Measurement of Areas

MEASUREMENT OF AREAS This is easy if the map at our disposal is drawn on an equal area projection. In that case we need simply cover the map with a network of squares—the area of each of which has been de termined with reference to the scale of the map—count the squares, and estimate the contents of those only partially enclosed within the boundary, and the result will give the area desired. A planimeter is still quicker.

When dealing with maps not drawn on an equal area projection we substitute quadrilaterals bounded by meridians and parallels, the areas for which are given in the "Smithsonian Geographical Tables" (1894), or similar works.

Models or Relief Maps.

These are intended to present a rep resentation of the ground which shall be absolutely true to nature.

The object, however, can be fully attained only if the scale of the map is sufficiently large, if the horizontal and vertical scales are identical, so that there shall be no exaggeration of the heights, and if regard is had, eventually, to the curvature of the earth's surface.

Relief maps on a small scale necessitate a generalization of the features of the ground, as in the case of ordinary maps, as like wise an exaggeration of the heights. Thus on a relief on a scale of :I,000,000 a mountain like Ben Nevis would only rise to a height of 1.3 millimetres.

The methods of producing reliefs vary according to the scale and the materials available. A simple plan is as follows: draw an outline of the country of which a map is to be produced upon a board ; mark all points the altitude of which is known or can be estimated by pins or wires clipped off so as to denote the heights; mark river-courses and suitable profiles by strips of vellum and finally finish your model with the aid of a good map, in clay or wax. A pantograph armed with cutting-files which carve the relief out of plaster of Paris may be used.

Globes.

It is impossible to represent on a plane the whole of the earth's surface, or even a large extent of it, without a con siderable amount of distortion. On the other hand a map drawn

on the surface of a sphere representing a terrestrial globe will prove true to nature, for it possesses, in combination, the qual ities which the ingenuity of no mathematician has hitherto suc ceeded in imparting to a projection intended for a map of some extent, namely, equivalence of areas, of distances and angles.

It should be observed here that our globes take no account of the oblateness of our sphere; but as the difference in length between the two axes of the earth only amounts to about it could be shown only on a globe of unusual size.

Map Printing.

Maps were first printed in the second half of the 15th century. Those in the Rudimentum novitiarum pub lished at Liibeck in 1475 are from woodcuts, while the maps in the first two editions of Ptolemy published in Italy in 1472 are from copper plates. Wood engraving kept its ground for a considerable period, especially in Germany, but copper in the end supplanted it. The art of lithography has greatly affected the production of maps. Owing to the great weight of stones, their cost and their liability of being fractured in the press, zinc plates or alu minium plates, have largely taken the place of stone. The proc esses of zincography are essentially the same as lithography. Photographic processes are utilized not only in reducing maps to a smaller scale, but also for producing stones and plates from which they may be printed. The manuscript maps intended to be produced by photographic processes upon stone, zinc or alumi nium, are drawn on a scale somewhat larger than the scale on which they are to be printed, thus eliminating all those imperfec tions which are inherent in a pen-drawing. The saving in time and cost by adopting this process is considerable.

For details of the various methods of reproduction see LITHOG RAPHY : Process, etc.