series, will serve to explain the construction of the atlas better than any verbal account. The student should, in a special manner, note the overlapping spaces in the index-plates and compare them with the corresponding spaces in the atlas maps. He will thus learn to recognise the value of those overlaps, and the means they supply for passing readily from one map to another. He will notice, further, that the numbers round the atlas maps (close by the circular frame) show what map to turn to, when the student wishes to pass, in any direction, beyond the limits of the map he is engaged with.

In comparing the heavens with the maps of this atlas, it is to be noticed that the whole of the space included in Map 1 is at all times visible. This is the polar map; and if on a clear night the student turn towards the north and raise his eyes to a point somewhat more than halfway from the horizon towards the point overhead, he will recognise, in the stars there seen, the group which lies at the centre of Map 1.

เ

It is customary to find the pole-star (marked Polaris) by means of the seven stars of the Great Bear (Ursa), shown at the top of Map 1. These stars cannot be mistaken, and the two marked a and ẞ serve as pointers to the pole, lying as they do very nearly on a line with Polaris. Fig. 7 shows where the seven stars are to be looked for at four seasons of the year, at the hours named beside the figure. It will be understood that fig. 6 presents one half of the celestial vault-the northern half. On examining different parts of the figure, the part marked overhead' is always to be regarded as the top, the semicircular boundary (corresponding to the horizon) being the bottom. For instance, in seeking to determine where the seven stars are at midnight on December 21 (or at ten on January 21), turn round fig. 7 until the group of seven stars, marked II., is under the point marked 'overhead' (so that the word north-east is horizontal). Then the seven stars are seen, the three forming the Bear's tail (or the horses of the Waggon, or the handle of the Plough), being lowermost. From the position of the seven stars the student learns that if he looks due north-east, and towards a point exactly halfway between

Pole-star is at

FIG. 7, showing the elevation and bearing of the Pointers, Pole-star, &c., at the following seasons and hours:

1

December 21

January 5

January 21

February 5

II.

II.

2

April 23

May 8

III.

III.

3

July 7

July 22

August 7

IV.

IV.

the horizon and the point overhead, his view will be directed towards the middle of the group of four stars forming the Waggon or the body of the Plough. He can therefore readily find the seven bright stars, and the two which lie uppermost (almost on a horizontal line) are the Pointers. They show him the pole-star on their left,—and at the moment nearly on the same level, at the place marked 2,—the three bright stars of the Little Bear lying in the position marked 11. And so with the cases corresponding to other seasons. easy for him to see where the seven stars will be at intermediate hours or seasons. The large arrows indicate the direction in which the seven stars are carried by the daily rotation of the star-sphere. The course of the pair of stars (called 'the Guardians of the Pole') belonging to the Little Bear is also shown by arrows; and arrows are placed on the Pointers in the four several positions indicated in the figure.

Also it is very

Now the learner, being able at all seasons of the year to find these leading stars of Map 1, can not only always study any of the constellations belonging to that map, but can at any time pass from that map to any of the other maps (2, 3, 4—to 11) the stars belonging to which are at that time suitably placed for observation. He can at once see from Map 1 itself which of the other maps can be most conveniently used. For instance, supposing the date to be March 25, and the hour midnight, he will find that the Great Bear is as at III., fig. 7, nearly overhead; and to compare Map 1 with the heavens, he holds it with Ursa uppermost, and finds Cassiopeia low down towards the north, the stars of Draco towards the north-east high up, and so forth. Now if he wishes to examine the stars lying beyond the Great Bear, or on the southern side of the point overhead, Map 1 at once tells him which maps to employ. For he finds on the edge, close by the 's even stars' of Ursa, the words Map 8 on one side and Map 6 on the other; so that either of these maps will serve his purpose. He turns to Map 8 and finds in it, near the top (where the words Map 1 are written), the three tail-stars, and can so proceed to find the stars of Boötes, Serpens, and so on. Or he turns to Map 6,

and finds again at the top the Pointers and another of the four body stars, and can thence proceed to find the stars of Leo, Gemini, and so forth.

But it is convenient for him to know, in an independent manner, what maps of the series 2, 3, 4-11, can be most usefully studied at any season of the year. It is also well for him to know in what position he may expect to find the spaces corresponding to the different maps.

For this purpose figs. 8 and 9 have been provided. I here represent severally the whole celestial vault, the centre of each being the point overhead, and the circumference being the horizon; and they show how the spaces corresponding to the several maps of the series are arranged when either 2, 4, 6, 8, or 10 has its centre due south, or else 3, 5, 7, 9, or 11. In fig. 8 Map 2 is shown with its centre due south, in fig. 9 Map 3; and it will be observed that the rotation of the heavens carries the space corresponding to Map 2, from the position shown in fig. 8 to the position shown in fig. 9, in the tenth part of a day, or in 2 h. 24 m.

The following tables serve to show at what hours and seasons the centres of the several maps occupy such positions as are indicated in figs. 8 and 9.

The interpretation of these tables is exceedingly simple, as is also the method of employing them. Thus the first table

* These figures have both been carefully drawn, so that the actual position of each map, not only with respect to the compass points, but also as regards elevation above the horizon, is exactly indicated. For example, in fig. 8, the common intersection of Maps 2, 3, and 4 is seen to lie almost exactly towards the south point, marked S.E., and almost exactly four-ninths of the way from that point towards the centre of the map. The corresponding point on the heavens (close by & Arietis) lies as nearly due S.E., and as nearly 36° above the horizon at midnight on Sept. 21. And so of all other points of intersection as well as of all points round the circumference of the different maps. The construction of both the figures involved some interesting—but not altogether simple-geometrical problems. It may be added that the equations to the curves formed in the projection by the really circular boundaries of the maps are rather singular in form.

C

shows us that at 10 P.M, on March 16, the celestial space corresponding to Map 8 lies towards the east (in the position occupied by Map 4 in fig. 8); the space corresponding to

FIG. 8.

Showing the arrangement of the spaces included in the maps of this atlas, when the centre of one of the Maps 2, 4, 6, 8 or 10 is due south.

The actual arrangement is such that Fig. 8 corresponds to the aspect of the heavens at midnight

(The student should make five tracings of each map, num

Map 6 is due south (in the position occupied by Map 2 in fig. 8); and so on. Again, suppose we require to know when the space corresponding to Map 7 will be well placed for ob