route maps which were prepared under the direction of King Sesostris, probably during the 12th dynasty; certain old maps in the Alexandrian Library referred to by Strabo and probably collected by Eratosthenes, and the map on papyrus in the museum at Turin, which represents the topographical features of a gold mining district in Nubia. Maps of equal if not greater antiquity are recorded among the ancient Babylonians, who originated the idea of dividing the ecliptic into the 12 signs of the zodiac and also the sexagesimal system of numeration which led to the custom of dividing the circle into 360 degrees of 60 minutes each, with each minute subdivided into 60 seconds, and also to the corresponding divisions of the hour.

Among the Greeks the first map appears to be that of Anaximander about 560 B.C. His work was followed about 100 years later by that of Democritus of Abdera, whose work appears to have been based upon data obtained by him

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formation prior to the 16th century. In this connection it is well to understand that from the time of Aristotle (384 B.C.) the mathematicians, astronomers and geographers were well aware of the fact that the earth was a sphere and not the flat disc of the Ionic Greeks in the days of Anaximander, the ancient Egyptians and the Babylonians. Therefore, the mapmaking problem solved by Hipparchus and the successful solution of which formed the foundation for Ptolemy's work involved the devising of a projection by means of which the spherical surface of the earth could be represented on a plane surface. Although Ptolemy is credited with being the father of rational cartography, it does not appear that any maps were actually drawn by him. The oldest editions of the Ptolemaic maps on record appear to be the work of Agathodæmon, a mathematician who lived in the 5th century A.D., and constructed maps accurately based upon Ptolemy's data.

self in his travels, which extended to Persia and perhaps as far as India, and added considerably to the east and west dimensions of the known world areas. These circumstances probably led to the depiction of the world disc in the form of an oval, a distinct departure from the circular form employed by Anaximander and others. About 150 B.C. Hipparchus introduced among the Greeks the Babylonian system of numeration, and discarding the unreliable geographical data of Erastosthenes and others, which were mainly obtained from travelers, suggested the use of only actual astronomical determinations of the latitudes and longitudes of the various points as the true basis for checking distances and directions. His suggestions were practically carried out by Marinus of Tyre, whose work was subsequently corrected by Ptolemy about the 2d century A.D., into a map which is generally considered to be the most complete summary of geographical in

Among the Romans the art of map-making was confined to various kinds of sketch maps valuable for military and political purposes. They did not apply the scientific methods of the Greeks, and although both Cicero and Seneca mention general and topographical maps, and it is a fact that a survey of the whole Roman Empire was made during the reign of Augustus, the grave errors of Ptolemy's maps in all of the Mediterranean countries awaited rectification until the later Middle Ages.

During the earlier Middle Ages cartography, together with all the other branches of scientific culture, took a step backwards. The ban of the Church was laid heavily on the doctrine of the sphericity of the earth and resulted in the resurrection of the ancient Greek idea of a flat circular earth surrounded by an ocean limited by the edge of the celestial vault. In this way the few maps constructed during this period assumed the form shown in the accompanying

Outline Sketch of Borgia Map (15th Century). nautical charts called "loxodromic" or "compass" maps made their appearance in Italy and were extensively used for navigating purposes between the ports on the shores of the Mediterranean Sea. They were constructed with the aid of the compass and consisted of numerous straight lines which radiated from each port to all the other ports shown on the map. These lines marked with bearings and distances gave the ship courses between the various ports, and the maps embodied in a crude way the basic principle of modern map construction from the data obtained by the triangulations of trigonometrical surveys. With the aid of the loxodromic maps a very accurate representation of

Portion of Loxodromic Map (13th Century).

the coasts of the Mediterranean countries was obtained and served admirably to correct the errors of the Ptolemaic maps which the Renaissance had introduced once more into western Europe.

The close of the 15th century witnessed a

great revival in the art of map-making, which was materially aided by the newly perfected arts of wood and copper engraving. Furthermore, Purbach, Regiomontanus and others introduced trigonometry, and attempts were made to construct maps based on systematic geographical triangulations. Map-making became a favorite occupation with the Germans, French and Italians, and many valuable editions of maps were produced at Strassburg, Ulm, Basle, Cologne, Paris, Lyons, Vicenza, Venice, Bologna and Rome, representing the work of numerous eminent map-makers, among which those of Joh. Ruysch, Nicolaus Donis and Jacob Angelus de Scarparia were of especial prominence and value.

