It behoves me at this point to speak of star-maps. Such maps are of many different kinds. There are the Observatory maps, in which the places of thousands of stars are recorded with an amazing accuracy. Our beginner is not likely to make use of, or to want, such maps as these. Then there are maps merely intended to give a good general idea of the appearance of the heavens at different hours and seasons. Plate I. presents four maps of this sort; but a more complete series of eight maps has been published by Messrs. Walton and Maberly in an octavo work; and my own 'Constellation-Seasons' give, at the same price, twelve quarto maps (of four of which those in Plate I. are miniatures), showing the appearance of the sky at any hour from month to month, or on any night, at successive intervals of two hours. But maps intermediate in character to these and to Observatory maps are required by the amateur observer. Such are the Society's six gnomonic maps, the set of six gnomonic maps in Johnstone's 'Atlas of Astronomy,' and my own set of twelve gnomonic maps. The Society's maps are a remarkably good set, containing on the scale of a ten-inch globe all the stars in the Catalogue of the Astronomical Society (down to the fifth magnitude). The distortion, however, is necessarily enormous when the celestial sphere is presented in only six gnomonic maps. In my maps all the stars of the British Association Catalogue down to the fifth magnitude are included on the scale of a six-inch globe. The distortion is scarcely a fourth of that in the Society's maps. The maps are so arranged that the relative positions of all the stars in each hemisphere can be readily gathered from a single view; and black duplicate-maps serve to show the appearance of the constellations. It is often convenient to make small maps of a part of the heavens we may wish to study closely. My 'Handbook of the Stars' has been prepared to aid the student in the construction of such maps. In selecting maps it is well to be able to recognise the amount of distortion and scale-variation. This may be done by examining the spaces included between successive parallels and meridians, near the edges and angles of the maps, and comparing these either with those in the centre of the map, or with the known figures and dimensions of the corresponding spaces on a globe. We may now proceed to discuss the different tests which the intending purchaser of a telescope should apply to the instrument.