as Gore and Newcomb, held strongly to the belief in a limited universe, comprising all the stars and nebula within the reach of telescopic vision. "That collection of stars which we call the universe is limited in extent," wrote Newcomb in 1901. "This,' he added, "does not preclude the possibility that far outside of our universe there may be other collections of stars of which we know nothing."

The reopening of the question during the last decade has been due to certain more or less reliable measures and estimates of the distances of spiral nebulæ and star-clusters, combined with the results of spectroscopic observations and theoretical considerations. In November 1911 Prof. F. W. Very, the American astronomer, contributed to Astronomische Nachrichten an important article "On the White Nebular Galaxies," in which, after an elaborate discussion of the dimensions of the Milky Way, he concluded that the faint white nebula were island universes-the smallest and faintest being distant about a million light-years. In 1912 Dr. V. M. Slipher commenced at the Lowell Observatory his remarkable series of measurements of the radial velocities of the spiral nebulæ. Grave doubts had already been thrown on their supposed gaseous nature by the evidence of the spectroscope. The spectrum of the typical spiral is continuous. Slipher's investigations have shown that "the average velocity of the spirals is about twenty-five times the average stellar velocity." This fact differentiates them sharply from the ordinary irregular nebulæ; so does the peculiarity of their distribution. Unlike the planetary and extended nebula, they avoid the galactic regions altogether, being most numerous near the galactic poles. These remarkable characteristics seemed to emphasize the non-nebular, extra-galactic nature of the spirals, and accordingly the island universe theoryof the spirals-began to find a measure of support among the leading astronomers.

Remarkable progress has been made in recent years in the study of stellar clusters. In 1913 Prof. Hertzsprung estimated the distance of the Nubecula Minor, from a study of its Cepheid variables, at 10,000 parsecs, corresponding to about 30,000 lightyears. About the same time Dr. Harlow Shapley began at Mount Wilson his classical researches on clusters of stars which have

been published in his series of papers on "Studies based on the Colours and Magnitudes in Stellar Clusters." The first cluster exhaustively studied was that in Hercules (M 13) and in his paper on "Thirteen Hundred Stars in the Hercules Cluster," dated August 1915, Shapley computed its distance from "considerations of its variable stars, its fragmentary luminosity-curves, and the average apparent brightness of certain colour-groups." The estimate reached, 100,000 light-years, was confirmed by the researches of Hertzsprung. Adopting this estimate as approximately true, Shapley estimated the diameter of the cluster at 1100 light-years. The provisional conclusion reached was that "the peculiar distribution of globular clusters and their great distances from the Earth show that they do not form a part of the galactic stellar system. Each globular cluster is a complete and separate system by itself." Of course, these researches, while they indicate a much greater distance for M 13 and for globular clusters in general than was previously accepted, also indicated them to be miniatures of the stellar universe rather than coequal systems. In a further paper by Dr. Shapley and Mr. Pease, published in 1917, the analogy between our Galaxy and the globular clusters was still further emphasized by the detection of "axes of symmetry' representing "the lines of intersection with the celestial sphere of the central plane of a system analogous in form to our own Galaxy."

Shapley's later researches have resulted in the determination of the distances of a number of other clusters. He finds the most distant cluster at present known to be N.G.C. 7006 at a distance of 67,000 parsecs, equal to 220,000 light-years; while the nearest is 21,000 light-years distant. These results are in harmony with the island universe hypothesis so long as we accept modest estimates of the dimensions of our own galactic system, such as that of Newcomb-about 6000 light-years. But Shapley, from his study of the Cepheid variables, now finds the most distant of these objects to be 20,000 light-years from the Sun. Our own galactic system then is considerably larger than the earlier estimates allowed. In his paper of April 1918, "Remarks on the Arrangement of the Sidereal Universe," Dr. Shapley has modified his original theory that the clusters are separate galaxies compared to our own. "So long as the diameter of the galactic system was

thought to be only a thousand light-years or so we had a fairly plausible case for the 'island universe' hypothesis," but "any external' universe must now be compared with a galactic system. probably more than three hundred thousand light-years in diameter."

Can we then speak of star-clusters as island universes? If we mean by island universes, systems independent of and coequal in dimensions with our galactic system, the answer is in the negative. Indeed, Prof Perrine pointed out over two years ago that "if the distribution of the globular clusters is in fact so closely related to the Galaxy (our stellar system), it seems improbable that these objects are strictly intergalactic." Perrine drew attention to the fact that "according to the N.G.C. there are also two groups of globular clusters in the regions of the two nubeculæ," adding that, if this be confirmed, "additional weight would be given to the probability that these bodies are dependents rather than primary systems." Apparently, they are distinctive subordinate systems. In Dr. Crommelin's view, they may be regarded as outer appendages of the galaxy; and recently Dr. Shapley suggestively wrote "Perhaps we should distinguish 'islands' and 'continents'; for in a certain sense I should now consider globular clusters and spirals as small islands in space." The globular clusters seem to be, at the present stage of cosmical history, self-governing units—outlying portions of the galactic domain, but not external and independent galaxies.

