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 sin1â„2D = sin a sin1â„2t, and since sin a = sin (90° − l) = cos t, it follows thatsin1â„2D = cos l sin1â„2t.If the latitudes differ, we have to solve an oblique-angled spherical triangle, of which two sides and the included angle are given. Thus,cos t =cos D − cos a cos bsin a sin bcos D = cos a cos b + sin a sin b cos t= sin l sin l′ + cos l cos l′ cos t.In order to adapt this formula to logarithms, we introduce a subsidiary angle p, such that cot p = cot l cos t; we then havecos D = sin l cos (l′ − p) / sin p.In the above formulae our earth is assumed to be a sphere, but when calculating and reducing to the sea-level, a base-line, or the side of a primary triangulation, account must be taken of the spheroidal shape of the earth and of the elevation above the sea-level. The error due to the neglect of the former would at most amount to 1%, while a reduction to the mean level of the sea necessitates but a trifling reduction, amounting, in the case of a base-line 100,000 metres in length, measured on a plateau of 3700 metres (12,000 ft.) in height, to 57 metres only.These orthodromic distances are of course shorter than those measured along a loxodromic line, which intersects all parallels at the same angle. Thus the distance between New York and Oporto, following the former (great circle sailing), amounts to 3000 m., while following the rhumb, as in Mercator sailing, it would amount to 3120 m.These direct distances may of course differ widely with the distance which it is necessary to travel between two places along a road, down a winding river or a sinuous coast-line. Thus, the direct distance, as the crow flies, between Brig and the hospice of the Simplon amounts to 4.42 geogr. m. (slope nearly 9°), while the distance by road measures 13.85 geogr. m. (slope nearly 3°). Distances such as these can be measured only on a topographical map of a fairly large scale, for on general maps many of the details needed for that purpose can no longer be represented. Space runners for facilitating these measurements, variously known as chartometers, curvimeters, opisometers, &c., have been devised in great variety. Nearly all these instruments register the revolution of a small wheel of known circumference, which is run along the line to be measured.The Measurement of Areasis easily effected 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 determined 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. Instead of drawing these squares upon the map itself, they may be engraved or etched upon glass, or drawn upon transparent celluloid or tracing-paper. Still more expeditious is the use of a planimeter, such as Captain Prytz’s “Hatchet Planimeter,†which yields fairly accurate results, or G. Coradi’s “Polar Planimeter,†one of the most trustworthy instruments of the kind.4When 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), in Professor H. Wagner’s tables in the geographicalJahrbuch, or similar works.It is obvious that the area of a group of mountains projected on a horizontal plane, such as is presented by a map, must differ widely from the area of the superficies or physical surface of those mountains exposed to the air. Thus, a slope of 45° having a surface of 100 sq. m. projected upon a horizontal plane only measures 59 sq. m., whilst 100 sq. m. of the snowclad Sentis in Appenzell are reduced to 10 sq. m. A hypsographical map affords the readiest solution of this question. Given the area A of the plane between the two horizontal contours, the height h of the upper above the lower contour, the length of the upper contour l, and the area of the face presented by the edge of the upper stratum t·h = A1, the slope α is found to be tan α = h·l / (A − A1); hence its superficies, A = A2sec α. The result is an approximation, for inequalities of the ground bounded by the two contours have not been considered.The hypsographical map facilitates likewise the determination of themean heightof a country, and this height, combined with the area, the determination of volume, or cubic contents, is a simple matter.5
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 sin1â„2D = sin a sin1â„2t, and since sin a = sin (90° − l) = cos t, it follows that
sin1â„2D = cos l sin1â„2t.
If the latitudes differ, we have to solve an oblique-angled spherical triangle, of which two sides and the included angle are given. Thus,
cos D = cos a cos b + sin a sin b cos t= sin l sin l′ + cos l cos l′ cos t.
In order to adapt this formula to logarithms, we introduce a subsidiary angle p, such that cot p = cot l cos t; we then have
cos D = sin l cos (l′ − p) / sin p.
In the above formulae our earth is assumed to be a sphere, but when calculating and reducing to the sea-level, a base-line, or the side of a primary triangulation, account must be taken of the spheroidal shape of the earth and of the elevation above the sea-level. The error due to the neglect of the former would at most amount to 1%, while a reduction to the mean level of the sea necessitates but a trifling reduction, amounting, in the case of a base-line 100,000 metres in length, measured on a plateau of 3700 metres (12,000 ft.) in height, to 57 metres only.
These orthodromic distances are of course shorter than those measured along a loxodromic line, which intersects all parallels at the same angle. Thus the distance between New York and Oporto, following the former (great circle sailing), amounts to 3000 m., while following the rhumb, as in Mercator sailing, it would amount to 3120 m.
These direct distances may of course differ widely with the distance which it is necessary to travel between two places along a road, down a winding river or a sinuous coast-line. Thus, the direct distance, as the crow flies, between Brig and the hospice of the Simplon amounts to 4.42 geogr. m. (slope nearly 9°), while the distance by road measures 13.85 geogr. m. (slope nearly 3°). Distances such as these can be measured only on a topographical map of a fairly large scale, for on general maps many of the details needed for that purpose can no longer be represented. Space runners for facilitating these measurements, variously known as chartometers, curvimeters, opisometers, &c., have been devised in great variety. Nearly all these instruments register the revolution of a small wheel of known circumference, which is run along the line to be measured.
The Measurement of Areasis easily effected 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 determined 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. Instead of drawing these squares upon the map itself, they may be engraved or etched upon glass, or drawn upon transparent celluloid or tracing-paper. Still more expeditious is the use of a planimeter, such as Captain Prytz’s “Hatchet Planimeter,†which yields fairly accurate results, or G. Coradi’s “Polar Planimeter,†one of the most trustworthy instruments of the kind.4
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), in Professor H. Wagner’s tables in the geographicalJahrbuch, or similar works.
It is obvious that the area of a group of mountains projected on a horizontal plane, such as is presented by a map, must differ widely from the area of the superficies or physical surface of those mountains exposed to the air. Thus, a slope of 45° having a surface of 100 sq. m. projected upon a horizontal plane only measures 59 sq. m., whilst 100 sq. m. of the snowclad Sentis in Appenzell are reduced to 10 sq. m. A hypsographical map affords the readiest solution of this question. Given the area A of the plane between the two horizontal contours, the height h of the upper above the lower contour, the length of the upper contour l, and the area of the face presented by the edge of the upper stratum t·h = A1, the slope α is found to be tan α = h·l / (A − A1); hence its superficies, A = A2sec α. The result is an approximation, for inequalities of the ground bounded by the two contours have not been considered.
The hypsographical map facilitates likewise the determination of themean heightof a country, and this height, combined with the area, the determination of volume, or cubic contents, is a simple matter.5
Relief Mapsare intended to present a representation 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 likewise an exaggeration of the heights. Thus on a relief on a scale of 1 : 1,000,000 a mountain like Ben Nevis would only rise to a height of 1.3 mm.
