they are to be looked for on the sky towards the south-east. Also, it is seen that the two stars lie about one-fourth of the way from the centre towards the circumference. Hence, on the sky, the stars will be found about one-fourth of the way from the zenith towards the horizon: Castor will be seen immediately above Pollux. Next, suppose that at one of the hours named the observer wishes to learn what stars are visible towards the west and north-west:—Turning the map until the portion of the circumference marked W ... N.W. is lowermost, he sees that in the direction named the square of Pegasus lies not very high above the horizon, one diagonal of the square being vertical, the other nearly horizontal. Above the square is Andromeda, to the right of which lies Cassiopeia, the stars β and ε of this constellation lying directly towards the north-west, while the star α lies almost exactly midway between the zenith and the horizon. Above Andromeda, a little towards the left, lies Perseus, Algol being almost exactly towards the west and one-third of the way from the zenith towards the horizon (because one-third of the way from the centre towards the circumference of the map). Almost exactly in the zenith is the star δ Aurigæ.

The four maps are miniatures of Maps I., IV., VII., and X. of my 'Constellation Seasons,' fourth-magnitude stars, however, being omitted.

PLATES II., III., IV., and V., illustrating Chapters II., III., IV., and V.

Plates II. and IV. contain four star-maps. They not only serve to indicate the configuration of certain important star-groups, but they illustrate the construction of maps, such as the observer should make for himself when he wishes to obtain an accurate knowledge of particular regions of the sky. They are all made to one scale, and on the conical projection—the simplest and best of all projections for maps of this sort. The way in which the meridians and parallels for this projection are laid down is described in my 'Handbook of the Stars.' With a little practice a few minutes will suffice for sweeping out the equidistant circular arcs which mark the parallels and ruling in the straight meridians.

The dotted line across three of the maps represents a portion of the horizontal circle midway between the zenith and the horizon at the hour at which the map is supposed to be used. At other hours, of course, this line would be differently situated.

Plates III. and V. represent fifty-two of the objects mentioned in the above-named chapters. As reference is made to these figures in the text, little comment is here required. It is to be remarked, however, that the circles, and especially the small circles, do not represent the whole of the telescope's field of view, only a small portion of it. The object of these figures is to enable the observer to know what to expect when he turns his telescope towards a difficult double star. Many of the objects depicted are very easy doubles: these are given as objects of reference. The observer having seen the correspondence between an easy double and its picture, as respects the relation between the line joining the components and the apparent path of the double across the telescope's field of view, will know how to interpret the picture of a difficult double in this respect. And as all the small figures are drawn to one scale, he will also know how far apart he may expect to find the components of a difficult double. Thus he will have an exact conception of the sort of duplicity he is to look for, and this is—crede experto—a great step towards the detection of the star's duplicity.

PLATES VI. and VII., illustrating Chapters VI. and VII.

The views of Mercury, Venus, and Mars in these plates (except the smaller view of Jupiter in Plate VII.) are supposed to be seen with the same "power."

The observer must not expect to see the details presented in the views of Mars with anything like the distinctness I have here given to them. If he place the plate at a distance of six or seven yards he will see the views more nearly as Mars is likely to appear in a good three-inch aperture.

The chart of Mars is a reduction of one I have constructed from views by Mr. Dawes. I believe that nearly all the features included in the chart are permanent, though not always visible. I take this opportunity of noting that the eighteen orthographic pictures of Mars presented with my shilling chart are to be looked on rather as maps than as representing telescopic views. They illustrate usefully the varying presentation of Mars towards the earth. The observer can obtain other such illustrations for himself by filling in outlines, traced from those given at the foot of Plate VI., with details from the chart. It is to be noted that Mars varies in presentation, not only as respects the greater or less opening out of his equator towards the north or south, but as respects the apparent slope of his polar axis to the right or left. The four projections as shown, or inverted, or seen from the back of the plate (held up to the light) give presentations of Mars towards the sun at twelve periods