The Ilinvenzoii Jlange. 



foremost, wus that nf his immediate precursor, Marinus of Tyre, or else those 

 gathered by himself from the more or less accurate reports of travellers and 

 seafarers. C*) All can see how defective such a method must Ite. From the 

 early itineraries traced without compass in determining the directions, without 

 chronometers for the intervals of time and distiinces, and without sufficient 

 knowledge of the marine and atmospheric currents, it was obviously impossible 

 to obtain other than quite hypothetic, and for the most part only roughly 

 approximate results. ('■') The reduction of the route distances to astronomic 

 notations (degrees and fractions of degrees) was made by Ptolemy with the 

 stadium luiit e(|uivalent to the 500th part of the equatorial degree. ('") But 

 we know that those routes were })ased on a different unit of measure, namely, 

 the Olympic stadium of 600 to the equatorial degree. Hence, if foi' instance, 

 it was a (piestion of an itinerary of ^^,000 stadia (in the direction of the 

 meridian), the number of corresponding degrees woidd be 5 of latitude 

 according to the Olympic measure, while according to Ptolemy it came to 6°. 

 And in general, to olitain the true, or the approximately true, differences of 

 latitudes and longitudes, we have to multiply by ;'; those given l)v the 

 Geographer, or, which is the same thing, reduce them by ^. At the same time 

 this single operation is very far from sufficing to introduce any accuracy into 

 the Ptoleniiuc tables. It cannot be asserted in the first place that all the 

 itineraries without exception were recorded in Olymjiic stadia; nor is the 

 possibility to be e.vcluded that for some of them tlie stadium of Eratosthenes 

 of 700 to the eciuatorial degree was taken as the unit : iii which case the 

 reduction should be by ?. Moreover, in a great many cases there occur ernjrs 

 of another nature, amongst wdiich outstanding are those <lerived from llie 

 imjierfect knowledge possessed by the ancients of many places and countries, 

 from the inevitable inaccuracies in the calculation of distances and in 

 determining the relative positions, from the windings of the route followed and 

 so on. Despite of all this it is remarkable, not to say absolutely astounding, 

 that the above-mentioned single reduction by } suffices for the geographical 

 sketch of the Upper Nile lands, such as is drawn by Ptolemy's (ieography, to 

 correspond broadly if not precisely with that presented to us by the modern 

 maps. On this no doubt quite casual coincidence it will not be useless to dwell 

 for a moment. 



The latitude of .\lexandria is given by Ptolemy as 30 30' X. (it is really 

 31° P2'); from Alexandria to the parallel of the eastern lake are therefore 

 reckoned 37' 30' E. = 37' E. Now the j of 37 ')' are equivalent to 3r 25' = 

 31° 15', and that lake thus falls under 0" 45' south latitude. A similar 

 calculation for the western lake brings us tn north latitude 0° 9'. (") These 



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