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. If contoured maps are available it is easy to build up a strata-relief, which facilitates the completion of the relief so that it shall be a fair representation of nature, which the strata-relief cannot claim to be. A pantograph armed with cutting-files6which carve the relief out of a block of gypsum, was employed in 1893-1900 by C. Perron of Geneva, in producing his relief map of Switzerland on a scale of 1 : 100,000. After copies of such reliefs have been taken in gypsum, cement, statuary pasteboard, fossil dust mixed with vegetable oil, or some other suitable material, they are painted. If a number of copies is required it may be advisable to print a map of the country represented in colours, and either to emboss this map, backed with papier-mâché, or paste it upon a copy of the relief—a task of some difficulty. Relief maps are frequently objected to onaccount of their cost, bulk and weight, but their great use in teaching geography is undeniable.
Globes.7—It is impossible to represent on a plane the whole of the earth’s surface, or even a large extent of it, without a considerable 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 qualities which the ingenuity of no mathematician has hitherto succeeded in imparting to a projection intended for a map of some extent, namely, equivalence of areas of distances and angles. Nevertheless, it should be observed that our globes take no account of the oblateness of our sphere; but as the difference in length between the circumference of the equator and the perimeter of a meridian ellipse only amounts to 0.16%, it could be shown only on a globe of unusual size.
The method of manufacturing a globe is much the same as it was at the beginning of the 16th century. A matrix of wood or iron is covered with successive layers of papers, pasted together so as to form pasteboard. The shell thus formed is then cut along the line of the intended equator into two hemispheres, they are then again glued together and made to revolve round an axis the ends of which passed through the poles and entered a metal meridian circle. The sphere is then coated with plaster or whiting, and when it has been smoothed on a lathe and dried, the lines representing meridians and parallels are drawn upon it. Finally the globe is covered with the paper gores upon which the map is drawn. The adaption of these gores to the curvature of the sphere calls for great care. Generally from 12 to 24 gores and two small segments for the polar regions printed on vellum paper are used for each globe. The method of preparing these gores was originally found empirically, but since the days of Albert Dürer it has also engaged the minds of many mathematicians, foremost among whom was Professor A. G. Kästner of Göttingen. One of the best instructions for the manufacture of globes we owe to Altmütter of Vienna.8
Larger globes are usually on a stand the top of which supports an artificial horizon. The globe itself rotates within a metallic meridian to which its axis is attached. Other accessories are an hour-circle, around the north pole, a compass placed beneath the globe, and a flexible quadrant used for finding the distances between places. These accessories are indispensable if it be proposed to solve the problems usually propounded in books on the “use of the globes,†but can be dispensed with if the globe is to serve only as a map of the world. The size of a globe is usually given in terms of its diameter. To find its scale divide the mean diameter of the earth (1,273,500 m.) by the diameter of the globe; to find its circumference multiply the diameter by π (3.1416).
Map Printing.—Maps were first printed in the second half of the 15th century. Those in theRudimentum novitiarumpublished at Lübeck 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, and owing to the beauty and clearness of the maps produced by a combination of engraving and etching it still maintains its ground. The objection that a copper plate shows signs of wear after a thousand impressions have been taken has been removed, since duplicate plates are readily produced by electrotyping, while transfers of copper engravings, on stone, zinc or aluminium, make it possible to turn out large editions in a printing-machine, which thus supersedes the slow-working hand-press.9These impressions from transfers, however, are liable to be inferior to impressions taken from an original plate or an electrotype. The art of lithography greatly affected the production of maps. The work is either engraved upon the stone (which yields the most satisfactory result at half the cost of copper-engraving), or it is drawn upon the stone by pen, brush or chalk (after the stone has been “grainedâ€), or it is transferred from a drawing upon transfer paper in lithographic ink. In chromolithography a stone is required for each colour. Owing to the great weight of stones, their cost and their liability of being fractured in the press, zinc plates, and more recently aluminium plates, have largely taken the place of stone. The processes of zincography and of algraphy (aluminium printing) are essentially the same as lithography. Zincographs are generally used for producing surface blocks or plates which may be printed in the same way as a wood-cut. Another process of producing such blocks is known as cerography (Gr.κηÏός), wax. A copper plate having been coated with wax, outline and ornament are cut into the wax, the lettering is impressed with type, and the intaglio thus produced is electrotyped.10Movable types are utilized in several other ways in the production of maps. Thus the lettering of the map, having been set up in type, is inked in and transferred to a stone or a zinc-plate, or it is impressed upon transfer-paper and transferred to the stone. Photographic processes have been 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 aluminium, are drawn on a scale somewhat larger than the scale on which they are to be printed, thus eliminating all those imperfections which are inherent in a pen-drawing. The saving in time and cost by adopting this process is considerable, for a plan, the engraving of which takes two years, can now be produced in two days. Another process, photo- or heliogravure, for obtaining an engraved image on a copper plate, was for the first time employed on a large scale for producing a new topographical map of the Austrian Empire in 718 sheets, on a scale of 1 : 75,000, which was completed in seventeen years (1873-1890). The original drawings for this map had to be done with exceptional neatness, the draughtsman spending twelve months on that which he would have completed in four months had it been intended to engrave the map on copper; yet an average chart, measuring 530 by 630 mm., which would have taken two years and nine months for drawing and engraving, was completed in less than fifteen months—fifty days of which were spent in “retouching†the copper plate. It only cost £169 as compared with £360 had the old method been pursued.
For details of the various methods of reproduction seeLithography;Process, &c.
For details of the various methods of reproduction seeLithography;Process, &c.
History of Cartography
A capacity to understand the nature of maps is possessed even by peoples whom we are in the habit of describing as “savages.†Wandering tribes naturally enjoy a great advantage in this respect over sedentary ones. Our arctic voyagers—Sir E. W. Parry, Sir J. Ross, Sir F. L. MacClintock and others—have profited from rough maps drawn for them by Eskimos. Specimens of such maps are given in C. F. Hall’sLife with the Esquimaux(London, 1864). Henry Youle Hind, in his work on the Labrador Peninsula (London, 1863) praises the map which the Montagnais and Nasquapee Indians drew upon bark. Similar essays at map-making are reported in connexion with Australians, Maoris and Polynesians. Tupaya, a Tahitian, who accompanied Captain Cook in the “Endeavour†to Europe, supplied his patron with maps; Raraka drew a map in chalk of the Paumotu archipelago on the deck of Captain Wilkes’s vessel; the Marshall islanders, according to Captain Winkler (Marine Rundschau, Oct. 1893) possess maps upon which the bearings of the islands are indicated by small strokes. Far superior were the maps found among the semi-civilized Mexicans when theSpaniardsfirst discovered and invaded their country. Among them were cadastral plans of villages, maps of the provinces of the empire of the Aztecs, of towns and of the coast. Montezuma presented Cortes with a map, painted on Nequen cloth, of the Gulf coast. Another map did the Conquistador good service on his campaign against Honduras (Lorenzana,Historia de nueva España, Mexico, 1770; W. H. Prescott,History of the Conquest of Mexico, NewYork, 1843). Peru, the empire of the Incas, had not only ordinary maps, but also maps in relief, for Pedro Sarmiento da Gamboa (History of the Incas, translated by A. R. Markham, 1907) tells us that the 9th Inca (who died in 1191) ordered such reliefs to be produced of certain localities in a district which he had recently conquered and intended to colonize. These were the first relief maps on record. It is possible that these primitive efforts of American Indians might have been further developed, but the Spanish conquest put a stop to all progress, and for a consecutive history of the map and map-making we must turn to the Old World, and trace this history from Egypt and Babylon, through Greece, to our own age.
