as he now calls himself, can study and measure the plates at his leisure. The great revelations of our times have come through the application of this method to the measurement of motions in the line of sight from us to a star. No achievement of the intellect of man would have seemed farther without the range of possibility to the thinker of half a century ago than the discoveries of invisible bodies which are now being made by such measurements. The revelations of the telescope take us by surprise. But if we consider what the thinker alluded to might regard as attainable, they are far surpassed by those of the spectroscope. The dark bodies, planets we may call them, which are revolving round the stars, must be for ever invisible in any telescope that it would be possible to construct. They would remain invisible if the power of the instrument were increased ten thousand times. And yet if there are inhabitants on these planets, our astronomers could tell them more of the motions of the world on which they live than the human race knew of the motions of the earth before the time of Copernicus. The men and institutions which have contributed to this result are so few in number that it will not be tedious to mention at least the principal actors. The possibility of measuring the motions of the stars in the line of sight by means of the spectroscope was first pointed out by Mr. now Sir William Huggins. He actually put the method into operation. As soon as its feasibility was demonstrated it was taken up at Applying the Greenwich. In these earlier attempts, eye methods alone were used, and the results were not always reliable. Then spectrum photography was applied at the German astrophysical observatory of Potsdam by Vogel, who introduced into the method a degree of precision which had never before been reached. His measures of the motions of the stars in the line of sight opened up the last era in science. method to the variable star Algol, he proved that the loss of light which it undergoes at intervals of nearly three days is merely a partial eclipse by a dark planet, almost as large as itself, revolving round it. Thus was discovered a new order of bodies in the universe, telescopic binary systems, pairs of stars, or stars and planets, revolving round each other by their mutual gravitation; although no telescope that it is possible to make would ever show that more than a single body was present. Thence the photographic method soon spread to Meudon and Pulkova. But, as often happens when new fields of research are opened, we find them cultivated in quarters where we should least expect. The successful application of the method requires not only the best spectroscope, but the most powerful telescope at command. Ten years ago the most powerful telescope in the world was at the Lick Observatory. A few years later Mr. D. O. Mills put at its eye end the best spectrograph that human art could make at that time, the work of Brashear. It is Campbell who, with this instrument, has inaugurated a series of discoveries in this line which are without a parallel. He finds that about one star in thirteen The has a planet revolving round it, so massive as to change the motion of the star by an amount visible in the spectroscope. The more or less eccentric orbits of these bodies are being determined. final conclusion from all his work is that isolated stars may be the exception rather than the rule; that possibly a great majority at least of the stars are composed of two or more bodies revolving round each other, though they appear in our telescopes as single. The study of variable stars from being little more than a scientific amusement, has grown into an important branch of astronomical science. It has now joined hands with spectroscopy to make it probable that in most cases the variations of light in a star are due to changes in its constitution produced by invisible planets revolving round it. All these results naturally involve a great increase in the number of men who are devoting themselves. to astronomical research. When we study the work of this small army of investigators, and compare the possibilities of the field they are exploring with what has been done in the past, we feel that astronomy, although the oldest of the sciences in years, is reaching a stage of vigorous youth, and that the twentieth century will open up views of the universe of which quite possibly we, at its beginning, have no conception. A mere survey of what has been done in the various lines we have mentioned would be far from giving an idea of the real significance of the advance we are considering. Cataloguing the stars, estimating their magnitudes, recording and comparing their spectra, and determining their motions might be considered as, after all, barren of results of the highest human interest. When we know the exact position of every star in the heavens, the direction in which it is moving, and the character of its spectral lines, how much wiser are we? What could hardly have been foreseen fifty years ago, is that these various classes of results are now made to combine and converge upon the greatest problem which the mind of man has ever attempted to grasp that of the structure of the universe. The study of variable stars has suddenly fallen into line, so to speak, so that now it is uniting itself to the study of all the other celestial objects, to give us at least a faint conception of what the solution of this problem may be. One of the principal objects of the present work is to make a comparison of these various researches, and discuss the views respecting the constitution of the stars individually, as well as of the universe as a whole, to which they lead us. But there are a number of details to be considered singly before we can combine results in this way. Our early chapters will, therefore, be devoted to the special features and individual problems of stellar astronomy which have occupied the minds of astronomers from the beginning of their work to the present time. Keeping these details in mind, we can profitably proceed to the consideration of the general conclusions to be drawn from them. CHAPTER II MAGNITUDES OF THE STARS And one star differeth from another star in glory.-PAUL. THE apparent brightness of a star, as we see it from the earth, depends upon two causes-its intrinsic brilliancy, or the quantity of light which it actually emits, and its distance from us. It follows that if all the stars were of equal intrinsic brightness we could determine their relative distances by measuring the respective amounts of light which we receive from them. The quantity of light in such a case varies inversely as the square of the distance. This will be seen by the figure, where S represents the position of a star, regarded as a luminous point, while A and B B B B are screens placed at such distances that each will receive the same amount of light from the star. If the |