TRANSACTIONS OF SECTION E. '705 



preceded bim, for before a map like bis could be produced mucb preliminary work 

 'had been accomplisbed. Parmenides of Elea (460 b.c.) bad demonstrated that 

 our eartb was a globe, and Eratosthenes (276-196 B.C.) bad approximately deter- 

 mmed its size. Hipparcbus (190-120), the greatest astronomer of antiquity, the 

 discoverer of the precession of the equinoxes, and the author of a catalogue of stars, 

 had transferred to our earth the auxiliary lines drawn by biui across the heavens. 

 He had taught cartographers to lay down places according to their latitude and 

 longitude, and how to project a sphere upon a plane. It is to bim we are indebted 

 for the stereograpbic and orthographic projections of the sphere. Ptolemy himself 

 invented the tangential conical projection. 



The gnomon or sun-dial, an instrument known to the Chinese 600 years before 

 Christ, had long been used for the determination of latitudes, and the results were 

 relatively correct, although uniformly subject to an error of 16 minutes, which 

 was due to the observers taking the altitude of the upper limb of the sun, 

 when measuring the shadow case by their dial, instead" of that of the sun's 

 -centre. 



It was known, likewise, that differences of longitude could be determined by 

 the simultaneous observation of eclipses of the sun or moon, or of occultations of 

 stars, and Hipparcbus actually calculated Ephemerides for six years in advance to 

 focilitate computations. Ptolemy himself suggested the use of lunar distances. 

 But so imperfect were the astrolabes and other instruments used by the ancient 

 astronomers, and especially their time-keepers, that precise results were quite out 

 of the question. 



Ptolemy, in fact, contented himself with accepting eight latitudes determined 

 by actual observation, of which four were in Egypt, whilst of the three longitudes 

 known to bim be only utilised one in the construction of his map. Unfortunately, 

 the one selected proved the least accurate, being erroneous to the extent of 32 per 

 cent., whilst the error of the two which he rejected did not exceed 13 per cent.* 

 This want of judgment, pardonable, no doubt, under the circumstances, vitiated 

 Ptolemy's delineation of the Mediterranean to a most deplorable extent, far more 

 ■so than did his assumption that a degree only measured live hundred stades, when 

 in reality it measures six hundred. For whilst the breadth of his Mediterranean, 

 being dependent upon the relatively correct latitudes of Alexandria, Rhodes, 

 Rome, and Massilia, fairly approximates the truth, its length is exaggerated to the 

 •extent of nearly 50 per cent., measuring 62° instead of 41° 40'. This capital error 

 of Ptolemy is due therefore to the unfortunate acceptance of an incorrect longitude, 

 quite as much as to an exaggeration of itinerary distances. It is probable that 

 Ptolemy would have presented us with a fairer likeness of our great inland sea 

 bad he rejected observed latitudes and longitudes altogether and trusted exclusively 

 to his itineraries and to such bearings as the marmers of the period could have 

 supplied bim with. 



No copy of Ptolemy's original set of maps has reached us, for the maps drawn 

 by Agatbodaemon in the fifth century are, under the most favourable circumstances, 

 merely reductions of Ptolemy's originals, or they are compiled from Ptolemy's 

 ■' Geography,' which, apart from a few explanatory chapters, consists almost wholly 

 of lists of places, with their latitudes and longitudes. 



An examination of Ptolemy's maps shows very clearly that they were almost 

 wholly compiled from itineraries, the greater number of which their author borrowed 

 from his predecessor Marinus. It shows, too, that Ptolemy's critical acumen as a 

 •compiler cannot be rated very high, and that he failed to utilise much information 

 ■ol a geographical nature which was available in his day. His great merit consisted 

 in having taught cartographers to construct their maps according to a scientific 



' The three longitudes are the following : — 



ReMill of ancient Adorte>i bv Actual difler- 



observations Ptoleuiv ence of longitude 



Arbela . . 45° E. of Carthage . . . 45° " . 34° 



Babylon . . 12° SO' E. of Alexandria . . 18° 30' 14° 18' 



^ome . . 20° E. of Alexandria . . 23° 50' . 17° 24' 



1891 



Z7 



