proportionate to the amount of information it is intended to exhibit, and that this expenditure should be proportional to the importance of the area to be surveyed, that is, to its wealth and the density of its population, seems evident; and this would lead us to infer that the mostly thickly settled and richest countries must have the most accurate maps. This, however, is not uniformly the case; the general intelligence of the people, or their rulers, their habits of thought, and their appreciation of the practical use to which scientifically accurate work may be put, are also important factors, as will perhaps be discovered from what is said further on in these pages.

The determination of the scale to be adopted in any topographical survey means, then, the determination of the accuracy with which it is to be conducted, or the amount of detail to be put into the work. And it does not appear difficult to understand that, in a large country or state, it may be advisable to employ several different scales, or to proportion the accuracy of the survey to the importance of any separate division. A country like Belgium, of very small area, and with a population about equally distributed over its surface, would naturally be satisfied with much less variety of scale than would be advisable in Norway or Sweden, some portions of whose territory are very thinly inhabited. The same considerations would apply still more forcibly to our own country, great areas of which are almost worthless, or at best of no importance, except as having to be passed over in order to get in the shortest way from one part to another of our extended territory. It is true, however, that the same country usually requires maps on more than one scale, even if the survey is to be equally accurate over the whole area. For local details and for ordinary practical use, a map on a large scale is needed; but this requires that the work shall occupy a great number of sheets, on each of which only a small area can be given; so that, for general geographical purposes, where the eye needs to have before it at one time a considerable extent of territory, in order to obtain a connected idea of its physical features, it is necessary that a compilation on a reduced scale should be made, by which a considerable number of sheets are compressed within the limits of one. Thus in the Ordnance Survey of Great Britain, maps

on both the six-inch and the one-inch scale are furnished, and are equally in demand.

Having determined the degree of accuracy with which the work shall be prosecuted and the scale or scales which shall be used, it is necessary to decide how the vertical element, already alluded to, shall be exhibited. And this is a matter of some difficulty, and one in regard to which there have been formerly considerable differences of opinion. We have seen how an idea of the relief of the surface can be given by means of light and shade, in the case of the photographic copy of a model, which is wonderfully effective in conveying the idea of differences of elevation, the effect depending exclusively on the distribution of the light and shade caused by the obliquely falling rays of the sun; were a photograph to be taken from such a model, with the rays descending vertically on it, the illusion or perception of the relief of the surface would be entirely lost. The same thing can be done, although less perfectly, by a skilful handling of the brush on paper, or by the lithographer on the stone with the crayon, giving a sort of bird's-eye view of the region to be mapped; and, in the hands of a thoroughly artistic worker, with an eye for topography, much may be accomplished in this way. This method of indicating the relief of the surface is used now to some extent, especially in maps of regions covered by mountain ranges, where a considerable area is to be shown at once, and where, from the nature of the country, as well as from the necessarily small scale adopted, it is not expected that anything more than a general idea of the topography can be given. The map of the Thian-Schan range, recently published by Petermann, and that of California and Nevada, by the Geological Survey of the firstnamed State, are good instances of the application of this method.

But for an accurate topographical survey, where it is desired and expected that a close approximation to the vertical element shall be obtainable from the map, and not merely a picture conveying a general idea to the mind, other methods have to be adopted. An approach to accuracy is made by shading the hills by means of short, straight lines, or hachures, as they are generally called. Most of our ordinary geographical maps

have the position and direction of the mountain ranges delineated on them by these hachures, which, as ordinarily used, are only a sort of conventional symbol, intended to indicate vaguely the existence of a hill or ridge, or series of ridges, and too frequently having a perverse resemblance to a cluster of caterpillars crawling over the surface of the map. The original idea of these lines is, that they indicate the course which a stream of water would take in running down the side of the range, in the line of most direct descent, thus furnishing a clew to the direction of the slope. Many years ago a German topographer, named Lehmann, gave a more precise value to these hachure lines, by proportioning their thickness to the angle of slope of the surface they were intended to represent. Thus, by this system the steeper portions of the slopes appear on the map in darker shade than the less inclined surfaces, so that the relief is indicated something in the same way as if the hill-shading were done by the brush, in the manner indicated above, while the eye can determine from the thickness of the lines employed, although only approximately, the angle of the slopes. Many beautiful maps have been made, according to this system or some modification of it. Thus the Dufour map of Switzerland, as it is called, in which Lehmann's method, modified by the introduction of an oblique illumination, was used, is a masterpiece of the chartographic art.

