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 ASTRONOMY arrangement. But, with the exception of the few stars whose parallax can be measured, the distances of the individual stars are a matter of extremely vague and uncertain inference, and not even the mean distance of any class or group can be settled definitely by any one method of research. It will conduce to clearness in bringing out the bearing of various facts on the problem in question if we state its main point in advance. The most definite form in which it may be considered by the astronomer is this:—As, by increasing the power of our telescopes, we see smaller and smaller stars—are the smallest that are brought into view no more distant than others already known; are they within the sphere of others already observed, or, does every increase of telescopic power bring into view stars farther away 1 To put the question into another shape Is the universe of stars limited in extent? Intimately associated with this is the question of the actual distribution in space of the stars which we see with our telescopes. Whether the universe is finite or infinite, it is certain that the portion which we see is of finite extent. Has this visible portion a definite boundary, and, if so, what is the figure of this boundary ? The statement of this question may suggest a doubt as to the possibility of answering it. Since the range of vision of our telescopes is necessarily limited, is it not necessarily impossible for us to gather evidence of the finitude of the universe? If Limit of with every increase of power we see smaller universe. gtars 0f wi1ic]1 we cannot estimate the distance, how can we decide that we are not simply penetrating farther into a mass of infinite extent ? An answer to this is reached by the following consideration :—So far as stars of various magnitudes have yet been counted there are about three times as many of each order as of the order next brighter. For example, there are three times as many stars of the 7th magnitude as of the 6th, three times more of the 8th, and so on, to at least the 10th or 11th magnitude, a point beyond which the count is uncertain. An individual star of each order gives about four-tenths the light of one of the next brighter order. It follows that the total amount of light which we receive from all the stars of any one order continually increases as we go to the fainter orders, the greater number of the stars more than compensating for the less amount of light received from each Consequently, if the stars continued indefinitely so would the total amount of light received from them, and the heavens would be filled with a blaze as bright as the sun. As such is not the case, the series must stop. Where the stopping-point is, we cannot exactly say ; but, so far as we can judge from appearances, it can go little farther than the count has thus far extended, except perhaps in the Milky Way. We have therefore every reason to believe that by an increase in the power of our telescopes the number of new stars brought into view would begin to diminish, thus showing the total number to be limited. Hence we conclude that the universe of stars which we study has some bounding limit. The question now is, Can we form any conception of the limit and of the arrangement of the universe within it ? _ Direct observation of the apparent distribution of the stars, irrespective of any question of their arrangemen , makes one feature of the universe certain. I he stars which compose it are not equally numerous m every direction; a large majority lie m or near the zone of the Milky Way What follows from this fact may be readily seen from Fig. 4, which we conceive to represent Form of a section of the universe by a plane perpendicuuniverse. lar to the Milky Way, S being the position of the sun, which, for the moment, we may conceive to be near the centre. What we actually observe is that a

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very large majority of the stars are contained within the regions ASB and CSD, while the number contained within the larger angles, BSD and ASC, is relatively

small. An indefinite number of arrangements, all consistent with this fact, may be conceived; but they are all in some way intermediate between the following:— I. All, or at least the great mass of, the stars may be contained between two planes, AC and BD, parallel to the Milky Way. We see more stars in the region ASB and CSD, because there is, so to speak, a greater depth of stars there, while toward M and N we see only a comparatively thin stratum. This was the view developed first by the elder Herschel and then by Struve in his Etudes d’Astronomie Stellaire. II. The actual form of the universe may be spherical, the galaxy being formed by a dense ring of stars around the sphere. III. The same hypothesis of a universe spherical in general form may be made, but, instead of being a ring, the galaxy is a number of clusters of stars mostly situated near one central plane. The hypothesis that the boundary of the universe is spherical admits of being tested in a very simple way. Were such the case, the stars would be equally numerous throughout the regions ASC and BSD, the increase in their number beginning only when we reached the boundaiy of the Milky Way. But all the counts of stars yet made, from the time of Herschel till now, show that the number of stars per square degree continually increases from the two poles of the galaxy to the galaxy itself. Moreover, the rate of increase is as rapid as it would be if the boundary of the universe were two planes parallel to the galactic plane. Unless we make a very improbable hypothesis as to the distribution of the stars around us, this fact must lead us to the conclusion that we actually see to the limits of the universe in all directions away from the galaxy. For, if we did not, the increase in the number of stars in the direction of the galaxy could not be so rapid as it is. It would seem therefore that the first hypothesis of the form of the universe, that of Herschel and Struve, must be at least an approximation to the truth. But that it is not the whole truth will be evident on farther consideration. We have room only to state in the briefest way the main facts, so far brought to light, on which our conclusion must be based. Beginning with the region immediately around us, what evidence have we of the distribution of the stars, especially of their tendency to condense in the direction of the Milky Way? If we consider that greater brilliancy of the stars implies greater nearness to us, then we should answer this question by considering the relation of the brighter stars to the galaxy. It is a remarkable fact that the condensation towards the galactic zone begins with the brighter stars—we might even say with those of the first magnitude—though we can hardly conceive this to be anything else than the result of accident. From Schiaparelli’s maps of the distribution of the stars visible to the naked eye, the position of the Milky Way can be laid down with great exactness. But this