In 1900, for instance, the radial motions of about 300 stars were known; now we know the radial velocities of thousands. Accurate distances were then on record for possibly 150 of the brightest stars, and now for more than ten times as many. Spectra were then available for less than one-tenth of the stars for which we have the types to-day. Practically nothing was known at that time of the photometric and spectroscopic methods of determining distance; nothing of the radial velocities of globular clusters or of spiral nebulae, or even of the phenomenon of star streaming. As a further indication of the importance of examining anew the evidence on the size of stellar systems, let us consider the great globular cluster in Hercules-a vast sidereal organization concerning which we had until recently but vague ideas. Due to extensive and varied researches, carried on during the last few years at Mount Wilson and elsewhere, we now know the positions, magnitudes, and colors of all its brightest stars, and many relations between color, magnitude, distance from the center, and star density. We know some of these important correlations with greater certainty in the Hercules cluster than in the solar neighborhood. We now have the spectra of many of the individual stars, and the spectral type and radial velocity of the cluster as a whole. We know the types and periods of light variation of its variable stars, the colors and spectral types of these variables, and something also of the absolute luminosity of the brightest stars of the cluster from the appearance of their spectra. Is it surprising, therefore, that we venture to determine the distance of Messier 13 and similar systems with more confidence than was possible ten years ago when none of these facts was known, or even seriously considered in cosmic speculations?

If he were writing now, with knowledge of these relevant developments, I believe that Newcomb would not maintain his former view on the probable dimensions of the galactic system.

For instance, Professor Kapteyn has found occasion, with the progress of his elaborate studies of laws of stellar luminosity and density, to indicate larger dimensions of the galaxy than formerly accepted. In a paper just appearing as Mount Wilson Contribution, No. 188,1 he finds, as a result of the research extending over some 20 years, that the density of stars along the galactic plane is quite appreciable at a distance of 40,000 light-years—giving a 'The Contribution is published jointly with Dr. van Rhijn.

diameter of the galactic system, exclusive of distant star clouds of the Milky Way, about three times the value Curtis admits as a maximum for the entire galaxy. Similarly Russell, Eddington, and, I believe, Hertzsprung, now subscribe to larger values of galactic dimensions; and Charlier, in a recent lecture before the Swedish Astronomical Association, has accepted the essential features of the larger galaxy, though formerly he identified the local system of B stars with the whole galactic system and obtained distances of the clusters and dimension of the galaxy only a hundredth as large as I derive.

SURVEYING THE SOLAR NEIGHBORHOOD

Let us first recall that the stellar universe, as we know it, appears to be a very oblate spheroid or ellipsoid-a disk-shaped system composed mainly of stars and nebulae. The solar system is not far from the middle plane of this flattened organization which we call the galactic system. Looking away from the plane we see relatively few stars; looking along the plane, through a great depth of star-populated space, we see great numbers of sidereal objects constituting the band of light we call the Milky Way. The loosely organized star clusters, such as the Pleiades, the diffuse nebulae such as the great nebula of Orion, the planetary nebulae, of which the ring nebula in Lyra is a good example, the dark nebulosities-all these sidereal types appear to be a part of the great galactic system, and they lie almost exclusively along the plane of the Milky Way. The globular clusters, though not in the Milky Way, are also affiliated with the galactic system; the spiral nebulae appear to be distant objects mainly if not entirely outside the most populous parts of the galactic region.

This conception of the galactic system, as a flattened, watchshaped organization of stars and nebulae, with globular clusters and spiral nebulae as external objects, is pretty generally agreed upon by students of the subject; but in the matter of the distances of the various sidereal objects-the size of the galactic systemthere are, as suggested above, widely divergent opinions. We shall, therefore, first consider briefly the dimensions of that part of the stellar universe concerning which there is essential unanimity of opinion, and later discuss in more detail the larger field,

THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 175

FIG. 1. The region of the Apennines on the surface of the moon as photographed with the 100-inch reflector. Photograph by F. G. Pease.

FIG. 2.-A group of sun-spots first appearing in February 1920 and lasting for about 100 days. The shaded and unshaded regions indicate magnetic polarities of opposite signs. Drawing by S. B. Nicholson.

