we do not realize how faint the great majority of the stars are as they appear to us, we shall not understand how distant they must be, and how great must be that universe which can contain bodies really so vast and so intensely bright, and yet, on account of their distance, apparently so extremely faint.

The table given earlier showed how rapidly the number of faint stars increases, as we go from magnitude to magnitude in the order of decreasing brightness. Their greater faintness, combined with their enormously increased numbers, allows of two possibilities. Does the increase in number as we proceed from one magnitude to the next fainter make the total brightness of each fainter class of star increase, so that the number of stars between one magnitude and the next may be sufficient, in spite of the increased faintness of each star, for their total light to exceed the total light of the magnitude one higher up, or does it make it diminish? The table gives the answer to this question by showing the number of stars of the 1st magnitude which would give an equal amount of light with the stars of each successive fainter magnitude. Stars of the 1st magnitude are the brightest of those that we see by the unassisted sight, and of these a few are really considerably brighter than the average 1st magnitude star. The brightest star is Sirius, which gives eleven times as much light as a typical star of the 1st magnitude. Then comes Canopus, giving six times the light of a 1st magnitude star, and Alpha Centauri, our nearest neighbour in the stellar depths, which is equal to two 1st magnitude stars. Eight stars follow down to the typical 1st magnitude star which together are equal in light to fourteen stars of the 1st magnitude, twenty-seven stars between the 1st and 2nd magnitudes, give an amount of light equal to seventeen stars of the adopted standard, and seventythree stars between the 2nd and 3rd magnitudes are equal to eighteen stars of the standard magnitude. As the table is followed downward, it will be seen that the equivalent light given by each succeeding magnitude increases till we reach the 10th magnitude, after which it begins to diminish. Thus some idea can be formed of the extreme faintness of these fainter stars. Two million stars between the 12th and 13th magnitudes only give light equal to fifty-one of the standard 1st magnitude, and as we pass to still fainter stars, twenty-five millions between the 16th and 17th magnitudes are only equal to sixteen standard stars.

Beyond the 17th magnitude, the numbers are not derived

I

directly from observation, but have been calculated from the numbers higher up, by a simple mathematical formula, and from this it appears that the stars between the 17th and 18th magnitudes would only give an amount of light equal to ten standard stars, and that the whole mass of stars fainter still would be barely equal to twelve of the 1st magnitude. Thus the total light of all stars, seen and unseen, would, it appears from this table, come to about that of 700 typical stars of the 1st magnitude. It has already been mentioned that half the stars are fainter than the 23rd or 24th magnitude, but their total light, though they number several hundred millions, does not equal the light of a single 1st magnitude star. Perhaps that single consideration gives as good an idea as we can possibly form of their almost unimaginable faintness.

But the table reveals another curious circumstance. The stars visible to the naked eye render to us only about one-fourth the total amount of starlight. If, therefore, all the stars that we can discern individually by our unassisted sight were blotted out, the total amount of starlight would only be diminished by one-quarter. The midnight sky would not be seriously less luminous than it is at present, though it is needless to say its beauty and interest would suffer woefully.

The light which the stars send to us can be measured in another way by comparing it with the light of the full moon. It is, of course, clear to everyone that when there is a full moon the night is much lighter than when there is no moon at all, and we are dependent simply upon the light of the stars. It has been calculated that the total light of all the stars is only one-hundredth that of the full moon. Or the total starlight may be compared to the light of an ordinary electric lamp of 16 candle-power placed at a distance of from 45 to 50 yards. Such a lamp would give us as much light as we receive from all these many millions of stars put together.

But the light of the stars does not reach us with the uninteresting homogeneity which characterizes the light from the ordinary electric lamp. The starlight is differentiated not only in direction and colour but in many other ways, and from these variations, as we learn to interpret them better, we shall gain more and more knowledge of the stellar universe. It is this tiny stream of light, though in its brightness it is only equal to that of an ordinary 16 candle-power lamp, placed at a distance of 45 yards, that has furnished us with all the knowledge of the heavenly bodies which we possess. It is to this that we owe the profound influence which astronomy has

exercised upon our ideas of the universe, of man's place in it, and of the almighty power of God.

DISCUSSION.

The CHAIRMAN (PROFESSOR D. S. MARGOLIOUTH): Ladies and Gentlemen, it is my very pleasant duty to ask you to join with me in thanking the Lecturer for his exceedingly lucid and admirable discourse upon a subject which I am convinced is of the greatest interest to all of us. I am sure we all have to thank him, both for his lucidity and also for the beautiful slides with which he has illustrated his lecture. I have, myself, heard a great deal on the subject of the International Photographic Map of the Heavens, because Professor H. H. Turner, the Savilian Professor of Astronomy in Oxford, is a colleague of mine with whom I am much associated, and we in Oxford are very glad to get an opportunity of obtaining fresh information on this abstruse subject when he is lecturing upon it. . . . I do not wish to speak for anyone else in the audience, but for my own part, I can only say that a considerable number of the facts which Dr. Chapman has brought before us this afternoon, were new to me, and I now know a good deal more about the Number of the Stars and the light which we receive from them than I did when I entered this room. I feel sure that all here will join with me in thanking the Lecturer most heartily for his admirable discourse.

