[Commercially in the New World.] When the circumstances mentioned come to be realized, the Philippines, or, at any rate, the principal market for their commerce, will finally fall within the limits of the western hemisphere, to which indeed they were relegated by the illustrious Spanish geographers at Badajoz. [The Pope's world-partitive.] The Bull issued by Alexander VI, [7] on May 4, 1493, which divided the earth into two hemispheres, decreed that all heathen lands discovered in the eastern half should belong to the Portuguese; in the western half to the Spaniards. According to this arrangement, the latter could only claim the Philippines under the pretext that they were situated in the western hemisphere. The demarcation line was to run from the north to the south, a hundred leagues to the south-west of all the so-called Azores and Cape de Verde Islands. In accordance with the treaty of Tordesillas, negotiated between Spain and Portugal on June 7, 1494, and approved by Julius II, in 1506, this line was drawn three hundred and seventy leagues west of the Cape de Verde Islands. [Faulty Spanish and Portuguese geography.] At that time Spanish and Portuguese geographers reckoned seventeen and one-half leagues to a degree on the equator. In the latitude of the Cape de Verde Islands, three hundred and seventy leagues made 21° 55'. If to this we add the longitudinal difference between the westernmost point of the group and Cadiz, a difference of 18° 48', we get 40° 43' west, and 139° 17' east from Cadiz (in round numbers 47° west and 133° east), as the limits of the Spanish hemisphere. At that time, however, the existing means for such calculations were entirely insufficient. [Extravagant Spanish claims thru ignorance.] The latitude was measured with imperfect astrolabes, or wooden quadrants, and calculated from very deficient tables; the variation of the compass, moreover, was almost unknown, as well as the use of the log. [8] Both method and instruments were wanting for useful longitudinal calculations. It was under these circumstances that the Spaniards attempted, at Badajoz, to prove to the protesting Portuguese that the eastern boundary line intersected the mouths of the Ganges, and proceeded to lay claim to the possession of the Spice Islands. [Spain's error in calculation.] The eastern boundary should, in reality, have been drawn 46 1/2° further to the east, that is to say, as much further as it is from Berlin to the coast of Labrador, or to the lesser Altai; for, in the latitude of Calcutta 46 1/2° are equivalent to two thousand five hundred and seventy-five nautical miles. Albo's log-book gives the difference in longitude between the most eastern islands of the Archipelago and Cape Fermoso (Magellan's Straits), as 106° 30', while in reality it amounts to 159° 85'.