Page:Dictionary of Greek and Roman Biography and Mythology (1870) - Volume 3.djvu/591

Rh PTOLEMAEUS. strjiiglit lines which converge, north of the equator, towards the common centre of the arcs which repre- sents the parallels of latitude ; and, south of it, to- wards a corresponding point, representing the South Pole. Having laid down these lines, he proceeds to show how to give to them a curved form, so as to make them a truer representation of the meri- dians on the globe itself. The portion of the sur- face of the earth thus delineated is, in length, a whole hemisphere, and, in breadth, the part which lies ])etween 63° of north latitude and 1 6f^° of south latitude. 2. The Historical or Positive Geography of Pto- lemy. — The limits just mentioned, as those within which Ptolemy's projection of the sphere was con- tained, were also those which he assigned to the known world. His own account of its extent and divisions is given in the fifth chapter of his seventh book. The boundaries which he there mentions are, on the east, the unknown land adjacent to the eastern nations of Asia, namely, the Sinae and the people of Serica ; on the south, the unknown land which encloses the Indian Sea, and that adja- cent to the district of Aethiopia called Agisymba, on the south of Libya ; on the west, the unknown land which surrounds the Aethiopic gulf of Libya, and the Western Ocean ; and on the north, the continuation of the ocean, which surrounds the British islands and the northern parts of Europe, and the unknown land adjacent to the northern regions of Asia, namely Sarmatia, Scythia, and Serica. He also defines the boundaries by meridians and parallels, as follows. The southern limit is the pa- rallel of 16-^*^ S. lat., which passes through a point as far south of the equator, as Meroe is north of it, and which he elsewhere describes as the parallel through Prasum, a promontory of Aethiopia : and the nortliern limit is the parallel of 63° N. lat., which passes through the island of Thule : so that the whole extent from north to south is 79^5°, or in round numbers, 80° ; that is, as nearly as pos- sible, 40,000 stadia. Theeas^er« limit is the meridian which passes through the metropolis of the Sinae, which is 119^° east of Alexandria, or just about eight hours : and the western limit is the meridian drawn through the Lisulae Fortunatae (the Canaries) which is 60^°, or four hours, west of Alexandria, and therefore 180°, or twelve hours, west of the easternmost meridian. The various lengths of the earth, in itinerary measure, he reckons at 90,000 stadia along the equator (500 stadia to a degree), 40,000 stadia along the northernmost parallel (222| stadia to a degree), and 72,000 stadia along the parallel through Rhodes (400 stadia to a de- gree), along which parallel most of the measure- ments had been reckoned. In comparing these computations with the actual distances, it is not necessary to determine the true position of such doubtful localities as Thule and the metropolis of the Sinae ; for there are many other indications in Ptolemy's work, from which we can ascertain nearly enough what limits he intends. We cannot be far wrong in placing his northern bound- ary at about the parallel of the Zetland Isles, and his eastern boundary at about the eastern coast of Co- chin China, in fact just at the meridian of 1 10° E. long, (from Greenwich), or perhaps at the opposite side ol the Chinese Sea, namely, at the Philippine Islands at the meridian of 120°. It will then be seen that he is not far wrong in his dimensions from north to PTOLEMAEUS. 579 south ; a circumstance natural enough, since the methods of taking latitudes with tolerable precision had long been known, and he was very careful to avail himself of every recorded observation which he could discover. But his longitudes are very wide of the truth, his length of the known world, from east to west, being much too great. The westernmost of the Canaries is in a little more than 1 8** W. long., so that Ptolemy's easternmost meri- dian (which, as just stated, is in 110° or 120° E. long.) ought to have been that of 128 or 138°, or in round numbers 130° or 140°, instead of 180°; a difference of 50° or 40°, that is, from l-7th to l-9th of the earth's circumference. It is well worthy, however, of remark in passing, that the modern world owes much to this error ; for it tended to encourage that belief in the prac- ticability of a western passage to the Indies, which occasioned the discovery of America by Columbus. There has been much speculation and discussion as to the cause of Ptolemy's great error in this matter ; but, after making due allowance for the uncertainties attending the computations of dis- tance on which he proceeded, it seems to us that the chief cause of the error is to be found in the fact already stated, that he took the length of a degree exactly one sixth too small, namely, 500 stadia instead of 600. As we have already stated, on his own authority, he was extremely careful to make use of every trustworthy observation of lati- tude and longitude which he could find ; but he him- self complains of the paucity of such observations ; and it is manifest that those of longitude must have been fewer and less accurate than those of latitude, both for other reasons, and chiefly on account oi the greater difficulty of taking them. He had, therefore, to depend for his longitudes chiefly on the process of turning into degrees the distances computed in stadia ; and hence, supposing the dis- tances to be tolerably correct, his error as to the longitudes followed inevitably from the error in his scale. Taking Ptolemy's own computation in stadia, and turning it into degrees of 600 stadia each, we get the following results. The length of the known world, measured along the equator, is 90,000 stadia ; and hence its length in degrees is 90'0j"" = 150° ; the error being thus reduced from 50° or 40° to 20° or 10°. But a still fairer me- thod is to take the measurement along the parallel of Rhodes, namely 72,000 stadia. Now the true length of a degree of latitude in that parallel is about 47' = 42 of a degree of a great circle = ^^ x 600 stadia = 470 stadia, instead of 400 ; and the 72,000 stadia give a little over 153 degrees, a result lamost identical with the former. The remaining error of 20° at the most, or 10° at the least, is, we think, sufficiently accounted for by the errors in the itinerary measures, which ex- perience shows to be almost always on the side of making distances too great, and which, in this case, would of course go on increasing, the further the process was continued eastward. Of this source of error Ptolemy was himself aware ; and accordingly he tells us that, among the various computations of a distance, he always chose tho least ; but, for the reason just stated, that least one was probably still too great The method pursued by Ptolemy in laying down the actual positions of places has already been in- cidentally mentioned in the foregoing discussion. He fixed as many positions as possible by tfaoic PP 2