central body. It can be easily shown from the principles of dynamics that the attractive power varies inversely as the square of the periodic time. Hence, then, the attractive power of Sirius must bear to the attractive power of the sun, the proportion which the square of 225 has to the square of 49. As the distances are in each case supposed to be equal, the attractive powers will be proportional to the masses, and hence we conclude that the mass of Sirius, together with that of his companion, is to the mass of the sun in the ratio of 20 to 1. We had already learned that Sirius was much brighter than the sun; now we have learned that it is also much more massive.

Before we leave the consideration of Sirius, there is one additional point of considerable interest which it is necessary to consider. It is remarkable to observe the contrast between the brilliancy of Sirius and his companion. Sirius is a star far transcending all other stars of the first magnitude, while his companion is extremely faint. Even if it were completely withdrawn from the dazzling proximity of Sirius, the companion would be only a small star of the eighth or ninth magnitude, far below the limits of visibility of the unaided eye. To put the matter in numerical language, Sirius is 5,000 times as bright as its companion, but only about twice as heavy! Here is a very great contrast; and this point will appear even more forcible if we contrast the companion of Sirius with our sun. The companion is seven times as heavy as our sun; seven suns equal to ours in one pan of the scales, would only just turn with the companion in the other pan; but in spite of its inferior bulk, our sun is much more powerful as a light-giver. One hundred of the companions to Sirius would not give as much light as our sun! This is a result of very considerable significance. It teaches us that besides the great bodies in the universe which attract attention by their brilliancy, there are also other bodies of stupendous mass which have but little brilliancy, probably some of them none at all. This suggests a greatly enhanced conception of the majestic scale of the universe. It almost invites us to the belief that the universe which we behold, bears but a small ratio to the far larger part

which is invisible in the sombre shades of night. In the wide extent of the material universe we have here or there a star or a mass of gaseous matter sufficiently heated to become luminous, and thus to become visible from the earth; but our observation of these luminous points can tell us little of the remaining contents of the universe.

For the purposes of practical astronomy it has been found convenient to divide the stars into groups, according to their relative degrees of brightness. In this way we denote the brightness of the star by a certain number which is called the magnitude of the star, and the lower the number which expresses the magnitude, the brighter is the star. Of the stars of the first magnitude, which include all the brightest stars in the heavens, there are about twenty. Among this number Sirius is included, though if the classification were to be carried out with logical precision, a distinct class of exceptional brilliancy would have to be created for the reception of Sirius alone.

The stars of the second magnitude are those in which there is one distinct step downwards from the brilliancy of the first magnitude. The brighter stars in the constellation of the Great Bear may be taken as examples. In the entire heavens we have about 65 stars of the second magnitude. Immediately below the second magnitude we have the stars of the third magnitude, to the number of 190. Next comes the fourth, 425; the fifth, 1,100; and so on down to the sixth, 3,200, which completes the stars visible to the unaided eye. In stars of telescopic magnitude we have the seventh, to the number of about 13,000; while the eighth has 40,000, and the ninth 142,000.

It will thus be seen that the number of stars increases when we approach the lower magnitudes, and when we come to the magnitudes still lower than the ninth the numbers speedily swell from thousands to millions. The minutest stars visible in powerful telescopes are usually stated to be of the fourteenth or fifteenth magnitude, while in the very greatest instruments magnitudes two or three steps lower can be observed.

The number of stars visible without a telescope in England

may be estimated at about 3,000. Argelander has given to the world a well-known catalogue of the stars in the northern hemisphere, accompanied by a series of charts on which these stars are depicted. All the stars of the first nine magnitudes are included, as well as a very large number of stars lying between the ninth and the tenth magnitudes. The total number of these stars is 324,188, and yet they are all within reach of a telescope of three inches in aperture!

Amid the hosts of stars, a considerable number specially attract our attention by the peculiar changes they undergo in brilliancy. They are known as variable stars; some of them run through a cycle of changes in a day or two, some take many months. Some appear once, and never appear again. Some are conspicuous to the unaided eye, some are faint telescopic objects. Though the number of variable stars is very large, yet, compared with the ordinary fixed stars, they must be regarded as very infrequent.

