Marinus' estimate of the "length" of the inhabited earth over land (from west to east) may be stated in three parts, (I) from the "Fortunate islands" to Hierapolis on the Euphrates 28,800 stades, (2) from Hierapolis to the "Stone Tower" (near the Pamir?) 26,280, and (3) from the "Stone Tower" to Sera, the capital of the Serae (? inland China), 36,20o stades, making 91,28o stades in all. Ptolemy reduced the last two estimates to 24,000 and 18,1o° respectively, thus arriving at a total of 70,90o stades. Reckoning 400 stades as the proper length of a degree of longitude measured at the latitude of Rhodes (36°), we have as the "length" according to Marinus 228°, which he rounded down to 225°, and as Ptolemy's estimate 177° 15', in round figures 18o°. The measurement by Marinus of the distance by sea gave 125° from the Fortunate islands to K,ory, a promontory in India opposite the northern point of Ceylon, and 61° more to the "Golden Chersonese"; the distances from the Golden Cher sonese eastwards to Zaba and thence nearly south to Kattigara Marinus only gave in days of sailing. Ptolemy reduced the figure of 61° to 48', and the difference in longitude between the Golden Chersonese and Kattigara he made 17° 1o'. Thus Ptolemy's total became + 48' ± 17° 1o' =176° 58' say 177°, to which he added 3° for the difference in longitude between Katti gara and the capital of the Sinae (sea-coast of China), making 180° as before.
But in thus estimating the length and breadth of the known world, Ptolemy attached a very different sense to these terms from that which they had generally borne. Most earlier Greek geographers and "cosmographers" supposed the inhabited world to be surrounded on all sides by sea, and to form a vast island in the midst of a circumfluous ocean. This notion (perhaps de rived from the Homeric "ocean stream," and certainly not based upon direct observation) was nevertheless in accordance with truth, great as was the misconception involved of the continents included. But Ptolemy in this respect went back to Hipparchus, and assumed that the land extended indefinitely north in the case of eastern Europe, east, south-east and north in that of Asia, and south, south-west and south-east in that of Africa. His boun dary line was in each of these cases an arbitrary limit, beyond which lay the Unknown Land, as he calls it. But in Africa he was not content with this extension southward; he also prolonged the continent eastward from its southernmost known point, so as to form a connection with south-east Asia. In Asia he took the line of coast from the Golden Chersonese as making a great bay towards the Sinae, and then proceeding southwards to Kattigara. The effect was to enclose the Indian ocean as one vast lake sur rounded by Unknown Land. It must be noticed that Ptolemy's extension of Asia eastwards, so as to diminish by 50° of longi tude the interval between easternmost Asia and westernmost Europe, fostered Columbus' belief that it was possible to reach the former from the latter by direct navigation, crossing the Atlantic.
Ptolemy proceeds (i. 19 sq.) to consider the question of maps and methods of constructing them. He first describes (i. a method of conical projection in which the meridian circles are represented as straight lines all meeting in a certain point (a kind of north pole) and the parallels of latitude (in parti cular those passing through Thule, Rhodes, Meroe and Agisymba) as circles with that point as centre. (The fixed "pole," or centre of projection is as nearly as possible the vertex of the cone pass ing through the actual parallel circle of Thule and the equator.) A more elaborate system, in which the meridians are represented as actual arcs of circle and not straight lines, is then described (s. 10 sqq.).
Books ii. to vii. contain Ptolemy's systematic tabular location of places and features in terms of latitude and longitude for all countries. He deals in order with Europe and the Mediterranean, then Africa, then Asia, beginning with Asia Minor and passing to Palestine, Mesopotamia, Arabia, India, etc. Under Europe, the first countries dealt with are the "Britannic islands," Ireland and Albion ; then comes Spain in three divisions, then Gaul in four divisions, then Germany, and so on. The arrangement of the subject-matter in tabular form, instead of being at once embodied in a map, suggests that Ptolemy's object was to enable the stu dent to construct his maps for himself. Nevertheless, the work was from the time of its first publication accompanied by maps, which are regularly referred to in Book viii. How far the maps which are appended to the extant mss. represent the original series is a moot point. It is possible, however, that they have been transmitted by uninterrupted tradition from the time of Ptolemy.
In spite of the merits of Ptolemy's geographical work it can not be regarded as a complete or satisfactory treatise upon the subject. It was the work of an astronomer rather than a geog rapher. Not only did its plan exclude all description of the coun tries with which it dealt, their climate, natural productions, in habitants and peculiar features, but even its physical geography proper is treated in an irregular and perfunctory manner. While Strabo was fully alive to the importance of the rivers and moun tain chains which (in his own phrase) "geographize" a country, Ptolemy deals with this part of his subject in so careless a man tier as to be often worse than useless. In Gaul, for instance, the few notices he gives of the rivers that play so important a part in its geography are disfigured by some astounding errors; while he does not notice any of the great tributaries of the Rhine, though mentioning an obscure streamlet, otherwise unknown, because it happened to be the boundary between two Roman provinces.