Observations for latitude.
The astrolabe.
There was not much difficulty in computing latitude either by the altitude of the polar star or by using tables of the sun's declination, which the astronomers of the time were equal to calculating. The astrolabe used for gauging the altitude was a simple instrument, which had been long in use among the Mediterranean seamen, and had been described by Raymond Lullius in the latter part of the thirteenth century. Before Columbus's time it had been somewhat improved by Johannes Müller of Königsberg, who became better known from the Latin form of his native town as Regiomontanus. He had, perhaps, the best reputation in his day as a nautical astronomer, and Humboldt has explained the importance of his labors in the help which he afforded in an age of discovery.
Dead reckoning.
It is quite certain that the navigators of Prince Henry, and even Columbus, practiced no artificial method for ascertaining the speed of their ships. With vessels of the model of those days, no great rapidity was possible, and the utmost a ship could do under favorable circumstances was not usually beyond four miles an hour. The hourglass gave them the time, and afforded the multiple according as the eye adjusted the apparent number of miles which the ship was making hour by hour. This was the method by which Columbus, in 1492, calculated the distances, which he recorded day by day in his journal. Of course the practiced seaman made allowances for drift in the ocean currents, and met with more or less intelligence the various deterrent elements in beating to windward.
The seaman's log.
Humboldt, with his keen insight into all such problems concerning their relations to oceanic discoveries, tells us in his Cosmos how he has made the history of the log a subject of special investigation in the sixth volume of his Examen Critique de l'Histoire de la Géographie, which, unfortunately, the world has never seen; but he gives, apparently, the results in his later Cosmos.
THE ASTROLABE OF REGIOMONTANUS.
It is perhaps surprising that the Mediterranean peoples had not perceived a method, somewhat clumsy as it was, which had been in use by the Romans in the time of the republic. Though the habit of throwing the log is still, in our day, kept up on ocean steamers, I find that experienced commanders quite as willingly depend on the report of their engineers as to the number of revolutions which the wheel or screw has made in the twenty-four hours. In this they were anticipated by these republicans of Rome who attached wheels of four feet diameter to the sides of their ships and let the passage of the water turn them. Their revolutions were then recorded by a device which threw a pebble into a tally-pot for each revolution.