The most celebrated of all the variable stars is that known as Algol, whose position in the constellation of Perseus is shown in Fig. 70. This star is very conveniently placed for observation, being visible every night in the northern hemisphere, and its wondrous and regular changes can be observed without any telescopic aid. Every one who desires to become acquainted with the great truths of astronomy should be able to recognise this star, and should have also followed it during one of its periods of change. Algol is usually a star of the second magnitude, but in a period between two or three days, or, more accurately, in an interval of 2 days 20 hours 48 minutes and 55 seconds, its brilliancy goes through a most remarkable cycle of variations. The series commences with a gradual decline of the star's brightness, which in the course of three or four hours falls from the second magnitude down to the fourth. At this lowest stage of brightness Algol remains for about twenty minutes, and then begins to increase, until in three or four hours it regains the second magnitude, at which it continues for about 2 days 13 hours, when the same series commences anew. It seems that the period

required by Algol to go through its changes is itself subject to a slow but certain variation.

The claim of our sun to be admitted as a star having been conceded, the question arises as to whether he shall be entitled to the distinction of being admitted to the select class of variable stars, or whether he shall not take rank among the far more numerous class which dispense their beams with uniformity. I do not think we can have much hesitation in answering the question. It is obvious that the light from our sun is for all practical purposes absolutely constant. No doubt the spots and the other objects on the sun are variable, but it would be merely fantastic to speak of the sun as a variable star. It is no doubt variable to the close observation of terrestrial beings who are placed in its immediate vicinity; it is not variable in the sense in which we speak of Algol, or any of the other variable stars which diversify the brilliancy of the sky.

That the sun is no more than a star, and the stars are no less than suns, is the cardinal doctrine of astronomy. The imposing magnificence of this truth is only realised when we attempt to estimate the countless myriads of stars. This is a problem on which our calculations are necessarily vain. Let us, therefore, invoke the aid of the poet to attempt to express the innumerable, and conclude this chapter with the following lines of Mr. Allingham :

:

"But number every grain of sand,
Wherever salt wave touches land;
Number in single drops the sea;
Number the leaves on every tree,
Number earth's living creatures, all

That run, that fly, that swim, that crawl.

Of sands, drops, leaves, and lives, the count

Add up into one vast amount,

And then for every separate one

Of all those, let a flaming SUN

Whirl in the boundless skies, with each

Its massy planets, to outreach

All sight, all thought: for all we see,
Encircled with infinity,

Is but an island."

CHAPTER XX.

DOUBLE STARS.

Interesting Stellar Objects-What is a Double Star ?-Stars Optically Double-The great Discovery of the Binary Stars made by Herschel-The Binary Stars describe Elliptic Paths-Why is this so important ?-The Law of Gravitation -Special Double Stars-Castor-Mizar-The Pole Star-The Coloured Double Stars-8 Cygni, y Andromedæ.

THE sidereal heavens contain few more interesting objects for the telescope than can be found in the numerous class of double stars. They are to be counted now in thousands; indeed, many thousands can be found in the catalogues devoted to this special branch of astronomy. Many of these objects are, no doubt, small and comparatively uninteresting, but some of them are among the most, conspicuous stars in the heavens. We shall in this brief account select for special discussion and illustration a few of the more remarkable double stars. We shall particularly notice some of those that can be readily observed with a small telescope, and we have indicated on the sketches of the constellations in a previous chapter how the positions of these objects in the heavens can be ascertained.

In 1678, about 100 years before Herschel's observations commenced, it had been shown by Cassini that certain stars, which to the unaided eye appeared single points of light, really consisted of two or more stars, so close together that the telescope was required for their separation. The number of these objects was gradually increased by fresh discoveries, until in 1781 (the same year in which Herschel discovered Uranus) a list, containing eighty double stars, was published by the astronomer Bode. These interesting objects claimed the attention of Herschel during his memorable researches. The list of known doubles rapidly swelled. Herschel's discoveries are to be enumerated by hundreds, while he also commenced systematic measurements of the distance by which the stars.