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'.

[Moluccan rights sold to Portugal.] The disputes between the Spaniards
and the Portuguese, occasioned by the uncertainty of the eastern
boundary--Portugal had already founded a settlement in the Spice
Islands--were set at rest by an agreement made in 1529, in which
Charles V. abandoned his pretended rights to the Moluccas in favor
of Portugal, for the sum of 350,000 ducats. The Philippines, at that
time, were of no value.

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