810 ROYAL SOCIETY OF CANADA 



to Ferrer's statement (Ai)peiKlix D) will show that he (Ferrer) did not 

 give a valuation of 21-875 (21 "jg) but a valuation of 21-625 (21 ''[g) 

 leagues for liis equinoctial degree. Ferrer's arithmetic was wrong accord- 

 ing to his datum, and his other measurements are also wrong. The only 

 one which concerns tliis inquiry is that on the latitude of the Cape 

 Verde Islands, which he states to be 15°, and he gives the corresponding 

 length of a degree on that pamllel as 20 "Ig leagues ; whereas a correct 

 calculation from the data of Eratosthenes (w^hich he gives correctly 

 enough) would make it 21 ^jg (21-129) leagues. These are not four 

 valuations of the league, but four valuations of the degree. It will be 

 seen from the table (Appendix E) that Ferrer, in following Eratosthenes, 

 made the globe one-sixth larger than it is, and in his statement (App. 

 D, para. 10) it will also be seen th'.it he knew very little about the ancient 

 cosmographers ; for he enumerates among his learned men "Ambrosi, 

 Maerobi, Teodosi," as three distinct persons, whereas thoy are one, to 

 wit. Aurelius Tlieodosius Macrobius, and, above all. he wïis wrong in 

 assuming the 500 stadi-.s of Ptolemy and tlie 700 stades of Eratosthenes 

 to express a degree of the same absolute length — to be in short identical 

 concrete quantities. Of what value are the sines or tangents of such 

 quantities as these ? Or wlmt mathematical results can be based upon 

 the statements of an authority who did not reason correctly, even from 

 his own erroneous data ? 



Again, vnth regard to Enciso, we read (at p. 105) that "in Enciso's 

 "sphere, the value of the equatorial degree was 16 -660 leagues," and 

 lower dowm "Enciso's equatorial degree contained 18-0498 of his 

 "leagues," and (at p. 192) the windrose in Enciso's Suma, "seems to 

 " have been calculated on the basis of 17 ^|„ leagues." Mr. Harrisse 

 in this case thinks tlmt "logic requires" him to select 16 ^[g leagues as 

 the proper quantity. That is open to question, ])ut here again, what 

 value c<an such data (as these have upon which to base a mathematical 

 argument ? 



It would be wrong, however, to suppose that Mr. Harrisse thinks 

 he is dealing with real leagues. It is the inaccuracy of writing "leagues" 

 of Enciso or Ferrer, etc., when he means "degrees" which is misleading. 

 In a note at p. 193, he says, " The probability is that the league, wliich 

 "is always a imit usual and fixed, was the same for Enciso and Ferrer ; 

 " that is at the rate of 32 stades for one league." This throws an ad- 

 ditional vagueness over the matter. It is like saying that it is probable 

 that the three angles of a triangle are er^ual to two right angles, and 

 then going on to argue inijuirtially, by trigonometrical methods, on botli 

 hypotheees — that they are and that they are not thus equal. The effect 

 is confusing and tends to reopen the theories of "fancy leagues" which 



