318 ROYAL SOCIETY OF (CANADA 



Antonio, the western island ; according to the shifting political neces- 

 sities which from time to time arose. For reasons stated on a previous 

 page, tho western island must be considered to be the legal point of 

 departure, and it — San Antonio — is in 17° 12' of north latitude and 

 25° 5' 7" of west longitude. 



Upon reflection, it will appear that there are only two inquiries 

 concerning the location of the line of demarcation which can yield any 

 result of historical interest. First, where does this line fall under 

 present conditions of nautical science ? and second, where was it sup- 

 posed to fall by the Spaniards and Portuguese governments, under the 

 conditions existing at the time of the treaty, or as near as possible to 

 it ? This latter problem may be solved by the aid of maps ; but 

 not by weaving a tissue of hypotheses out of Jaime Ferrer's errors or 

 by performing mathematical processes on globes of imaginary dimen- 

 sions. If the distances had been stated in degrees the case would be 

 different, but the Pope and the plenipotentiaries avoided degrees and 

 laid down the distance in leagues. The degree is a relative term of 

 length having no intrinsic value but depending on the circle of which 

 it is the three hundred and sixtieth part. It is the same on a library 

 globe as on the globe of tlie earth — the league is a definite concrete 

 quantity independent of globes or circles. The terrestrial globe of 

 Ferrer was 252,000 stades in circumference ; Enciso had two sizes in 

 his Suma, one (which Mr. Harrisse adopts) of 192,000 stades, and an- 

 other which he gave out to practical sailors of 201,600 stades ; Colum- 

 bus imagined a globe of 163,200 -stades only, and to that he clung all 

 his life. It is manifest that 370 leagues measured upon four globes so 

 different in magnitude would extend over greatly different numbers of 

 degrees, and. when all these varying quantities are combined with 

 others as problematical and turned round in a mathematical kaleido- 

 scope, the effect is bewildering. 



Returning to the first question, I would repeat that the real latitude 

 of the island of San Antonio is J 7° 12' north, and would add that, on 

 that parallel, degrees of longitude are 57-32 of our nautical miles in 

 length. It has been shown, on previous pages, that four Roman or old 

 Italian miles, of 1618 English yards each, were reckoned to a league, 

 and therefore, the 370 leagues of Tordesillas multiplied by four were 

 1480 Italian miles. As the English nautical mile contains 2029 Eng- 

 lish yards, the following sum in simple arithemetic will tell us what 

 these leagues are in our familiar measure : — 



yds. yds. Ital. miles. Eng. naut. miles. 



2029 : 1618 : : 1480 : 1180-2 



The 370 leagues are, therefore, equivalent to 1180 of our marine 

 miles, omitting the fraction. 



