the nearer the star is to the pole of the heavens. A star which, when due north, is about 13 degrees above the horizon, is almost exactly overhead when half a circuit has been completed. Stars nearer to the pole than this are due north when at their highest in their circuit as well as when at their lowest.

But let the student be reminded that all these varieties of motion are the effects of but one single turning movement. He must not suffer himself to be confused by these motions as described (I have, however, described them as clearly as I could); but if he finds doubt arising in his mind, when he is actually studying the stars, let him face due north, and, looking towards the north pole of the heavens (a point rather more than halfway above the northern horizon towards the point overhead), let him remember that the stellar sphere moves as though turning bodily round on an axis,-running from that pole through his own station (which is at the centre of the sphere) to a point directly opposite the former,—the rotation being such that stars near the pole move round it in a direction contrary to that in which the hands of a watch move. will serve equally well if he faces due south, and remembers that the stellar sphere is being carried round from left to right, as though on an axis passing through his station and the invisible pole (which lies below the southern horizon, and rather more than halfway down towards the point directly beneath him).

It

The rate at which the stellar sphere rotates must next be considered.

Roughly speaking, the sphere of stars may be said to turn round once in each day; but in reality it turns rather more quickly, so as to make one complete rotation in about four minutes less than a day. Thus a star which rises in the east takes six hours (less about one minute) to reach the highest part of its path, when it is due south; and it takes the same interval in passing to its setting-place in the west. It is, therefore, twelve hours above the horizon. Stars whose place of rising lies nearer the south are less than twelve hours above the horizon. Stars which rise to the north of the east point are more than twelve hours above the horizon. Stars which touch

or pass above the northern horizon take twenty-four hours (less about four minutes) in circling round the pole of the heavens.

It is well to remember that the resulting motion of the stars can be easily recognised in a very few minutes. This may be shown in a variety of ways. If a star is seen above or beside some distant object, as a tree or house, then if the student remain in an unchanged position for a few minutes only, he will see that the star has perceptibly changed its place. If the star is towards the east, it seems to have moved upwards and towards the right. If it is towards the west, it seems to have moved towards the right, and downwards. If it is towards either the south or the north, it seems to have moved horizontally towards the right. (All stars near the horizon move towards the right, though only those towards the north and south move horizontally.) Ten minutes will produce an unmistakable change of place.*

* It is strange how little familiar most persons are with the fact that the stellar motions are thus obvious. The notion seems to prevail that only the astronomer in his protracted night-watching can become cognizant of the stellar motions. One of the most beautiful and touching descriptions in all Dickens's works-the death of Stephen Blackpool, in Hard Times-is somewhat impaired by the introduction of an impossible star, shining for hours down the deep chasm into which the poor fellow had fallen. The mouth of the Old Hell Shaft was so narrow a chasm as to be concealed by tall grass. Stephen fell far down ; and the star was so bright that he could show it to Rachael among all the other stars visible on an autumn night. Certainly no such star exists in the catalogues of astronomers. It is probable, however, that Dickens may have heard some such story about a bright star-Venus or Jupiter -only the star cannot have been seen just overhead. Novelists and poets sometimes introduce astronomical details rather unhappily. One has made the new moon rise at one o'clock in the morning; another makes midnight moonless though the moon had risen at eleven; in the 'Portent' (a tale which appeared in one of the early numbers of the Cornhill) a star is made to shine midway between the horns of the crescent moon! But, perhaps, all the slips of the sort ever made are outvied by one in the opening line of Chapter XII. Book IV. of Our Mutual Friend. Tennyson is singularly accurate in all astronomical details. In Mayd such details are somewhat freely introduced; but so correctly that Mr. Hind himself could take no exception to any of the astronomical state

So much for the motions of the stars on any given night. But there is also an apparent motion of the star-sphere from day to day. I have mentioned that the star-sphere turns once completely round on its axis in the course of rather less than twenty-four hours. Thus in twenty-four hours it has gone rather more than once round. Hence, if we look at the heavens night after night at the same time, we notice precisely the same kind of change as when we look at the heavens hour after hour on the same night. Suppose that we look at the stars at ten o'clock on any night and note their position, and that again we note the position of the stars at eleven o'clock on the same night; then, if afterwards we examine the stars night after night at ten o'clock, we shall find that at the end of about fifteen days they have at this hour the same position that they had on the first night at eleven o'clock-that is, they have advanced by one hour's motion. In a month or thereabouts, they will be found to have advanced by two hours' motion. In a year they advance by twenty-four hours' motion, that is, by one complete rotation, so that they have resumed their original positions. In fact, in the course of a year the starsphere turns round once oftener than there are days in the year.*

If the learner, recalling the nature of the rotation to which the star-sphere is subject, remembers also that (roughly) the star-sphere turns round once in a day, he will know what changes to expect as any night progresses, and if he further remembers that (roughly) the star-sphere makes one extra turn in the year, he will know what changes to expect as the year progresses.