The ancient Egyptians were famed as “geometers,†and as early as the days of Rameses II. (Sesostris of the Greeks, 1333-1300B.C.) there had been made a cadastral survey of the country showing the rows of pillars which separated the nomens as well as the boundaries of landed estates. It was upon a map based upon such a source that Eratosthenes (276-196B.C.) measured the distance between Syene and Alexandria which he required for his determination of the length of a degree. Ptolemy, who had access to the treasures of the famous library of Alexandria was able, no doubt, to utilize these cadastral plans when compiling hisgeography. It should be noted that he places Syene only two degrees to the east of Alexandria instead of three degrees, the actual meridian distance between the two places; a difference which would result from an error of only 7° is the orientation of the map used by Ptolemy. Scarcely any specimens of ancient Egyptian cartography have survived. In the Turin Museum are preserved two papyri with rough drawings of gold mines established by Sesostris in the Nubian Desert.11These drawings have been commented upon by S. Birch, F. Chabas, R. J. Lauth and other Egyptologists, and have been referred to as the two most ancient maps in existence. They can, however, hardly be described as maps, while in age they are surpassed by several cartographical clay tablets discovered in Babylonia. On another papyrus in the same museum is depicted the victorious return of Seti I. (1366-1333) from Syria, showing the road from Pelusium to Heroopolis, the canal from the Nile with crocodiles, and a lake (mod. Lake Timsah) with fish in it. Apollonius of Rhodes who succeeded Eratosthenes as chief librarian at Alexandria (196B.C.) reports in hisArgonautica(iv. 279) that the inhabitants of Colchis whom, like Herodotus (ii., 104) he looks upon as the descendants of Egyptian colonists, preserved, as heirlooms, certain graven tablets (κÏÏβεις) on which land and sea, roads and towns were accurately indicated.12Eustathius (since 1160 archbishop of Thessalonica) in his commentary on Dionysius Periegetes, mentions route-maps which Sesostris caused to be prepared, while Strabo (i., 1. 5) dwells at length upon the wealth of geographical documents to be found in the library of Alexandria.
A cadastral survey for purposes of taxation was already at work in Babylonia in the age of Sargon of Akkad, 3800B.C.In the British Museum may be seen a series of clay tablets, circular in shape and dating back to 2300 or 2100B.C., which contain surveys of lands. One of these depicts in a rough way lower Babylonia encircled by a “salt water river,†Oceanus.
Development of Map-making among the Greeks.13—Ionian mercenaries and traders first arrived in Egypt, on the invitation of Psammetichus I. about the middle of the 7th centuryB.C.Among the visitors to Egypt, there were, no doubt, some who took an interest in the science of the Egyptians. One of the most distinguished among them was Thales of Miletus (640-543B.C.), the founder of the Ionian school of philosophy, whose pupil, Anaximander (611-546B.C.) is credited by Eratosthenes with having designed the first map of the world. Anaximander looked upon the earth as a section of a cylinder, of considerable thickness, suspended in the centre of the circular vault of the heavens, an idea perhaps borrowed from the Babylonians, for Job (xxvi. 7) already speaks of the earth as “hanging upon nothing.†Like Homer he looked upon the habitable world (οἰκουμÎνη) as being circular in outline and bounded by a circumfluent river. The geographical knowledge of Anaximander was naturally more ample than that of Homer, for it extended from the Cassiterides or Tin Islands in the west to the Caspian in the east, which he conceived to open out into Oceanus. The Aegean Sea occupied the centre of the map, while the line where ocean and firmament seemed to meet represented an enlarged horizon.
Anaximenes, a pupil of Anaximander, was the first to reject the view that the earth was a circular plane, but held it to be an oblong rectangle, buoyed up in the midst of the heavens by the compressed air upon which it rested. Circular maps, however, remained in the popular favour long after their erroneousness had been recognized by the learned.
Even Hecataeus of Miletus (549-472B.C.), the author of aPeriodosor description of the earth, of whom Herodotus borrowed the terse saying that Egypt was the gift of the Nile, retained this circular shape and circumfluent ocean when producing his map of the world, although he had at his disposal the results of the voyage of Scylax of Caryanda from the Indus to the Red Sea, of Darius’ campaign in Scythia (513), the information to be gathered among the merchants from all parts of the world who frequented an emporium like Miletus, and what he had learned in the course of his own extensive travels. Hecataeus was probably the author of the “bronze tablets upon which was engraved the whole circuit of the earth, the sea and rivers†(Herod, v. 49), which Aristagoras, the tyrant of Miletus, showed to Cleomenes, the king of Sparta, in 504, whose aid he sought in vain in a proposed revolt against Darius, which resulted disastrously in 494 in the destruction of Miletus. The map of the world brought upon the stage in Aristophanes’ comedy ofThe Clouds(423B.C.), whereon a disciple of the Sophists points out upon it the position of Athens and of other places known to the audience, was probably of the popular circular type, which Herodotus (iv. 36) not many years before had derided and which was discarded by Greek cartographers ever after. Thus Democritus of Abdera (b.c.450, d. after 360), the great philosopher and founder, with Leucippus, of the atomic theory, was also the author of a map of the inhabited world which he supposed to be half as long again from west to east, as it was broad.
Dicaearcus of Messana in Sicily, a pupil of Aristotle (326-296B.C.), is the author of a topographical account of Hellas, with maps, of which only fragments are preserved; he is credited with having estimated the size of the earth, and, as far as known he was the first to draw a parallel across a map.14This parallel, or dividing line, calleddiaphragm(partition) by a commentator, extended due east from the Pillars of Hercules, through the Mediterranean, and along the Taurus and Imaus (Himalaya) to the eastern ocean. It divided the inhabited world, as then known, into a northern and a southern half. In compiling his map he was able to avail himself of the information obtained by thebematists(surveyors who determined distances by pacing) who accompanied Alexander the Great on his campaigns; of the results of the voyage of Nearchus from the Indus to the Euphrates, and of the “Periplus†of Scylax of Caryanda, which described the coast from between India and the head of the Arabian Gulf. On the other hand he unwisely rejected the results of the observations for latitude made by Pytheas in 326B.C.at his native town, Massilia, and during a subsequent voyage to northern Europe. In the end the map of Dicaearcus resembled that of Democritus.
