[s. E. DAWSON] THE LINES OF DEMARCATION 503 



To the statesmen of the sixteenth century the ownership of the 

 Moluccas and the western limit of Brazil depended upon the solution 

 of this question. To sailors and scholars it involved the great riddle 

 of the age, "the secret of longitude;" for on the unquiet ocean, these 

 leagues of Tordesillas could not be measured, nor marked, save by 

 astronomical methods requiring a knowledge of the length of a great 

 circle of the eftrth and consequently of the length of a degree of the 

 equator. 



Now, so far as the absolute distance is concerned, to wit, the three 

 ' hundred and seventy leagues of the treaty, the circumference of the 

 earth had no more to do with it than the circumference of the moon. 

 The difficulty was solely in the practical measurement of distances at sea 

 which the necessity of the case required to be resolved into degrees of 

 longitude. The only method then known was by dead reckoning, and 

 the deceptive character of that mode is manifest in the simple fact that, 

 lat the convention of Badajoz in 1524, the maps shovm differed by forty- 

 six degrees. We now know, within a few miles, the circumference of 

 the earth and all are agreed as to the length of a degree, but so hard is 

 it to realize the difficulties of past ages that many writers, down to even 

 recent periods, have transposed and applied to marine leagues, the un- 

 certainties which really existed with regard to degrees only. This is 

 confusing to the student, for 'all the old navigators reckoned in leagues 

 and whether we are following the journals of Columbus, or Cartier, or 

 Champlain, it is necessary, if we wish to be exact, to have clear notions 

 concerning this general standard of sea distances. By unguarded 

 language ou tliis subject, Mr. Harrisse is entangling our early history 

 anew ; for in his Diplomatic History, he writes of leagues of Enciso, 

 leagues^ of Ferrer, leagues of Columbus, as if they differed in length, 

 instead of writing of degrees of Enciso, of Ferrer, of Columbus ; for, 

 while the lea,gues were the same, the degrees differed in the number 

 of leagues they contained, and when Mr. Harrisse takes varying and 

 erroneous quantities and makes them perform trigonometrical functions, 

 the confusion is made worse ; since tJie sine, cosine, tangent or square 

 of an erroneous quantity acquires no value from being found in mathe- 

 m.atical tables — rather the contrary, because to square a mistake is to 

 raise it to a higher power of error. 



It is beyond the scope of this paper to discuss the numerous 

 national and provincial land leagues or miles. The inquiry will be 

 confined to the marine league of Columbus and other siailors during 

 the period of the great expansion of European nautical enterprise. For 

 ready reference, it is convenient here to remind the reader that the 

 circimiference of the earth is now taken to be 21,600 nautical or geo- 



