"May I express my deep sympathy with the very sad story you have told me?" he said.

"My story? I have told you no story. I hope I do not disturb you. I have no right here, I know; mine is a third-class ticket, but the guard put me in here last time we stopped because the people in the carriage where I was were so noisy."

"I am amazed, bewildered," he stammered; "certainly you told me your story."

The little woman had pride; she set her lips firmly, and spoke coldly.

"I do not speak of my affairs to strangers," she said; "even if they were of any interest I should not."

Her pride touched him more than all, it was so impotent, so gentle. He moved along the seat till he was opposite her, looking straight into the patient, proud, pathetic face; he spoke tenderly, gently, and with infinite reverence.

"I am sure, though you have not told me your story, that the story which has in some strange way come within my knowledge is your story, and I want to hear the end. Do you mind telling me where you are going now?"

"I am going to be a drudge among strangers. What is it to you?" What, indeed? A little plain, faded woman, what did it mean that he, a man in the prime of life, handsome, rich, overburdened with friends, felt the tears rise in his eyes, and a great ache in his heart? She might well look at him in wonder. He stretched out his hands towards her, he could scarcely speak.

"I know it all," he said, "I have felt it all. You have suffered so much. You shall not suffer any more. I will make your life so bright to you if you will let me."

"I don't understand," she faltered.

"Neither do I," he cried, "neither do I, not how I know so much, or why I love you. I only know that I must take you right into my heart and keep you warm there, for I do love you !"

"Oh no! me, impossible!"

But looking in his eyes she saw it was possible, and true, and she held out her hands, trembling, wondering, questioning. He answered the question with words that seemed to come through him, as if they were a message, and not only his own thought.

"Every human soul is lovable; we could not hold back from loving every soul on earth, could we once see it. But we cannot. Beauty hides the soul equally with deformity. To-day God has been good to me: I have seen the soul of a woman—and loved it."

331

THE SUN AMONG HIS PEERS.

THE

HE Sun is a star, and the stars are suns. This fact has been a familiar one to astronomers for many years, and is probably known to most of my readers. That the stars shine by their own inherent light, and not by light reflected from another body, like the planets of the solar system, may be easily proved. That many of them at least are very similar to our own sun is clearly shown by several considerations. I will mention three facts which prove this conclusively. First, their great intrinsic brilliancy compared with their small apparent diameter, a diameter so small that the highest powers of the largest telescopes fail to show them as anything but mere points of light without measurable magnitude. Second, their vast distance from the earth, a distance so great that the diameter of the earth's orbit dwindles almost to a point in comparison. This accounts satisfactorily for the first fact. Third, the spectroscope-that unerring instrument of modern research-shows that the light emitted by many of them is very similar to that radiated by the sun. Their chemical and physical constitution is, therefore, probably analogous to that of our central luminary. The red stars certainly show spectra differing considerably from the solar spectrum, but these objects are comparatively rare, and may perhaps be considered as forming exceptions to the general rule.

The stellar spectra have been divided into four types or classes. The first class includes stars like Sirius, in which the strong development of the hydrogen lines seems to indicate the preponderance of this gaseous metal in the fiery envelopes of these distant suns. The second class includes stars in which the spectrum closely resembles the solar spectrum. The third and fourth types include those which show a banded spectrum, the rainbow-tinted streak being crossed by a number of dark bands or shadings, in striking contrast to the solar spectrum, in which fine lines only are visible. These are mostly of an orange or red colour of various degrees of intensity, and many of them are variable in their light. There is some reason to suppose that stars of the first type are probably the

hottest and intrinsically the brightest of all, and are not, therefore, fairly comparable with our sun. In considering, therefore, the sun's rank in size and brightness among the stellar hosts, we should compare it with stars which show a similar spectrum.

But how are we to compare the sun with any star? It is clear that the first thing we require to know is the star's distance from the earth. The apparent size and brightness of an object depends on its distance from the eye. A candle placed a few feet from us will look larger and give more light than a brilliant electric lamp several miles away. Venus is, at its brightest, considerably brighter than Jupiter, although the former is a much smaller planet than the latter. Unfortunately the distance of but few of the fixed stars has been ascertained with any approach to accuracy. Failure in the attempt. to measure the distance of a star implies, of course, that it lies at a vast distance from the earth. In several cases, however, the efforts of astronomers have been rewarded with success, although the result found for some stars is still open to much uncertainty. In addition to their distance we also require to know the apparent brightness of the sun with reference to the star with which it is to be compared. Owing to the excessive brilliancy of the sun compared with even the brightest stars, this is a matter of no small difficulty. Photometric measures, made with the aid of the moon as a "medium," have, however, yielded a fairly reliable result, and it is now generally assumed by astronomers that on the scale of stellar magnitudes which represents the brightest stars as of the first magnitude, and those near the limit of ordinary eyesight as sixth magnitude, the sun's light may be expressed as about 26 magnitudes brighter than an average star of the first magnitude, such as Altair or Spica. This may seem to some rather a surprising result. It may be asked, if there is a difference of five magnitudes between a sixth magnitude star and one of the first magnitude, should not the difference between a first magnitude star and the sun be much more than 26 magnitudes? At first sight the number representing the sun's stellar magnitude certainly does seem small, but a little consideration will soon dispel this feeling of surprise. The explanation of the apparent difficulty is a simple one, and will be easily understood by those familiar with the rules of arithmetic. The numbers denoting star magnitudes really form a geometrical series. Thus a star of the fifth magnitude is about two and a half times (more correctly 2'512 times) brighter than a star of the sixth magnitude; a star of the fourth two and a half times brighter than one of the fifth, and so on. This series increases very rapidly, like the question of the nails in a horse's shoe in books