Scientific geography profited largely from the labours of Eratosthenes of Cyrene, whom Ptolemy Euergetes appointedkeeper of the famous library of Alexandria in 247B.C., and died in that city in 195B.C.He won fame as having been the first to determine the size of the earth by a scientific method. Having determined the difference of latitude between Alexandria and Syene which he erroneously believed to lie on the same meridian, and obtained the distance of those places from each other from the surveys made by Egyptian geometers, he concluded that a degree of themeridianmeasured 700 stadia.15
Eratosthenes is the author of a treatise which deals systematically with the geographical knowledge of his time, but of which only fragments have been preserved by Strabo and others. This treatise was intended to illustrate and explain his map of the world. In this task he was much helped by the materials collected in his library. Among the travellers of whose information he was thus able to avail himself were Pytheas of Massilia, Patroclus, who had visited the Caspian (285-282B.C.), Megasthenes, who visited Palibothra on the Ganges, as ambassador of Seleucus Nicator (302-291B.C.), Timosthenus of Rhodes, the commander of the fleet of Ptolemy Philadelphus (284-246B.C.) who wrote a treatise “On harbours,†and Philo, who visited Meroe on the upper Nile. His map formed a parallelogram measuring 75,800 stadia from Usisama (Ushant island) or Sacrum Promontorium in the west to the mouth of the Ganges and the land of the Coniaci (Comorin) in the east, and 46,000 stadia from Thule in the north to the supposed southern limit of Libya. Across it were drawn seven parallels, running through Meroe, Syene, Alexandria, Rhodes, Lysimachia on the Hellespont, the mouth of the Borysthenes and Thule, and these were crossed at right angles by seven meridians, drawn at irregular intervals, and passing through the Pillars of Hercules, Carthage, Alexandria, Thapsacus on the Euphrates, the Caspian gates, the mouth of the Indus and that of the Ganges. The position of all the places mentioned was supposed to have been determined by trustworthy authorities. The inhabited world thus delineated formed an island of irregular shape, surrounded on all sides by the ocean, the Erythrean Sea freely communicating with the western ocean. In his text Eratosthenes ignored the popular division of the world into Europe, Asia and Libya, and substituted for it a northern and southern division, divided by the parallel of Rhodes, each of which he subdivided intosphragidesorplinthia—seals or plinths. The principles on which these divisions were made remain an enigma to the present day.
This map of Eratosthenes, notwithstanding its many errors, such as the assumed connexion of the Caspian with a northern ocean and the supposition that Carthage, Sicily and Rome lay on the same meridian, enjoyed a high reputation in his day. Even Strabo (c.30B.C.) adopted its main features, but while he improved the European frontier, he rejected the valuable information secured by Pytheas and retained the connexion between the Caspian and the outer ocean. In the extreme east his information extended no further than that of Eratosthenes, viz. to India and Taprobane (Ceylon) and the Sacae (Kirghiz).
Hipparchus, the famous astronomer, on the other hand, (c.150B.C.) proved a somewhat captious critic. He justly objected to the arbitrary network of the map of Eratosthenes. The parallels orclimata16drawn through places, of which the longest day is of equal length and the decimation (distance) from the equator is the same, he maintained, ought to have been inserted at equal intervals, say of half an hour, and the meridians inserted on a like principle. In fact, he demanded that maps should be based upon a regular projection, several descriptions of which he had adopted for his star maps. He moreover accuses Eratosthenes, (whose determination of a degree he accepts without hesitation) with trusting too much to hypothesis in compiling his map instead of having recourse to latitudes and longitudes deduced by astronomical observations. Such observations, however, were but rarely available at the time. A few latitudes had indeed been observed, but although Hipparchus had shown how longitudes could be determined by the observation of eclipses, this method was in reality not available for want of trustworthy time-keepers. The determination of an ocean surrounding the inhabited earth he declared to be based on a mere hypothesis and that it would be equally allowable to describe the Erythraea as a sea surrounded by land. Hipparchus is not known to have compiled a map himself.
About the same time Crates of Mallus (d. 145B.C.) embodied the views of the Stoic school of philosophy in a globe which has become typical as one of the insignia of royalty. On this globe an equatorial and a meridional ocean divide our earth into four quarters, each inhabited, thus anticipating the discovery of North and South America and Australia.17
The period between Eratosthenes and Marinus of Tyre was one of great political importance. Carthage had been destroyed (146B.C.), Julius Caesar had carried on his campaign in Gaul (58-51B.C.), Egypt had been occupied (30B.C.), Britannia conquered (A.D.41-79), and the Roman empire had attained its greatest extent and power under the emperor Trajan (A.D.98-117). But although military operations added to our knowledge of the world, scientific cartography was utterly neglected.
Among Greek works written during this period there are several which either give us an idea of the maps available at that time, or furnish information of direct service to the compiler of a map. Among the latter a Periplus or coastal guide of the Erythrean Sea, which clearly reveals the peninsular shape of India (A.D.90) and Arrian’sPeriplus Ponti Euxeni(A.D.131) which Festus Avienus translated into Latin. Among travellers Eudoxus of Cyzicus occupies a foremost rank, since, between 115-87B.C.he visited India and the east coast of Africa, which subsequently he attempted in vain to circumnavigate byfollowing the route of Hanno, along the west coast. Among geographers should be mentioned Posidonius (135-51), the head of the Stoic school of Rhodes, who is stated to be responsible for having reduced the length of a degree to 500 stadia; Artemidorus of Ephesus, whose “Geographumena†(c.100B.C.) are based upon his own travels and a study of itineraries, and above all, Strabo, who has already been referred to. Among historians who looked upon geography as an important aid in their work are numbered Polybius (c.210-120B.C.), Diodorus Siculus (c.30B.C.) and Agathachidus of Cnidus (c.120B.C.) to whom we are indebted for a valuable account of the Erythrean Sea and the adjoining parts of Arabia and Ethiopia. ThePeriegesisof Dionysius of Alexandria is a popular description of the world in hexameters, of no particular scientific value (c.A.D.130). He as well as Artemidorus and others accepted a circular or ellipsoidal shape of the world and a circumfluent ocean; Strabo alone adhered to the scientific theories of Eratosthenes.
The credit of having returned to the scientific principles innovated by Eratosthenes and Hipparchus is due to Marinus of Tyre (c.A.D.120) which, though no longer occupying the pre-eminent position of former times, was yet an emporium of no inconsiderable importance, having extensive connexions by sea and land. The map of Marinus and the descriptive accounts which accompanied it have perished, but we learn sufficient concerning them from Ptolemy to be able to appreciate their merits and demerits. Marinus was the first who laid down the position of places on a projection according to their latitude and longitude, but the projection used by him was of the rudest. Parallels and meridians were represented by straight lines intersecting each other at right angles, the relative proportions between degrees of longitude and latitude being retained only along the parallel of Rhodes. The distortion of the countries represented would thus increase with the distance, north and south, from this central parallel. The number of places whose position had been determined by astronomical observation was as yet very small, and the map had thus to be compiled mainly from itineraries furnished by travellers or the dead reckoning of seamen. The errors due to an exaggeration of distances were still further increased on account of his assuming a degree to be equal to 500 stadia, as determined by Posidonius, instead of accepting the 700 stadia of Eratosthenes. He was thus led to assume that the distance from the first meridian drawn through the Fortunate islands to Sera (mod. Si-ngan-fu), the capital of China, was equal to 225°, which Ptolemy reduced to 177°, but which in reality only amount to 126°. A like overestimate of the distances covering the march of Julius Maternus to Agisymba, which Marinus places 24° south of the equator, a latitude which Ptolemy reduces to 18°, but which is probably no farther south than lat. 12° N. The map of Marinus was accompanied by a list of places arranged according to latitude and longitude. It must have been much in demand, for three editions of it were prepared. Masudi (10th century) saw a copy of it and declared it to be superior to Ptolemy’s map.