Topographical maps were formerly made, in Europe, almost exclusively for the purposes of military defence, that is, to guide generals in arranging the movements of their armies ; and it is only in later years that the civil uses of these surveys have become more prominent. Hence, as the demands of commerce, agriculture, and manufactures have begun to be heard more frequently and louder than those of war, more accurate work has been required, and the insufficiencies of the hachure method for details have become evident. The angle of a slope was the important element when the movement of artillery up or down it was the question to be decided; but the civil engineer, who has the more peaceful object in view of building a railroad or cutting a ditch, wants a section of the line he has to pass over, or, indeed, sections of many lines, that he may choose the one best adapted to his purpose; and

he wishes to know the absolute height of each point in that section above the sea-level, or some other datum line, which may have been selected as the plane to which all the heights should be referred. This is done by means of contour lines drawn upon the map, so as to connect points having the same elevation above the datum line, and at greater or less vertical distance from each other, according to the amount of accuracy and detail which may be required. The steeper the slope the nearer to each other the contours will fall, so that an increased steepness of the ranges will be indicated to the eye at once by the crowding together of the lines, thus reproducing, in a measure, the effect of the brush-shading spoken of above. This method may be understood more easily by those unaccustomed to maps made in this way by using a simple illustration. If we suppose in a lake a mountainous island, a thousand feet high at its highest point, to be sunk by ten successive stages of one hundred feet each, then at each stage of the sinking the water will meet the land and mark a line upon it connecting all the points which are respectively 100, 200, 300, and so on, feet above the original level of the lake. The lines thus marked by the rising edge of the water would be exactly in the places which contour lines accurately run at vertical distances of 100 feet would occupy. Any person looking at such contour lines would see at a glance what portions of the island were 100, 200, and so on, feet above the lake level; and if the slopes were pretty regular, he would be able to get a good idea of the relative heights of all the other points intermediate between those lines. The advantage of this system of contouring, as it is called, is, that from any map on which such contour lines are indicated a section can be drawn at once, which will more or less accurately reproduce the slopes and exhibit the elevation of all points on that section. And such sections are invaluable and, in fact, indispensable, in operations connected with the building of roads, railroads, ditches, canals, and engineering work of all kinds. The degree of accuracy with which such sections can be drawn. depends on the distance apart of the contours. In cases of great importance, and over limited areas, they may be fixed at a distance of two or three feet apart vertically. In ordinary

topographical surveys they may be drawn at distances of from twenty to a hundred feet or more, according to the nature of the country and the contemplated accuracy of the work.

A good topographical map of any region, therefore, will have indicated upon it all natural objects, such as lakes, rivers, and smaller water-courses; artificial ones, namely, boundaries of fields, enclosures, roads, houses, etc.; and, besides these, it will exhibit to the eye and furnish for use the vertical elevation at all points above the level of the sea, this being usually chosen as the datum line from which the altitudes are reckoned. And by "level of the sea" is usually meant mean low tide, or else the mean between mean low and mean high tide.

Thus far we have chiefly confined our remarks to the methods by which topographical information is brought into an available form, so as to be presented to the public on paper. And, indeed, many persons are so little acquainted with this kind of work, that they imagine the plotting of the survey and putting it into the form of a map to be the essential thing. This is the case indeed with most or all school-maps and with many others which are offered to the public, especially in this country; they are simply compilations and workings over of other people's labors. But wherever an accurate map exists, there must have been done by somebody, and at somebody's expense, in the field, an amount of labor, and that of a kind demanding the highest degree of skill and immense patience, compared with which the mere plotting and engraving of the work is comparatively insignificant. Few persons, except those themselves professionally engaged in such surveys, have any idea of the amount of labor, and of course of time and money, required by a thoroughly accurate topographical survey, even if the area over which it extends be one of moderate dimensions. It may seem an easy matter to measure a line on the ground of half a dozen miles in length; and so it is, if the region be level and it be a matter of no consequence whether the measurement be correct, provided it comes within a few inches of the truth. If a traveller wished to know the distance from one town to another, he would consider it quite a superfluous degree of accuracy that he should be informed to the nearest rod; while in