on arithmetic. With the "ratio" of two and a half, a star of the first magnitude would be a hundred times brighter than one of the sixth. A difference of ten magnitudes between two stars would denote that one is 10,000 times brighter than the other; and if we go on to 26 times above the first magnitude, we arrive at a very large number indeed. In fact, the number 26 implies that the sun is equal in brightness to 39,811,000,000, or nearly forty thousand millions of stars of the first magnitude, like Altair or Spica.

Knowing, then, the sun's stellar magnitude, we can easily calculate what its apparent brightness would be if placed at the distance of a star of which the distance from the earth has been determined. For, as light varies inversely as the square of the distance, we have simply to express the distance of the star in terms of the sun's distance from the earth, square this number, and then find how many stellar magnitudes would give the diminution of light indicated. by the number thus obtained. A "parallax" of one second of arc would represent a stellar distance of 206,265 times the sun's mean distance from the earth. At this distance the sun would shine as an average star of the first magnitude. If the star's parallax is only a fraction of a second-as it always is-we have to divide 206,265 by the parallax to obtain the distance sought. For example, the most reliable measures give a parallax for Sirius of about four-tenths of a second of arc. Dividing this into 206,265, we have the distance of Sirius, equal to 515,662 times the sun's distance from the earth. I find that the square of this number represents a diminution of light of 28 stellar magnitudes. Subtracting 26 from this, we have the result that the sun's light would be reduced to two magnitudes below the first, or to the third magnitude, if it were placed at the distance of Sirius. In other words, Sirius, which is about two magnitudes brighter than an average first magnitude star, is four stellar magnitudes, or about forty times brighter than the sun would be in the same position as seen from the earth.

From observations of a faint companion which revolves round Sirius in a period of about 58 years, I find that the combined mass of this brilliant star-the brightest of the stellar hosts—and its companion is about three times the mass of the sun. Now, if Sirius were of th

density.

sun's

Star

me intrinsic brightness as the sun, and of the same

r would be 6.32 (the square root of 40) times the is mass would be 6:32 cubed, or 253 times the ce, then, that Sirius is enormously bright in proin other words, that it is a much less massive liancy would lead us to imagine. It must,

therefore, differ considerably in its physical constitution from that of our sun. Other stars of the same class are probably comparable with Sirius in the exceptional brilliancy of their luminous surface. Stars of the first type are, therefore, of probably small mass in proportion to their brightness, and cannot be fairly compared with the sun in size, or at least in the quantity of matter they contain. Professor Pickering finds that the brighter stars of the Milky Way belong to the Sirius type, and Dr. Gill concludes, from an examination of Galactic photographs, that the smaller stars composing the Milky Way are for the most part blue stars, and have probably spectra of the Sirius type. If this be so, they are probably really as well as apparently small, a conclusion which had been previously arrived at from other considerations.

Let us now consider stars of the second or solar type. Among the brighter stars of this class we have Capella, Arcturus, Aldebaran, Pollux, Alpha Cygni, Alpha Arietis, Alpha Cassiopeiæ, &c., in the Northern hemisphere, and Canopus and Alpha Centauri in the Southern.

For Capella, rivalling Arcturus and Vega (and forming with them the most brilliant trio in the Northern hemisphere), Dr. Elkin finds a parallax of only slightly more than one-tenth of a second of arc. At the distance indicated by this result-nearly two million times the sun's distance from the earth-the sun would shine as a star of only the sixth magnitude. This implies that Capella is about 250 times brighter than the sun. If of the same intrinsic brilliancy of surface its diameter would, therefore, be about sixteen times the sun's diameter, or nearly fourteen millions of miles! As the spectrum of Capella is almost identical with the solar spectrum, it seems probable that the physical constitution of the sun and star are similar. We must, therefore, if its measured distance be reliable, consider Capella to be a vastly larger body than our sun. The above diameter would imply a volume equal to 4,000 suns, a truly stupendous globe!

A minute parallax of about one-sixtieth of a second of arc found for Arcturus by Lr. Elkin gives a still more astounding result. This small parallax implies a distance from the earth equal to about twelve million times the sun's distance. This vast distance would produce a diminution of light of about 354 magnitudes, so that the sun placed at the distance of Arcturus would be reduced to a star of only 9 magnitude! It would not be visible with an opera glass! Arcturus is, therefore, in round numbers, 9 magnitudes, or over 6,000 times brighter than the sun would be at the same distance.