Ptolemy (q.v.) was the author of aGeography18(c.A.D.150) in eight books. “Geography,†in the sense in which he uses the term, signifies the delineation of the known world, in the shape of a map, while chorography carries out the same objects in fuller detail, with regard to a particular country. In Book I. he deals with the principles of mathematical geography, map projections, and sources of information with special reference to his predecessor Marinus. Books II. to VII. form an index to the maps. They contain about 8000 names, with their latitudes and longitudes, and with their aid it is possible to reconstruct the maps. These maps existed, as a matter of course, before such an index could be compiled, but it is doubtful whether the maps in our available manuscript, which are attributed to Agathodaemon, are copies of Ptolemy’s originals or have been compiled, after their loss, from this index. Book VIII. gives further details with reference to the principal towns of each map, as to geographical position, length of day, climata, &c.
Ptolemy’s great merit consists in having accepted the views of Hipparchus with respect to a projection suited for a map of the world. Of the two projections proposed by him one is a modified conical projection with curved parallels and straight meridians; in the second projection (see fig. 3) both parallels and meridians are curved. The correct relations in the length of degrees of latitude and longitude are maintained in the first case along the latitude of Thule and the equator, in the second along the parallel of Agisymba, the equator and the parallels of Meroe, Syene and Thule. Following Hipparchus he divided the equator into 360° drawing his prime meridian through the Fortunate Islands (Canaries). The 26 special maps are drawn on a rectangular projection. As a map compiler Ptolemy does not take a high rank. In the main he copied Marinus whose work he revised and supplemented in some points, but he failed to realize the peninsular shape of India, erroneously exaggerated the size of Taprobane (Ceylon), and suggested that the Indian Ocean had no connexion with the western ocean, but formed Mare Clausum. Ptolemy knew but of a few latitudes which had been determined by actual observation, while of three longitudes resulting from simultaneous observation of eclipses he unfortunately accepted the least satisfactory, namely, that which placed Arbela 45° to the east of Carthage, while the actual meridian distance only amounts to 34°. An even graver source of error was Ptolemy’s acceptance of a degree of 500 instead of 700 stadia. The extent to which the more correct proportion would have affected the delineation of the Mediterranean is illustrated by fig. 4. But in spite of his errors the scientific method pursued by Ptolemy was correct, and though he was neglected by the Romans and during the middle ages, once he had become known, in the 15th century, he became the teacher of the modern world.
Map-Making among the Romans.—We learn from Cicero, Vitruvius, Seneca, Suetonius, Pliny and others, that the Romans had both general and topographical maps. Thus, Varro (De rustici) mentions a map of Italy engraved on marble, in the temple of Tellus, Pliny, a map of the seat of war in Armenia, of the time of the emperor Nero, and the more famous map of the Roman Empire which was ordered to be prepared for Julius Caesar (44B.C.), but only completed in the reign of Augustus, who placed a copy of it, engraved in marble, in the Porticus of his sister Octavia (7B.C.). M. Vipsanius Agrippa, the son-in-law of Augustus (d. 12B.C.), who superintended the completion of this famous map, also wrote a commentary illustrating it, quotations from which of Ammianus Marcellinus of Antioch (d. 330), Pliny and others, afford the only means of judging of its character. The map is supposed to be based upon actual surveys or rather reconnaissances, and if it be borne in mind that the Roman Empire at that time was traversed in all directions by roads furnished with mile-stones, that the Agrimensores employed upon such a duty were skilled surveyors, and that the official reports of the commanders of military expeditions and of provincial governors were available, this map, as well as the provincial maps upon which it was based, must have been a work of superior excellence, the loss of which is much to be regretted. A copy of it may possibly have been utilized by Marinus and Ptolemy in their compilations. The Romans have been reproached for having neglected the scientific methods of map-making advocated by Hipparchus. Their maps, however, seem to have met the practical requirements of political administration and of military undertakings.
Only two specimens of Roman cartography have come down to us, viz. parts of a plan of Rome, of the time of the emperorSeptimius Severus (A.D.193-211), now in the Museo Capitolino, and anitinerarium scriptum, or road map of the world, compressed within a strip 745 mm. in length and 34 mm. broad. Of its character the reduced copy of one of its 12 sections (fig. 5) conveys an idea. The map, apparently of the 3rd century, was copied by a monk at Colmar, in 1265, who fortunately contented himself with adding a few scriptural names, and having been acquired by the learned Conrad Peutinger of Augsburg it became known asTabula peutingeriana. The original is now in the imperial library of Vienna.19
Map-Making in the Middle Ages.—In scientific matters the early middle ages were marked by stagnation and retrogression. The fathers of the church did not encourage scientific pursuits, which Lactantius (4th century) declared to be unprofitable. The doctrine of the sphericity of the earth was still held by the more learned, but the heads of the church held it to be unscriptural. Pope Zachary, when in 741 he condemned the views of Virgilius, the learned bishop of Salzburg, an Irishman who had been denounced as a heretic by St Boniface, declares it to beperversa et iniqua doctrina. Even after Gerbert of Aurillac, better known as Pope Sylvester II. (999-1063), Adam of Bremen (1075), Albertus Magnus (d. 1286), Roger Bacon (d. 1294), and indeed all men of leading had accepted as a fact and not a mere hypothesis the geocentric system of the universe and sphericity of the globe, the authors of maps of the world, nearly all of whom were monks, still looked in the main to the Holy Scriptures for guidance in outlining the inhabited world. We have to deal thus with three types of these early maps, viz. an oblong rectangular, a circular and an oval type, the latter being either a compromise between the two former, or an artistic development of the circular type. In every instance the inhabited world is surrounded by the ocean. The authors of rectangular maps look upon the Tabernacle as an image of the world at large, and believe that such expressions as the “four corners of the earth†(Isa. x. 12), could be reconciled only with a rectangular world. On the other hand there was the expression “circuit of the earth†(Isa. xl. 22), and the statement (Ezek. v. 5) that “God had set Jerusalem in the midst of the nations and countries.†Innearly every case the East occupies the top of the map. Neither parallels nor meridians are indicated, nor is there a scale. Other features frequently met with are the Paradise in the Far East, miniatures of towns, plants, animals, human beings and monsters, and an indication of the twelve winds around the margin.
