It was this same Martin Behaim (Humboldt, “Cosmos,” 1860, Vol. II. p. 255) who received a charge from King John II of Portugal to compute tables for the sun’s declination and to teach pilots how to “navigate by the altitudes of the sun and stars.” It cannot now be decided whether at the close of the fifteenth century the use of the log was known as a means of estimating the distance traversed while the direction is indicated by the compass; but it is certain that the distinguished voyager Francisco Antonio Pigafetta (1491–1534) the friend and companion of Magellan--Magalhæns--speaks of the log (_la catena a poppa_) as of a well-known means of measuring the course passed over. Nothing is to be found regarding way-measurers in the literature of the Middle Ages until we come to the period of several “books of nautical instruction,” written or printed by this same Pigafetta (“Trattato di Navigazione,” probably before 1530); by Francisco Falero, a brother of Ruy Falero, the astronomer (“Regimiento para observar la longitud en la mar,” 1535); by Pedro da Medina, of Seville (“Arte de Navegar,” 1545); by Martin Cortez, of Bujalaroz (“Breve Compendio de la esfera, y de la arte de navegar,” 1551), and by Andres Garcia de Cespedes (“Regimiento de Navigacion y Hidrografia,” 1606). From almost all these works--some of which, if not all, have naturally become very scarce--as well as from the “Summa de Geografia” which Martin Fernandez de Enciso had published in 1519, we learn most distinctly that the “distance sailed over” was then ascertained in Spanish and Portuguese ships not by any distinct measurement, but only through estimation of the eye, according to certain established principles. Medina says (lib. iii. caps. 11–12): “In order to know the course of the ship, as to the length of distance passed over, the pilot must set down in his register how much distance the vessel hath made according to hours (_i. e._ guided by the hour-glass, _ampoleta_); and, for this, he must know that the most a ship advances in an hour is four miles, and, with feebler breezes, three or only two.” Cespedes, in his “Regimiento” (pp. 99 and 156) calls this mode of proceeding _echar punto por fantasia_, and he justly remarks that if great errors are to be avoided, this _fantasia_ must depend on the pilot’s knowledge of the qualities of his ship. Columbus, Juan de la Cosa, Sebastian Cabot and Vasco da Gama, were not acquainted with the log and its mode of application, and they all estimated the ship’s speed merely by the eye, while they ascertained the distance they had made merely through the running down of the sand in the glasses known as _ampoletas_.