FIG. 3.-Two successive photographs on the same plate of the diffuse nebula N. G. C. 221, made with the 100-inch reflector to illustrate the possibility of greatly increasing the photographic power of a large reflector through the use of accessory devices. The exposure time for the picture on the left was fifteen minutes; it was five minutes for the picture on the right, which was made with the aid of the photographic intensifier described in Proc. Nat. Acad. Sci., 6, 127, 1920. In preparing the figure the two photographs were enlarged to the same scale.

where there appears to be a need for modification of the older conventional view.

Possibly the most convenient way of illustrating the scale of the sidereal universe is in terms of our measuring rods, going from terrestrial units to those of stellar systems. On the earth's surface we express distances in units such as inches, feet, or miles. On the moon, as seen in the accompanying photograph made with the 100-inch reflector, the mile is still a usable measuring unit; a scale of 100 miles is indicated on the lunar scene.

Our measuring scale must be greatly increased, however, when we consider the dimensions of a star-distances on the surface of our sun, for example. The large sun-spots shown in the illustration cannot be measured conveniently in units appropriate to earthly distance-in fact, the whole earth itself is none too large. The unit for measuring the distances from the sun to its attendant planets, is, however, 12,000 times the diameter of the earth; it is the so-called astronomical unit, the average distance from earth to sun. This unit, 93,000,000 miles in length, is ample for the distances of planets and comets. It would probably suffice to measure the distances of whatever planets and comets there may be in the vicinity of other stars; but it, in turn, becomes cumbersome in expressing the distances from one star to another, for some of them are hundreds of millions, even a thousand million, astronomical units away.

This leads us to abandon the astronomical unit and to introduce the light-year as a measure for sounding the depth of stellar space. The distance light travels in a year is something less than six million million miles. The distance from the earth to the sun is, in these units, eight light-minutes. The distance to the moon is 1.2 light-seconds. In some phases of our astronomical problems (studying photographs of stellar spectra) we make direct microscopic measures of a ten-thousandth of an inch; and indirectly we measure changes in the wave-length of light a million times smaller than this; in discussing the arrangement of globular clusters in space, we must measure a hundred thousand lightyears. Expressing these large and small measures with reference to the velocity of light, we have an illustration of the scale of the astronomer's universe-his measures range from the trillionth of a billionth part of one light-second, to more than a thousand

light-centuries. The ratio of the greatest measure to the smallest is as 1033 to 1.

It is to be noticed that light plays an all-important rôle in the study of the universe; we know the physics and chemistry of stars only through their light, and their distance from us we express by means of the velocity of light. The light-year, moreover, has a double value in sidereal exploration; it is geometrical, as we have seen, and it is historical. It tells us not only how far away an object is, but also how long ago the light we examine was started on its way. You do not see the sun where it is, but where it was eight minutes ago. You do not see faint stars of the Milky Way as they are now, but more probably as they were when the pyramids of Egypt were being built; and the ancient Egyptians saw them as they were at a time still more remote. We are, therefore, chronologically far behind events when we study conditions or dynamical behavior in remote stellar systems; the motions, light-emissions, and variations now investigated in the Hercules cluster are not contemporary, but, if my value of the distance is correct, they are the phenomena of 36,000 years ago. The great age of these incoming pulses of radiant energy is, however, no disadvantage; in fact, their antiquity has been turned to good purpose in testing the speed of stellar evolution, in indicating the enormous ages of stars, in suggesting the vast extent of the universe in time as well as in space.

Taking the light-year as a satisfactory unit for expressing the dimensions of sidereal systems, let us consider the distances of neighboring stars and clusters, and briefly mention the methods of deducing their space positions. For nearby stellar objects we can make direct trigonometric measures of distance (parallax), using the earth's orbit or the sun's path through space as a base line. For many of the more distant stars spectroscopic methods are available, using the appearance of the stellar spectra and the readily measurable apparent brightness of the stars. For certain types of stars, too distant for spectroscopic data, there is still a chance of obtaining the distance by means of the photometric method. This method is particularly suited to studies of globular clusters; it consists first in determining, by some means, the real luminosity of a star, that is, its so-called absolute magnitude, and second, in measuring its apparent magnitude. Obviously, if a star of known real brightness is moved away to greater and greater