The oldest rectangular map of the world is contained in a most valuable work written by Cosmas, an Alexandrian monk, surnamed Indicopleustes, after returning from a voyage to India (535A.D.), and entitledChristian Topography. According to Cosmas (fig. 6) the inhabited earth has the shape of an oblong rectangle surrounded by an ocean which breaks in in four great gulfs—the Roman or Mediterranean, the Arabian, Persian and Caspian Sea. Beyond this ocean lies another world, which was occupied by man before the Deluge, and within which Cosmas placed the Terrestrial Paradise. Above this rise the walls of the heavens like unto the tent of the Tabernacle. Far more simple is a small map of the world of the 8th century found in a codex in the library of Albi, an archiepiscopal seat in the department of Tarn. Its scanty nomenclature is almost wholly derived from the “Historiae adversum paganos†of Paulus Orosius (418). Far greater interest attaches to the so-called Anglo-Saxon Map of the World in the British Museum (Cotton MSS.), where it is bound up in a codex which also contains a copy of thePeriegesisof Priscianus. Map and Periegesis are copies by the same hand, but no other connexion exists between them. More than half the nomenclature of the map is derived from Orosius, an annotated Anglo-Saxon version of which had been produced by King Alfred (871-901). The Anglo-Saxons of the time were of course well acquainted with Island (first thus named in 870) Slesvic and Norweci (Norway), and there is no need to have recourse to Adam of Bremen (1076) to account for their presence upon this map. The broad features of the map were derived no doubt from an older document which may likewise have served as the basis for the map of the world engraved on silver for Charlemagne, and was also consulted by the compilers of the Hereford and Ebstorf maps (see fig. 11).
The map or diagram of which Leonardo Dati in his poem on the Sphere (Della Spera) wrote in 1422 “un T dentre a uno O mostra il disegno†(a T within an O shows the design) is one of the most persistent types among the circular or wheel maps of the world. It perpetuates the tripartite division of the world by the ancient Greeks and survives in the Royal Orb. A diagram of this description will be found in Isidor of Seville’sOrigines(630), see fig. 9.
T maps of more elaborate design illustrate the MS. copies of Sallust’sBellum jugurthinum; one of these taken from a codex of the 11th century in the Leipzig town library is shown in fig. 10.
The outlines of several medieval maps resemble each other to such an extent that there can be no doubt that they are derived from the same original source. This source by some authors is assumed to have been the official map of the Roman Empire, but if we compare the crude outline given to the Mediterranean with the more correct delineation of Ptolemy, who was certainly in a position to avail himself of these official sources, such an assumption is untenable. The earliest delineation of the description has already been referred to as the Anglo-Saxon map of the world. Next in the order of age, follows the oval map which Henry, canon of Mayence Cathedral, dedicated to Mathilda, consort of the emperor Henry V. (1110). Of far greater importance is the map seen in Hereford Cathedral. It is the work of Richard of Haldingham, and has a diameter of 134 cm. (53 ins.). The “survey†ordered by Julius Caesar is referred to in the legend, evidently derived from the Cosmography ofAethicus a work widely read at the time, but this does not prove that the author was able to avail himself of a map based upon that survey. A map essentially identical with that of Hereford, but larger—its diameter is 15.6 cm. (6 in.), and consequently fuller of information—was discovered in 1830 in the old monastery of Ebstorf in Hanover. Its date is 1484. Both maps abound in miniature pictures of towns, animals, fabulous beings and other subjects. The Hereford map is surmounted by a picture of the Day of Judgment. Similar in design, though much smaller of scale and oval in form, are the maps which illustrate the popularPolychroniconof Ranulf Higden, a monk of St Werburgh’s Abbey of Chester (d. 1363).
Pomponius Mela tells us that beyond the Ethiopian Ocean which sweeps round Africa in the south and the uninhabitable torrid zone, there lies analter orbis, or fourth part of the world inhabited byAntichthones. On a diagram illustrating the origines of Isidore of Seville (d. 636) this country is shown, but is described as aterra inhabitabilis. It is shown likewise upon a number of maps which illustrate theCommentaries on the Apocalypse, by Beatus, a Benedictine monk of the abbey of Valcavado at the foot of the hills of Liebana in Asturia (776).
Our little map (fig. 12) is taken from a copy of Beatus’ work made in 1203, and preserved at Burgo de Osma in Castille. Similar maps illustrating theCommentariesexist at St Sever (1050), Paris (1203), and Tunis; others are rectangular, the oldest being in Lord Ashburnham’s library (970). Beatus, too, describes the southern land asinhabitabilis. The habitable world is divided among the twelve apostles, whose portraits are given. On the maps illustrating the encyclopaedicLiber floridusby Lambert, a canon of St Omer (1120), this south land “unknown to the sons of Adam,†is stated to be inhabited “according to the philosophers†by Antipodes. Lambert, indeed, seems to have believed in the sphericity of the earth. Fig. 13 shows his map of the world reduced from a MS. at Wolfenbüttel, to which is added a diagram of the zones from a MS. at Ghent, which illustrates Macrobius’ commentary on Cicero’sSomnium Scipionis. Diagrams illustrating the division of the world into climata, are to be found in theopus majusof Roger Bacon (d. 1294) and in Cardinal Pierre d’Ailly’sDe imagine Mundi(1410).
Among countries represented on a larger scale on maps, Palestine not unnaturally occupies a prominent place in this age of pilgrimages and crusades (1095-1291). The maps which accompany St Jerome’s translation of theOnomasticonof St Eusebius (388). The same subject is illustrated by a picture-map in mosaic, portions of which were discovered in 1896 on the floor of the church of Madaba to the east of the Dead Sea. This is the oldest original of a map in existence, for it dates back to the 6th century. Among more recent maps of Palestine, that by Petrus Vesconte (1320) is greatly superior to the earlier maps. It illustrates Marino Sanuto’sSecreta fidelium crucis, in which its author vainly appeals to Christendom to undertake another crusade. One of the earliest plans of Jerusalem is contained inGesta Francorum, a history of the Crusades up to 1106, based upon information furnished by Fulcherius of Chartres (c.1109).
There existed, no doubt, special maps of European countries, but the only documents of that description are two maps of Great Britain, the one of the 12th century, the other by Matthew of Paris, the famous historiographer of the monastery of St Albans (1236-1259).20
Celestial globes were known in the time of Bede; they formed part of the educational apparatus of the monastic schools. Gerbert of Aurillac is known to have made such globes (929). Their manufacture is described by Alphonso the Wise (1252), as also inDe sphaera solidaof G. Campanus of Novara (1303). Terrestrial globes, however, are not referred to.
Map-making among the Arabians and other Nations of the East.—Bagdad early became a famous seat of learning. Indian astronomers found apt pupils there among the Arabs; the works ofPtolemy were translated into Arabic, and in 827, in the reign of the caliph Abdullah al Mamun, an arc of the meridian was measured in the plain of Mesopotamia. Most famous among these Arabian astronomers were Al Batani (d. 998), Ibn Yunis of Cairo (d. 1008), Zarkala (Azarchel), who determined the meridian distance between his observatory in Toledo and Bagdad to amount to 51° 30′, an error of 3° only, as compared with Ptolemy’s error of 18°, and Abul Hassan (1230) who reduced the great axis of the Mediterranean to 44°.
