vents our seeing them there. In the same way, none of the great numbers of spiral nebulas are found in the plane of the Milky Way; we are sure that these objects also are at a great distance from us, and we believe that those in this particular position are hidden from us. In short, viewed from a great distance, our whole stellar universe might look much like the magnificent photographs of such flattened nebulas as are seen almost edgewise, the central, bright portion being surrounded by a flattened, nearly opaque, lens shaped mass of great extent. And this brings us, finally, to a brief consideration of the Spiral Nebulas, and to the almost startling suggestion met with in several recent papers in our astronomical journals, that these faint objects may be actual universes of stars, at an almost infinite distance away from our universe, and perhaps even comparable with it in size. Though there are many difficult and puzzling features about these objects, it may, however, be said at once that though the spiral nebulas are unquestionably of a very large size, this last assumption, is, in the light of the most recent work, very improbable.

Until recently it was supposed that the nebulas of a spiral form were probably not very different in their nature from planetary and irregular nebulas, and that they were probably condensing slowly into one or a few stars, Indeed, the Great Nebula of Andromeda, which has a spiral structure, was often described as a solar system, already far advanced in its development, and not very unlike what our own solar system must have been, many ages ago. The circumstance that the spectra of all spiral nebulas were found to be continuous, was, however, somewhat difficult of explanation.

When, however, the spectroscope was sufficiently perfected to enable the velocities of these objects in the line of sight to be measured with some accuracy, most interesting and unexpected results were found. Thus, at Mount Wilson, Pease found a radial velocity of no less than 735 miles a second, while the average from about thirty of these objects is about 355 miles. The Andromeda nebula itself is approaching us with a velocity of 238 miles a second. These very high velocities are

in striking contrast to those of nebulas known or believed to be within our system and condensing into stars, which always move far more slowly than the stars themselves.

From what has been said in the first part of this paper, it will not be found a matter of surprise that astronomers are in general agreed that such high velocities could not have been imparted to these nebulas by the action of our universe and that it is regarded as very probable that these objects are wholly outside of our system.

One computer, assuming that the great relative velocities of the spiral nebulas are principally caused by a rapid drift of our entire universe through space, has determined for this drift a speed of 420 miles a second along a line directed toward the constellation Capricornus. Later, additional, measures show, however, that the velocities belong to the nebulas themselves, and that they are not caused by a mere relative motion due to the drift of our universe of stars. But why the spiral nebulas should have such very high velocities is altogether unknown.

All thus far described might be fully explained by the assumption that the spiral nebulas are really distant universes, and that very high velocities are characteristic of the drift of universes through space. But recent careful measurement of photographs taken at the Mount Wilson Solar Observatory, have certainly established the fact that motions of the knots and certain other well defined points can be detected in photographs separated by so short and interval as sixteen years. Were these nebulas true universes so large as our own, the detection of such motions would be quite impossible, even assuming that they are characterized by the high velocities observed of hundreds of miles a second. Yet though neither so large nor so distant as the theory of so-called "Island Universes" would require, it is very probable that they are quite beyond the limits of our own star cloud.

It is probable that each of these nebulas is gradually developing into a cluster or small universe of stars, although it is not yet such a universe. A mathematical investigation of one such nebula shows that the knots on its spiral arms should be about