During the 16th century the number of mapmakers increased greatly and brought forward such illustrious cartographers as Johann Werner of Nuremberg, Sebastian Cabot and Gerhard Kramer (more commonly known as Mercator). The general endeavor of the Germans during this period was directed toward the improvement of the methods of projection originated by the Greeks, and led in the case of Mercator to the development of the projection which bears his name, and which is even at the present time very extensively used in the construction of nautical maps. About the latter part of the century the centre of map-making effort was transferred to Holland, mainly through the influence of the collection of maps published by Abraham Ortelius of Antwerp, under the title "Theatrum Orbis Terrarum, which included new engravings of the best maps from all countries. This great work passed through many editions, each successive edition being characterized by an increased number of maps. The 12th edition contained 92 maps. The earlier editions were printed in Latin, but later, editions in German, French, Dutch, Italian and English were produced and obtained world-wide circulation.

The beginning of the 17th century inaugurated a still further improvement in the art, The important inventions, such as the telescope, the sextant and the chronometer, provided means for the taking of more accurate observations relative to time, latitude and longitude, while the application of trigonometry to geodesy by Snellius and Picard's measurement of a degree of the meridian between Paris and Amiens introduced more precise methods of computation. Some of the most important productions of this epoch are those of Johann Baptist Homann of Nuremberg, and the work of Nicolas Sanson, Guill de l'Isle and Jean Baptiste Bourignon d'Anville and other eminent geographers of France working under the royal patronage, and Dowets Atlas published in England under the patronage of the Duke of Argyle.

These important works carry the art of mapmaking through a period of over 200 years and bring it to a point where instead of being treated as a matter of private business enterprise it was taken up as a governmental matter, and the original surveys, together with the maps based thereon, were executed at the cost of the state. The first step in this direction was taken by France, the object being the production of a series of maps for military purposes and as a cadastre for the land tax. For this purpose the entire country was covered with a network of

tion and cannot be made to satisfy any special conditions not included within the scope of their inherent characteristics. The three principal perspective projections were known to the andients, the orthographic and the stereographic being accredited to Hipparchus and the gnomonic to Thales. The globular projection was devised by Nicolisi. They served to introduce projection methods, but with the exception of the gnomonic, which is still used for the construction of star charts and some classes of nautical charts, they have been superseded in the construction of modern maps by the developed projections.

Developed Projections are obtained by the substitution of a cylindrical or a conical surface for the ordinary plane of projection, and that surface, being subsequently developed or rolled out in a plane, gives the projection. The application of this results in two general classes

the great obliquity of the intersections of the meridians and the parallels in the higher latitudes. This projection on account of the close similarity of the figures on the surface of the earth to the corresponding figures on the projection, and the uniformity of scale over the whole map is now extensively used for mapping not only areas of comparatively limited extent, but also for the representation of continental areas of large extent.

For the mathematical operations involved in the computation of the elements of these projections and for illustrations showing how they are plotted in the actual construction of maps, see article under the title PROJECTION in this Encyclopedia.

Practical Methods of Construction,- As a rule, and with but a few exceptions, the drawing of an accurate map is necessarily preceded by an accurate survey of the things to be

Orthographic Projection on the Plane of the Equator.

of developed projections- those employing a cylinder tangent to the sphere, usually at the equator, and those employing a cone tangent, usually at the middle parallel of latitude of the area mapped. Of these, the two most commonly used at the present time are the Mercator and the polyconic projections, the former employing a tangent cylinder and the latter an infinite number of tangent cones. The Mercator was purposely designed for the use of nautical maps and is principally employed for that purpose at the present time. On a map based on this projection the loxodromic curve, that is, the course of a vessel which intersects the successive meridians at a constant angle, is represented on the map as a straight line, thus facilitating the plotting of that course from day to day during the progress of the voyage, and materially assisting in determining the true distance and bearing of the objective point. The polyconic projection appears to have been devised for the purpose of providing a suitable base for the mapping of the Atlantic coast line of the United States by the United States Coast and Geodetic Survey. The direction of this coast line being nearly diagonal to the meridians and parallels, and having a great north and south amplitude, required for its representation a projection which avoided the inherent distortions of the various conic projections due to