It is perhaps scarcely legitimate at present to speak of clusters and spirals as more or less similar objects. Recent research has brought out several important points of difference between them. The radial velocities of clusters, so far as is known, are predominantly negative: that is to say, they are approaching the Sun, while the spirals as a class-"apparently regardless of the gravitational attraction of the galactic system," as Dr. Shapley points out -are receding with great velocities*. This, combined with the

*According to De Sitter (M. N. lxxviii. p. 26, "Einstein's Theory of Gravitation") these high radial velocities are spurious, if Einstein's theory is true. The displacement of the spectral lines would be due not to the motion of the spirals, but to their great distance, a conclusion which harmonises with the "island universe" theory.

known difference in distribution of the two classes of objects, indicates a fundamental difference between them. Accordingly, Shapley distinguishes them as two types of sidereal organization in · extra-galactic space--the evidence suggesting that the "galactic system now moves as a whole through space, driving the spiral nebulæ before it, and absorbing and disintegrating isolated stellar groups." This would suggest that gravitation prevails up to the distance of the clusters, and that repulsion is the ruling power so far as the spirals are concerned. In this connection a recent paper by Prof. Very on "The Luminiferous Ether" is suggestive. The paper is, of course, largely speculative, and is chiefly an exposition of Very's views on the atom, the ether, and gravitation; but his theoretical conclusions are certainly in accord with recent spectroscopic work on spirals. After pointing out the relative "sparsity of stellar material" in the galactic system, he emphasizes the comparative crowding of the spirals. "Since these objects have velocities of upwards of 1000 km. per sec., frequent collisions are inevitable unless there are mutual repulsions which develop upon arriving at too close proximity. This result might, however, be produced in another way, provided gravitational attraction, by which we assume the stellar movements are given, is not universal, but is limited to definite volumes around each galactic centre, within which gravity is controlled by definitely limited currents of the aura." One difficulty in this hypothesis is that the distances calculated by Very for some of these spirals-up to 80,000 lightyears are less than Shapley's estimated distances of the farthest clusters, which are obviously controlled by gravitation. If, however, we assume greater distances for the spirals, this difficulty is removed and Very's theory is strengthened.

Greater distances have, indeed, been computed. Discussions of the temporary stars in the Andromeda nebula, which has been called the nearest of the spirals and conforms with the novæ in the galactic system, have led to an estimated distance of 1,000,000 light-years and a diameter of 50,000 light-years for that nebula. The Messrs. Lindemann, in their recent preliminary application of photo-electric photometry to astronomy, have reached a somewhat similar estimate of the distance of the same nebula-350,000

parsecs; and they maintain that there is "nothing inconsistent in regarding this nebula as a galaxy very similar to our own."

The problem of the spirals is at present far from solution; and judgment on their exact status must be suspended until we are in possession of more detailed knowledge. Meanwhile, it would seem that there are three possible theories:--(1) That these spirals are within the galactic system and are not actually stellar, but nebulous; (2) that they are appendages of the galactic system, of the same order of distance as the globular clusters; and (3) that they are actually external galaxies, coequal with the stellar system. The first theory seems highly improbable, in view of the obvious differences between spiral and other nebulæ showing gaseous spectra. Dr. Shapley and others are inclined towards the second theorythat the spirals are about as distant as globular clusters. Why, then, it may be asked, are they irresolvable in the most powerful telescopes? It has been computed that their most luminous stars must be fainter than the 21st magnitude. This indicates either that (i) they are composed of dwarf stars-an idea by no means improbable, or (ii) that they are far beyond the clusters, in which case they must be true external universes. For this view there is also considerable support. At present we may look on the spirals as either independent galaxies or miniatures of the galactic system composed of dwarf stars. The spiral form is itself suggestive. "The two arms of the spiral," Prof. Eddington remarks, “have an interesting meaning for us in connection with stellar movements.

The two star streams" (in our galactic system) “and the double-branched spiral arise from the same cause."

In the present state of our knowledge we may compare our galactic system to a continent surrounded on all sides by the ocean of space, and the globular cluster to small islands lying at varying distances from its shores; while the spiral nebulæ would appear to be either smaller islands, or else independent "continents" shining dimly out of Immensity.