As to the longitude, I would say that I found so much difficulty in discovering it that I had to labor very hard to ascertain the distance I had made by means of longitude.  I found nothing better, at last, than to watch the opposition of the planets during the night, and especially that of the moon, with the other planets, because the moon is swifter in her course than any other of the heavenly bodies.  I compared my observations with the almanac of Giovanni da Monteregio, which was composed for the meridian of the city of Ferrara, verifying them with the calculations in the tables of King Alfonso, and, afterward, with the many observations I had myself made one night with another.

On August 23, 1499—­when the moon was in conjunction with Mars, which, according to the almanac, was to take place at midnight, or half an hour after—­I found that when the moon rose to the horizon, an hour and a half after the sun had set, the planet had passed in that part of the east.  I observed that the moon was about a degree and some minutes farther east than Mars, and at midnight she was five degrees and a half farther east, a little more or less.  So that, making the proportion, if twenty-four hours are equal to three hundred and sixty degrees, what are five hours and a half equal to?  I found the result to be eighty-two degrees and a half, which was equal to my longitude from the meridian of the city of Cadiz, then giving to every degree sixteen leagues and two-thirds, which is five thousand four hundred sixty-six miles and two-thirds.  The reason why I give sixteen leagues to each degree is because, according to Tolomeo and Alfagrano, the earth turns twenty-four thousand miles, which is equal to six thousand leagues, which, being divided by three hundred sixty degrees, gives to each degree sixteen leagues and two-thirds.  This calculation I certified many times conjointly with the pilots, and found it true and good.

It appears to me, most excellent Lorenzo, that by this voyage most of those philosophers are controverted who say that the torrid zone cannot be inhabited on account of the great heat.  I have found the case to be quite the contrary.  I have found that the air is fresher and more temperate in that region than beyond it, and that the inhabitants are also more numerous here than they are in the other zones, for reasons which will be given below.  Thus it is certain that practice is of more value than theory.

Thus far I have related the navigation I accomplished in the south and west.  It now remains for me to inform you of the appearance of the country we discovered, the nature of the inhabitants, and their customs, the animals we saw, and of many other things worthy of remembrance which fell under my observation.  After we turned our course to the north, the first land we found to be inhabited was an island at ten degrees distant from the equinoctial line.  When we arrived at it we saw on the sea-shore a great many