Orthographic Projection on the Plane of a Meridian. mapped, and the character of those things together with the purposes for which the survey is made, not only define the methods of surveying to be employed, but also the character of the map and its relative scale. The various methods of surveying are described under the title SURVEYING in this Encyclopedia. The various kinds of maps may be grouped into the following named general classes: "Geographical,» "physiographical," "topographical" and "geological maps. The representations of astronomical, hydrographical, nautical and statistical data belong more properly to the category of charts. The various forms of railroad maps are merely diagrams only useful for consultation with the accompanying railroad schedules. The amount of distortion required to fit them for the purposes for which they are used makes them entirely unreliable for any other purpose. The military maps are of various types and differ greatly according to the purposes for which they are used. Staff maps usually show every feature, natural and artificial, on the surface of the country mapped in the minutest detail and with the greatest accuracy. The differences of elevation of the various points are a matter of the greatest moment, and, therefore, are usually treated in the most complete manner both as to graphic effect and accuracy of information. The sketch maps are much simpler

in character and represent in the most elementary way the most important features which have a direct bearing on the particular kind of military operations involved.

In the construction of original maps the principal points to be considered are the "scale," the "projection," the "topographical representation" and the method of "duplication or reproduction" for publication.

Scale. The scale will depend upon the character of the survey and the data obtained thereby; the extent of the area to be represented on the map, and the process by which the map is to be reproduced. The original map should always be drawn on a scale sufficiently large to allow the draughtsman to plat the field notes easily and accurately. The difference between a large scale and a small scale and their relative effect on maps may be explained as fol

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In all cases the original maps may be subse quently reduced to any desired scale by hand, by pantagraph or by photographic methods. Reduction by pantagraph is satisfactory and useful only for the roughest classes of work. Photographic reductions of maps of limited size and prepared as copies for engravings may be made with fair accuracy and very slight distortion. Map sheets exceeding 15 to 20 inches square in the size of the final reduction cannot be reduced photographically with sufficient accuracy to satisfy the demands of absolutely accurate copper, steel and stone engravings. For such engravings the reductions should always be made by hand. The method of hand reduction usually employed is the simple but effective one of dividing the original and the copy into a system of equivalent squares and then drawing in all the details by hand. The very simplicity of the

lows: Suppose the fractional scale of a map is given as 60 it indicates that an interval of one inch on the map is equivalent to an interval or distance of 63,360 inches or one mile on the ground. Suppose the map to be 10 inches square, it would include an area of 100 square miles. Now suppose that while the size of the map remains the same the scale is reduced to

o, it would then include an area of 10,000 square miles. Any map scale which requires that the platting of measurements be made by the use of a scale with finer divisions than onehundredths of an inch is about the minimum limit for platting original work, although measurements requiring an accuracy of one twohundredths of an inch are commonly made in the construction of accurate projections for the mapping of exact trigonometrical surveys. The scale should be made larger directly in proportion to the increase in the amount of details to be shown on the map. The scale for maps in railroad work should always be large- 1 inch to 1, 2 or 300 feet. For the platting of plane table and other triangulations, and for work requiring the filling in of a great amount of topographical detail, the scale should not be less than one inch to one mile. All surveys such as the townships and sections of the Public Land Surveys, in which the measurements are made by chain or by stadia, should not be platted on a scale less than 1 inch to 40 chains or half a mile.

VOL. 18-17

Stereographic Projection on the Plane of a Horizon.

method demands the services of the most skilful and experienced draughtsmen, so that the resulting maps possess a far greater accuracy than any reductions that may be obtained by photo-mechanical methods. There are examples of hand-made maps in the office of the United States Coast and Geodetic Survey which are actually superior in accuracy, execution and beauty to the prints from the very fine copper engravings for which they served as a

copy.

If the maps are to be reproduced by being engraved on copper, steel or stone the reductions furnished the engravers should always be upon the "final scale" or scale of publication. This is also applicable to wax engravings when photographic methods of reduction are not available to the engraver. When the maps represent a great diversity of physical characteristics it is convenient to avoid confusion of details by using various conventional colors so as to distinguish the land from the water areas, the rivers and creeks from the roads, railroads, contour lines, etc. If the maps are to be reproduced by any of the photo-mechanical processes such as photo-engraving, photo-lithography or the half-tone process, the use of colors should be strictly avoided, and the map made in black and white on a scale that will allow about one-third reduction to the scale of publication.