In the representation of relief on the one inch series, two systems are common, contours and hachures. Contours represent the successive shore lines which water at rest would form in following the modelling of the ground at successive stages or elevations. If now we assume that the water, having reached the highest point, is allowed to retreat steadily to sea level the paths which the particles of water would take from all points of the surface are those which the engraver would endeavor to reproduce in the shade lines of a hachured map. In addition he would adopt an arbitrary scale of shade increasing with the steepness of the slopes, from white on a horizontal surface to dead black on slopes of forty-five degrees, or greater, to produce the effect of a model of the surface illuminated from above. In the Irish maps this effect is bolder and more artistic, an illumination from the northeast quarter having been carried out. The shade lines still preserve the paths of particles of water in motion on the surface, the color values being deeper on the eastern and southern slopes, shadows have even been projected across valleys and horizontal surfaces are in half tone, producing much the same effect as the illumination of the country at sunset in midsummer. The Irish maps exhibited are considered the finest specimens of careful hill shading and will bear critical examination. For comparison with these, other topographic maps are exhibited of many scales and countries. So far attention has simply been drawn to a few of the problems of map-making, which are, briefly: 1st. The reproduction on a finite scale on a plain surface, of the natural features of the terrain, with all the artificial boundaries and objects added by man, so far as the scale permits. 2d. The extension of such a series of maps to cover a large area of country still carried out with as little distortion as possible. 3d. The reproduction of such maps on suitable scales to meet all demands. If the conception is still carried out that the map, at a distance of two feet, is but the image of the ground viewed from above, then the cadastral map of England, from which areas of fields and estates are measured for valuation purposes, would represent a view of the country from above at a range of 5,000 feet or nearly one mile, and a town plan, an image at 1,000 feet or a possible view from a series of Eiffel towers. This suggestion of an observer stationed in a balloon will not have been valueless if it draws attention to the fact that vastly more information is given on the map than it would be possible for any single observer to discover from an elevated station with an unobstructed view, the map being the compilation of the results of hundreds of observations by many workers, and that its scale and the amount and character of the detail shown have been specially designed to meet definite ends.