Efforts have been made of late years to improve the available methods of representing ground, especially in Switzerland, but the so-called stereoscopic or relief maps produced by F. Becker, X. Imfeld, Kümmerly, F. Leuzinger and other able cartographers, however admirable as works of art, do not, from the point of utility, supersede the combination of horizontal contours with shaded slopes, such as have been long in use. There seems to be even less chance for the combination of coloured strata and hachures proposed by K. Peucker, whose theoretical disquisitions on aerial perspective are of interest, but have not hitherto led to satisfactory practical results.[3]
The above remarks apply more particularly to topographic maps. In the case of general maps on a smaller scale, the orographic features must be generalized by a skilful draughtsman and artist. One of the best modern examples of this kind is Vogel’s map of Germany, on a scale of 1 : 500,000.
Selection of Names and Orthography.—The nomenclature or “lettering” of maps is a subject deserving special attention. Not only should the names be carefully selected with special reference to the objects which the map is intended to serve, and to prevent overcrowding by the introduction of names which can serve no useful object, but they should also be arranged in such a manner as to be read easily by a person consulting the map. It is an accepted rule now that the spelling of names in countries using the Roman alphabet should be retained, with such exceptions as have been familiarized by long usage. In such cases, however, the correct native form should be added within brackets, as Florence (Firenze), Leghorn (Livorno), Cologne (Cöln) and so on. At the same time these corrupted forms should be eliminated as far as possible. Names in languages not using the Roman alphabet, or having no written alphabet should be spelt phonetically, as pronounced on the spot. An elaborate universal alphabet, abounding in diacritical marks, has been devised for the purpose by Professor Lepsius, and various other systems have been adopted for Oriental languages, and by certain missionary societies, adapted to the languages in which they teach. The following simple rules, laid down by a Committee of the Royal Geographical Society, will be found sufficient as a rule; according to this system the vowels are to be sounded as in Italian, the consonants as in English, and no redundant letters are to be introduced. The diphthong ai is to be pronounced as in aisle; au as ow in how; aw as in law. Ch is always to be sounded as in church, g is always hard; y always represents a consonant; whilst kh and gh stand for gutturals. One accent only is to be used, the acute, to denote the syllable on which stress is laid. This system has in great measure been followed throughout the present work, but it is obvious that in numerous instances these rules must prove inadequate. The introduction of additional diacritical marks, such as ˉ and ˜, used to express quantity, and the diaeresis, as in aï, to express consecutive vowels, which are to be pronounced separately, may prove of service, as also such letters as ä, ö and ü, to be pronounced as in German, and in lieu of the French ai, eu or u.
The United States Geographic Board acts upon rules practically identical with those indicated, and compiles official lists of place-names, the use of which is binding upon government departments, but which it would hardly be wise to follow universally in the case of names of places outside America.
Measurement on Maps
Measurement of Distance.—The shortest distance between two places on the surface of a globe is represented by the arc of a great circle. If the two places are upon the same meridian or upon the equator the exact distance separating them is to be found by reference to a table giving the lengths of arcs of a meridian and of the equator. In all other cases recourse must be had to a map, a globe or mathematical formula. Measurements made on a topographical map yield the most satisfactory results. Even a general map may be trusted, as long as we keep within ten degrees of its centre. In the case of more considerable distances, however, a globe of suitable size should be consulted, or—and this seems preferable—they should be calculated by the rules of spherical trigonometry. The problem then resolves itself in the solution of a spherical triangle.
In the formulae which follow we suppose l and l′ to represent the latitudes, a and b the co-latitudes (90 − l or 90° − l′), and t the difference in longitude between them or the meridian distance, whilst D is the distance required.
If both places have the same latitude we have to deal with an isosceles triangle, of which two sides and the included angle are given. This triangle, for the convenience of calculation, we divide into two right-angled triangles. Then we have sin 1⁄2 D = sin a sin 1⁄2 t, and since sin a = sin (90° − l) = cos t, it follows that
sin 1⁄2 D = cos l sin 1⁄2 t.
If the latitudes differ, we have to solve an oblique-angled spherical triangle, of which two sides and the included angle are given. Thus,