Further materials serviceable to the compilers of maps were supplied by numerous Arabian travellers and geographers, among whom Masudi (915-940), Istakhri (950), Ibn Haukal (942-970), Al Biruni (d. 1038), Ibn Batuta (1325-1356) and Abul Feda (1331-1370), occupy a foremost place, yet the few maps which have reached us are crude in the extreme. Masudi, who saw the maps in the Horismos or Rasm el Ard, a description of the world by Abu Jafar Mahommed ben Musa of Khiva, the librarian of the caliph el Mamun (833), declares them to be superior to the maps of Ptolemy or Marinus, but maps of a later date by Istakhri (950) or Ibn al Wardi (1349) are certainly of a most rudimentary type. Nor can Idrisi’s map of the world, which was engraved for King Roger of Sicily upon a silver plate, or the rectangular map in 70 sheets which accompanies his geography (Nushat-ul Mushtat) take rank with Ptolemy’s work. These maps are based upon information collected during many years at the instance of King Roger. The seven climates adopted by Idrisi are erroneously supposed to be equal in latitudinal extent. The Mediterranean occupies nearly half the inhabited world in longitude, and the east coast of Africa is shown as if it extended due east.
The Arabians are not known to have produced a terrestrial globe, but several of their celestial globes are to be found in our collections. The oldest of these globes was made at Valentia, and is now in the museum of Florence. Another globe (of 1225) is at Velletri; a third by Ibn Hula of Mosul (1275) is the property of the Royal Asiatic Society of London; a fourth (1289) from the observatory of Maragha, in the Dresden Museum, two globes of uncertain age at Paris (see fig. 17) and another in London. All these globes are of metal (bronze), or they might not have survived so many years.
The charts in use of the medieval navigators of the Indian Ocean—Arabs, Persians or Dravidas—were equal in value if not superior to the charts of the Mediterranean. Marco Polo mentions such charts; Vasco da Gama (1498) found them in the hands of his Indian pilot, and their nature is fully explained in theMohitor encyclopaedia of the sea compiled from ancient sources by the Turkish admiral Sidi Ali Ben Hosein in 1554.21These charts are covered with a close network of lines intersecting each other at right angles. The horizontal lines are parallels, depending upon the altitude of the pole star, the Calves of the Little Bear and the Barrow of the Great Bear above the horizon. This altitude was expressed inisbasor inches each equivalent to 1° 42′ 50″. Eachisbawas divided intozamsor eights. The interval between two parallels thus only amounted to 12′ 51″. These intervals were mistaken by the Portuguese occasionally for degrees, which account for Malacca, which is in lat. 2′ 13″ N., being placed on Cantino’s Chart (1502) in lat. 14′ S. It may have been a map of this kind which accounts for Ptolemy’s moderate exaggerations of the size of Taprobana (Ceylon). A first meridian, separating a leeward from a windward region, passed through Ras Kumhari (Comorin) and was thus nearly identical with the first meridian of the Indian astronomers which passed through the sacred city of Ujjain (Ozere of Ptolemy) or the meridian of Azin of the Arabs. Additional meridians were drawn at intervals ofzams, supposed to be equal to three hours’ sail.
In China, maps in the olden time were engraved on bronzeor stone, but after the 10th century they were printed from wood-blocks. Among the more important productions of more recent times, may be mentioned a map of the empire, said to be based upon actual surveys by Yhang (721), who also manufactured a celestial globe (an older globe by Ho-shing-tien, 4 metres in circumference, was produced in 450), and an atlas of the empire on a large scale by Thu-sie-pun (1311-1312) of which new enlarged editions with many maps were published in the 16th century and in 1799. None of these maps was graduated, which is all the more surprising as the Chinese astronomers are credited with having made use of the gnomon as early as 1000B.C.for determining latitudes.
In the case of Japan, the earliest reference to a map is of 646, in which year the emperor ordered surveys of certain provinces to be made.
Portolano Maps.—During the long period of stagnation in cartography, which we have already dealt with, there survived among the seamen of the Mediterranean charts of remarkable accuracy, illustrating thePortolanior sailing directories in use among them. Charts of this description are first mentioned in connexion with the Crusade of Louis XI. in 1270, but they originated long before that time, and in the eastern part of the Mediterranean they embody materials available even in the days before Ptolemy, while the correct delineation of the west seems to be of a later date, and may have been due to Catalan seamen. These charts are based upon estimated bearings and distances between the principal ports or capes, the intervening coast-line being filled in from more detailed surveys. The bearings were dependent upon the seaman’s observation of the heavens, for these charts were in use long before the compass had been introduced on board ship (as early as 1205, according to Guiot de Provins) although it became fully serviceable only after the needle had been attached to the compass card, an improvement probably introduced by Flavio Gioja of Amalfi in the beginning of the 14th century. The compass may of course have been used for improving these charts, but they originated without its aid, and it is therefore misleading to describe them asCompass or Loxodromiccharts, and they are now known asPortolanocharts.
None of these charts is graduated, and the horizontal and vertical lines which cross many of them represent neither parallels nor meridians. Their most characteristic feature, and one by which they can most readily be recognized, is presented by groups or systems of rhumb-lines, each group of these lines radiating from a common centre, the central group being generally encircled by eight or sixteen satellite groups. In the course of time the centres of radiation of all these groups had imposed upon them ornaterose dei venti, or windroses, such as may still be seen upon our compass-cards. Each chart was furnished with a scale of miles. These miles, however, were not the ordinary Roman miles of 1000 paces or 5000 ft., but smaller miles of Greek or Oriental origin, of which six were equal to five Roman miles, and as the latter were equal to 1480 metres, the Portolano miles had a length of only 1233 metres, and 75.2 of the former, and 90.3 of the latter were equal to a degree. The difference between these miles was known, however, only to the more learned among the map-makers, and when the charts were extended to the Atlantic seaboard the two were assumed to be identical.
On these old charts the Mediterranean is delineated with surprising fidelity. The meridian distance between the Straits of Gibraltar and Beirut in Syria amounts upon them to about 3000 Portolano miles, equal in lat. 36° N. to 40.9°, as compared with an actual difference of 41.2°, and a difference of 61° assumed by Ptolemy. There exists, however, a serious error of orientation, due, according to Professor H. Wagner, to the inexperience of the cartographers who first combined the charts of the separate basins of the Mediterranean so as to produce a chart of the whole. This accounts for Gibraltar and Alexandria being shown as lying due east and west of each other, although there is a difference of 5° of latitude between them, a fact known long before Ptolemy.
