The excellent map resulting from the arduous labours of these astronomers is simply a map: it does not pretend to be a picture. The asperities and depressions are symbolized by a conventional system of shading and no attempt is made to exhibit objects as they actually appear in the telescope. A casual observer comparing details on the map with the same details on the moon itself would fail to identify or recognize them except where the features are very conspicuous. Such an observer would be struck by the shadows by which the lunar objects reveal themselves: he would get to know them mostly by their shadows, since it is mainly by those that their forms are revealed to a terrestrial observer. But such a map as that under notice indicates no shadows, and objects have to be identified upon it rather by their positions with regard to one another or to the borders of the moon than by any notable features they actually present to view. This inconvenience occurred to us in our early use of Beer and Maedler’s chart, and we were induced to prepare for ourselves a map in which every object is shown somewhat, if imperfectly, as it actually appears at some period of a lunation. This was done by copying Beer and Maedler’s outlines and filling them up by appropriate shading. To do justice to our task we enlarged our map to a diameter of six feet. Upon a circle of this diameter the positions and dimensions of all objects were laid down from the German original. Then from our own observations we depicted the general aspect of each object: and we so adjusted the shading that all objects should be shown under about the same angle of illumination—a condition which is never fulfilled upon the moon itself, but which we consider ourselves justified in exhibiting for the purpose of conveying a fair impression of how the various lunar objects actually appear at some one or other part of a lunation. The picture-map thus produced has been photographed to the size convenient for this work: and in order to make it available for the identification of such objects as we may have occasion to refer to, we have placed around it a co-ordinate scale of arbitrary divisions by which any object can be found as by the latitude and longitude divisions upon a common geographical map. We have also prepared a skeleton map which includes the more conspicuous objects, and which faces the picture map (Plates IV. and V.) The numbers on the skeleton map are those given in the second column of the accompanying table. The table also gives the co-ordinate positions of the various craters, the names of which are, for convenience of reference, printed in alphabetical order. Name. Number. Map Ordinates.