Now, to aid the student in learning the names and features

The amount by which the stars have advanced each night on the position they held at the same hour on the preceding night is by no means so small as is, perhaps, commonly imagined. This is easily tested. Let there be an upright of any sort a few yards to the north of the observer's station, and let him notice the exact hour when a star (at a fair height above the horizon) appears from behind the edge of this upright. At this hour on the next night he will find that, as seen from the same station, the star is about two moon's breadths past the upright's edge. The observer should look through a fixed tube placed in the same position on each night.

of the star-groups, maps may be devised on one of two plans. Either we may have maps showing the aspect of the heavens at different hours and at different seasons; or, we may have maps constructed with sole reference to the star-sphere itself. Maps of the former kind form perhaps the simplest possible introduction to a knowledge of the heavens. If they are properly constructed, the learner can at once turn to the map representing the heavens at any hour and season of any year (such maps serve for all years), and then he can at his leisure compare the stars he sees with those pictured in the map. In my work, entitled Half-Hours with the Stars, the maps not only serve these purposes, but they show at once towards what point of the horizon and at what height each star is situated. Maps of the second class are, however, absolutely necessary to supplement the information given by the others. All considerations are sacrificed to simplicity in the construction of maps of the former kind; no meridians or parallels can be shown; none but the brighter stars can appear; only those parts of the star-sphere can be included which actually rise above the horizon; and a variety of details, which even the beginner soon begins to require,* must necessarily be omitted. Maps of the latter kind form an atlas of the stellar globe, and can be made to include any details which may be desired.

The present work is an atlas of this sort. It pictures in twelve maps the stellar sphere which surrounds our earth; and it is as suitable for use in one country as in others—at our

* It must not be supposed, however, that such maps are useful only for beginners. It is most convenient, even for the advanced student of astronomy, to have a book from which he can at once determine what stars are above the horizon, and in what positions, at any hour of any night. I believe, also, that such a work as my Constellation-Seasons (now out of print), in which the equator, ecliptic, colures, &c., were depicted, is calculated to serve very useful purposes. If the lithographs of those charts had been better drawn than they actually were (owing to the difficulties met with in transfer work), I should not have suffered the work to be out of print, especially as the sale of the first and only edition was very encouraging. If I should at any time republish the work, I should redraw the maps for photolithographic reproduction.

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antipodes as here in England, in the Western as in the Eastern Hemisphere.

But a globe may be pictured in maps in many different ways; some useful for one purpose, some for others. It is necessary to describe the plan on which the present atlas has been formed, before considering its use in helping the student of the heavens.

Any flat pictures of portions of a globe must necessarily be somewhat distorted. The larger the portion, the greater will be the distortion. Yet we must not divide the celestial globe into too many parts to form a celestial atlas; because if we do, the student will be puzzled to know how these parts fit in, so to speak, to form the globe. There is a similar objection to the irregular division of the celestial globe. Some regular plan of dividing the globe into a moderate number of portions must be employed.

Only two such plans (out of five which are possible) need be here considered. According to one, the globe is divided into six equal portions; according to the other, into twelve.

The first is easily understood. Imagine a case shaped like a die or cube—that is, with six square sides-the sides being made of some elastic material; and conceive that by blowing air into this case the six elastic sides are made to bulge out in such sort that the case becomes globe-shaped. Then the six sides, which had been square and flat, are changed into curved surfaces, all four-pointed and all alike in shape and size. If we suppose the star-sphere divided into six such portions, and an atlas constructed to show these portions in six separate maps, such an atlas would correspond to the first plan.

The fault of this mode of dividing the star-sphere is that the six parts are too large to be well shown on a flat surface. The distortion, especially for parts near the corners of the six portions, must be considerable. The plan has been employed in Mr. Keith Johnstone's atlas, and in the atlas published by the Society for Diffusing Useful Knowledge; but the distortion is so great in these atlases that a small space on the starsphere occupies an area more than five times greater if it falls near an angle of the map than if it falls near the centre. The