The production of these charts employed numerous licensed draughtsmen in the principal seaports of Italy and Catalonia, and among seamen these MS. charts remained popular long after the productions of the printing-press had become available. The oldest of these maps which have been preserved, the so-called “Pisan chart,†which belongs probably to the middle of the 13th century, and a set of eight charts, known by the name of its former owner, the Cavaliere Tamar Luxoro, of somewhat later date, are both the work of Genoese artists. Among more eminent Genoese cartographers are Joannes da Carignano (d. 1344), Petrus Vesconte, who worked in 1311 and 1327, and is the draughtsman of the maps illustrating Marino Sanuto’sLiber secretorum fidelium crucis, which was to have roused Christendom to engage in another crusade (figs. 19 and 21) Battista Beccario (1426, 1435) and Bartolomeo Pareto (1455). Venice ranks next to Genoa as a centre of cartographic activity. Associated with it are Francesco Pizigano (1367-1373), Francesco de Cesanis (1421), Giacomo Giroldi (1422-1446), Andrea Bianco (1436-1448) Giovanni Leardo (1442-1452), Alvise Cadamosto, who was associated with the Portuguese explorers on the west coast of Africa (1454-1456) and whosePortolanowas printed at Venice in 1490, and Fra Mauro (1457).
Associated with Ancona are Grazioso Benincasa and his son Andreas, whose numerous charts were produced between 1461 and 1508, and Count Ortomano Freducci (1497-1538).
The earliest among Majorcan and Catalonian cartographers is Angelino Dulcert (1325-1339) whom A. Managhi claims as a Genoese, whose true name according to him was Angelino Dalorto.Other Catalans are Jahuda Cresques, a Jew of Barcelona, the supposed author of the famous Catalan map of the world (1375), Guglielmo Solerio (1384), Mecia de Viladestes (1413-1433) Gabriel de Valleseche (1439-1447) and Pietro Roselli, a pupil of Beccario of Genoa (1462).
These maps were originally intended for the use of seamen navigating the Mediterranean and the coasts of the Atlantic, but in the course of time they were extended to the mainland and ultimately developed into maps of the whole world as then known. Thus Pizigano’s map of 1367 extends as far east as the Gulf of Persia, whilst the Medicean map of 1356 (at Florence) is remarkable on account of a fairly correct delineation of the Caspian, the Shari river in Africa, and the correct direction given to the west coast of India, which had already been pointed out in a letter of the friar Giovanni da Montecorvino of 1252. Most of the expansions of Portolano maps into maps of the world are circular in shape, and resemble the wheel maps of an earlier period. This is the character of the map of Petrus Vesconte of 1320 (fig. 21), of Giovanni Leardo (1448) and of a Catalan map of 1450. Jerusalem occupies the centre of these maps, Arab sources of information are largely drawn upon, while Ptolemy is neglected and contemporary travellers are ignored. Far superior to these maps is Fra Mauro’s map (1457), for the author has availed himself not only of the information collected by Marco Polo and earlier travellers, but was able, by personal intercourse, to gather additional information from Nicolo de’ Conti, who had returned from the east in 1440, and more especially from Abyssinians who lived in Italy at that time. His delineation of Abyssinia, though unduly spread over a wide area, is indeed wonderfully correct.
Very different in character is the Catalan map of 1375, for its author, discarding Ptolemy, shows India as a peninsula. On the other hand, an anonymous Genoese would-be reformer of maps (1457; fig. 24), still adheres to the erroneous Ptolemaic delineation of southern Asia, and the same error is perpetuated by Henricus Marvellus Germanus on a rough map showing the Portuguese discoveries up to 1489. None of these maps is graduated, but if we give the Mediterranean a length of 3000 Portolano miles, equivalent in 36° N. to 41°, then the longitudinal extent of the old world as measured on the Genoese map of 1457 would be 136° instead of 177° or more as given by Ptolemy.
The Revival of Ptolemy.—Ptolemy’s great work became known in western Europe after Jacobus Angelus de Scarparia had translated it into Latin in 1410. This version was first printed in 1475 at Vicenza, but its contents had become known through MS. copies before this, and their study influenced the construction of maps in two respects. They led firstly to the addition of degree lines to maps, and secondly to the compilation of new maps of those countries which had been inadequately represented by Ptolemy. Thus Claudius Clavus Swartha (Niger), who was at Rome in 1424, compiled a map of the world, extending westward as far as Greenland. The learned Cardinal Nicolaus Krebs, of Cusa (Cues) on the Moselle, who died 1464, drew a map of Germany which was first published in 1491; D. Nicolaus Germanus, a monk of Reichenbach, in 1466 prepared a set of Ptolemy’s maps on a new projection with converging meridians; and Paolo del Pozzo Toscanelli in 1474 compiled a new chart on a rectangular projection, which was to guide the explorer across the western ocean to Cathay and India.
Of the seven editions of Ptolemy which were published up to the close of the 15th century, all except that of Vicenza (1475) contained Ptolemy’s 27 maps, while Francesco Berlinghieri’s version (Florence 1478), and two editions published at Ulm (1482 and 1486), contained four or five modern maps in addition, those of Ulm being by Nicolaus Germanus.
The geographical ideas which prevailed at the time Columbus started in search of Cathay may be most readily gathered from two contemporary globes, the one known as the Laon globe because it was picked up in 1860 at a curiosity shop in that town, the other produced at Nuremberg in 1492 by Martin Behaim.22The Laon globe is of copper gilt, and has a diameter of 170 mm. The information which it furnishes, in spite of a legend intended to lead us to believe that it presents us with the results of Portuguese explorations up to the year 1493, is of more ancient date. The Nuremberg globe is a work of a more ambitious order. It was undertaken at the suggestion of George Holzschuher, a travelled member of the town council. The work was entrusted to Martin Behaim, who had resided for six years in Portugal and the Azores, and was believed to be a thoroughly qualified cosmographer.The globe is of pasteboard covered with whiting and parchment, and has a diameter of 507 mm. The author followed Ptolemy not only in Asia, but also in the Mediterranean. He did not avail himself of the materials available in his day. Not even the coasts of western Africa are laid down correctly, although the author claimed to have taken part in one of the Portuguese expeditions. The ocean separating Europe from Asia is assumed as being only 126° wide, in accordance with Toscanelli’s ideas of 1474. Very inadequate use has been made of the travels of Marco Polo, Nicolo de’ Conti, and of others in the east.23On the other hand, the globe is made gay with flags and other decorations, the work of George Glockendon, a well-known illuminator of the time.
The maritime discoveries and surveys of that age of great discoveries were laid down upon so-called “plane-charts,†that is, charts having merely equidistant parallels indicated upon them, together with the equator, the tropics and polar circles, or, in a more advanced stage, meridians also. The astrolabe quadrant or cross-staff enabled the mariner to determine his latitude with a certain amount of accuracy, but for his longitude he was dependent upon dead reckoning, for although various methods for determining a longitude were known, the available astronomical ephemerides were not trustworthy, and errors of 30° in longitude were by no means rare. It was only after the publication of Kepler’sRudolphine Table(1626) that more exact results could be obtained. A further difficulty arose in connexion with the variation of the compass, which induced Pedro Reinel to introduce two scales of latitude on his map of the northern Atlantic (1504; fig. 27).