Mr. E. WALTER MAUNDER: I think Mr. Chairman, that we owe a very great debt, indeed a double debt, to Dr. Chapman for having come here this afternoon for, as you know, he is not down upon our published programme. The lecture we had expected to have this afternoon, was one which Dr. C. H. W. Johns had promised to give us on "Early Semitic Migrations," but just before the last meeting of the Institute, we received a letter from Dr. Johns saying that failure of health would prevent his fulfilling his engagement. In this great difficulty, I wondered to whom I could turn for help in order that this afternoon should be filled up, and as I knew that Dr. Chapman had just completed an important research upon the subject of the Number of the Stars, I turned to him. I felt when I approached him that it was hardly a fair request that I was making to ask him at such short notice to come and give us an address of so much importance. But he acceded to my request at once with the

greatest possible good grace and willingness, and I think we are very deeply indebted to him on this special account, seeing that he had so short a time to prepare the paper for us. We owe a further great indebtedness to him in that he has given us the very latest results of his own special work. It was only at the last meeting of the Royal Astronomical Society that Dr. Chapman read a paper on the Total Light of the Stars, a subject which he has included in the address to which we have just listened.

The work from which Dr. Chapman has derived the results which he has given us this afternoon has been an extremely toilsome one; it has involved not only the counting of the star images in five thousand areas, carefully distributed over the heavens, but it has meant the creation of standards of stellar magnitude for each order of magnitude under examination, and the estimation of the magnitude of every star image examined. Our debt, therefore, to Dr. Chapman is exceedingly great, both for the self-sacrificing way in which he has come forward to supply our need, for the interest, the value and the freshness of the information which he has given us, and for the admirably clear way in which he has presented it.

THE ASTRONOMER ROYAL (Dr. F. W. DYSON) said that the last time he had had the pleasure of hearing an address in that hall it had been one given by the late Sir David Gill, who was, he believed, one of their Honorary Correspondents. He could not help thinking as he listened to Dr. Chapman's address how pleased Sir David would have been to hear of the progress that had been made, and was still being made, in this particular branch of astronomy, and he could imagine how delighted he would have been with the account which Dr. Chapman had just given of the results which had been obtained--largely from an enterprise which Sir David himself had originally inspired-in this interesting and difficult subject of the dimensions of the stellar universe. He thought that they were warranted in saying that there was on the whole a general agreement amongst astronomers that the universe of stars was bounded : it did not stretch out infinitely. They had now a definite idea as to the number and extent of the stars, and their knowledge concerning them was comparable with, but nothing like so accurate as, their knowledge of the solar system. Modern astronomers were largely concerned with the problem of finding out some analogy to the bright points of light that the stars present to us. The point of

view of astronomy is really a descriptive one; astronomy is a descriptive science, and he supposed that that was very largely true of science in general. It gives no precise answer to the questions, "How does this come about?" or "Why does it come?" The answers that it gives are mainly to the question, "What does it resemble?"

In thinking about the Number of the Stars, although that subject is so interesting in itself, it is almost as interesting to recollect how this knowledge has been acquired. It has been acquired by thought, but the thought itself has been supplemented in very curious fashions. It was certainly remarkable that had it not been that people had learnt to shape pieces of glass so as to make spectacles, and had then gradually developed this art of figuring glass until they formed the lenses of which Dr. Chapman has spoken, had it not been for the development of that art, our knowledge of the stars must have remained extremely limited. The telescope was a beautiful and wonderful instrument, simply on the ground that it magnified our faculties so much. The same remark applied to the microscope, and those electrical instruments by which whole series of phenomena had been discovered of which otherwise we should have known nothing at all. When they considered the heavens and the number and brightness of the stars themselves, he thought they would all feel still more impressively that as religious man had always looked with wonder and reverence on the skies, so that the more we learnt concerning them, the more that wonder and reverence was increased.

A MEMBER enquired how it was possible to find out the rate of movement of the stars by means of the spectroscope. Also what was, approximately, the centre of the stellar universe.

Capt. MCNEILE asked whether there were not many dark stars, and Mr. M. L. ROUSE asked how long it was since it was thought that the stars were suns.

The LECTURER in reply, said: The first question was as to our knowledge of the motions and of the constitution of the stars revealed to us by the spectroscope. I suppose that we all know, or have been told, that when a railway train is approaching us, and steam is being let off, so that its whistle is blowing, the note appears shriller than when it is going away from us. The sharp note as the train approaches is due to sound waves in the air, which travel with a certain definite speed. If the source of these waves is approaching us, we receive the waves more quickly than if the source were at