found unavoidable, in a case where what is substantially a single theme has been treated in the various forms which it assumed in the light of constantly growing knowledge. If the critical reader finds this a defect, the author can plead in extenuation only the difficulty of avoiding it under the circumstances. Although mainly astronomical, a number of discussions relating to general scientific subjects have been included.

Acknowledgment is due to the proprietors of the various periodicals from the pages of which most of the essays have been taken. Besides Harper's Magazine and the North American Review, these include McClure's Magazine, from which were taken the articles "The Unsolved Problems of Astronomy" and "How the Planets are Weighed." "The Structure of the Universe" appeared in the International Monthly, now the International Quarterly; "The Outlook for the Flying-Machine" is mainly from The New York Independent, but in part from McClure's Magazine; "The World's Debt to Astronomy" is from The Chautauquan; and "An Astronomical Friendship" from the Atlantic Monthly.

SIMON NEWCOMB. WASHINGTON, JUNE, 1906.

I

THE UNSOLVED PROBLEMS OF ASTRONOMY

The reader already knows what the solar system is: an immense central body, the sun, with a number of planets revolving round it at various distances. On one of these planets we dwell. Vast, indeed, are the distances of the planets when measured by our terrestrial standards. A cannon-ball fired from the earth to celebrate the signing of the Declaration of Independence, and continuing its course ever since with a velocity of eighteen hundred feet per second, would not yet be half-way to the orbit of Neptune, the outer planet. And yet the thousands of stars which stud the heavens are at distances so much greater than that of Neptune that our solar system is like a little colony, separated from the rest of the universe by an ocean of void space almost immeasurable in extent. The orbit of the earth round the sun is of such size that a railway train running sixty miles an hour, with never a stop, would take about three hundred and fifty years to cross it. Represent this orbit by a lady's finger-ring. Then the nearest fixed star will be about a mile and a half away; the next more than two miles; a few more from three to twenty miles; the great body at scores or hundreds of miles. Imagine the stars thus scattered from the Atlantic to the Mississippi, and keep this little finger-ring in mind as the orbit of the earth, and one may have some idea of the extent of the universe.

One of the most beautiful stars in the heavens, and one that can be seen most of the year, is a Lyrae, or Alpha of the Lyre, known also as Vega. In a spring evening it may be seen in the northeast, in the later summer near the zenith, in the autumn in the northwest. On the scale we have laid down with the earth's orbit as a finger-ring, its distance would be some eight or ten miles. The small stars around it in the same constellation are probably ten, twenty, or fifty times as far.

Now, the greatest fact which modern science has brought to light is that our whole solar system, including the sun, with all its planets, is on a journey towards the constellation Lyra. During our whole lives, in all probability during the whole of human history, we have been flying unceasingly towards this beautiful constellation with a speed to which no motion on earth can compare. The speed has recently been determined with a fair degree of certainty, though not with entire exactness; it is about ten miles a second, and therefore not far from three hundred millions of miles a year. But whatever it may be, it is unceasing and unchanging; for us mortals eternal. We are nearer the constellation by five or six hundred miles every minute we live; we are nearer to it now than we were ten years ago by thousands of millions of miles, and every future generation of our race will be nearer than its predecessor by thousands of millions of miles.

When, where, and how, if ever, did this journey begin—when, where, and how, if ever, will it end? This is the greatest of the unsolved problems of astronomy. An astronomer who should watch the heavens for ten thousand years might gather some faint suggestion of an answer, or he might not. All we can do is to seek for some hints by study and comparison with other stars.

The stars are suns. To put it in another way, the sun is one of the stars, and rather a small one at that. If the sun is moving in the way I have described, may not the stars also be in motion, each on a journey of its own through the wilderness of space? To this question astronomy gives an affirmative answer. Most of the stars nearest to us are found to be in motion, some faster than the sun, some more slowly, and the same is doubtless true of all; only the century of accurate observations at our disposal does not show the motion of the distant ones. A given motion seems slower the more distant the moving body; we have to watch a steamship on the horizon some little time to see that she moves at all. Thus it is that the unsolved problem of the motion of our sun is only one branch of a yet more stupendous one: What mean the motions of the stars—how did they begin, and how, if ever, will they end? So far as we can yet see, each star is going straight ahead on its own journey, without regard to its neighbors, if other stars can be so called. Is each describing some vast orbit which, though looking like a straight line during the short period of our observation, will really be seen to curve after ten thousand or a hundred thousand years, or will it go straight on forever? If the laws of motion are true for all space and all time, as we are forced to believe, then each moving star will go on in an unbending line forever unless hindered by the attraction of other stars. If they go on thus, they must, after countless years, scatter in all directions, so that the inhabitants of each shall see only a black, starless sky.

Mathematical science can throw only a few glimmers of light on the questions thus suggested. From what little we know of the masses, distances, and numbers of the stars we see a possibility that the more slow-moving ones may, in long ages, be stopped in their onward courses or brought into orbits of some sort by the attraction of their millions of fellows. But it is hard to admit even this possibility in the case of the swift-moving ones. Attraction, varying as the inverse square of the distance, diminishes so rapidly as the distance increases that, at the distances which separate the stars, it is small indeed. We could not, with the most delicate balance that science has yet invented, even show the attraction of the greatest known star. So far as we know, the two swiftest-moving stars are, first, Arcturus, and, second, one known in astronomy as 1830 Groombridge, the latter so called because it was first observed by the astronomer Groombridge, and is numbered 1830 in his catalogue of stars. If our determinations of the distances of these bodies are to be relied on, the velocity of their motion cannot be much less than two hundred miles a second. They would make the circuit of the earth every two or three minutes. A body massive enough to control this motion would throw a large part of the universe into disorder. Thus the problem where these stars came from and where they are going is for us insoluble, and is all the more so from the fact that the swiftly moving stars are moving in different directions and seem to have no connection with each other or with any known star.

It must not be supposed that these enormous velocities seem so to us. Not one of them, even the greatest, would be visible to the naked eye until after years of watching. On our finger-ring scale, 1830 Groombridge would be some ten miles and Arcturus thirty or forty miles away. Either of them would be moving only two or three feet in a year. To the oldest Assyrian priests Lyra