in Columbus’ time in Margry’s _Navigations Françaises_, p. 402, and in M. F. Navarrete’s _Sobre la historia de la náutica y de las ciencias matemáticas_, Madrid, 1846,—a work now become rare. The rudder, in place of two paddles, one on each quarter, had come into use before this time; but the reefing of sails seems not yet to have been practised. (Cf. _De Gama’s Voyages_, published by the Hakluyt Society, p. 242.) Columbus’ record of the speed of his ship seems to have been the result of observation by the unaided eye. The log was not yet known; the Romans had fixed a wheel to the sides of their galleys, each revolution of which threw a pebble into a tally-pot. The earliest description which we have in the new era of any device of the kind is in connection with Magellan’s voyage; for Pigafetta in his Journal (January, 1521), mentions the use of a chain at the hinder part of the ship to measure its speed. (Humboldt, _Cosmos_, Eng. tr., ii. 631; v. 56.) The log as we understand it is described in 1573 in Bourne’s _Regiment of the Sea_, nothing indicating the use of it being found in the earlier manuals of Medina, Cortes, and Gemma Frisius. Humfrey Cole is said to have invented it. Three years later than this earliest mention, Eden, in 1576, in his translation of Taisnier’s _Navigatione_, alludes to an artifice “not yet divulgate, which, placed in the pompe of a shyp, whyther the water hath recourse, and moved by the motion of the shypp, with wheels and weyghts, doth exactly shewe what space the shyp hath gone” (_Carter-Brown Catalogue_, i. no. 310),—a reminiscence of the Roman side-wheels, and a reminder of the modern patent-log. Cf. article on “Navigation” in _Encyclopedia Britannica_, ninth ed. vol. xvii.] An instrument which could more readily adapt itself to the swaying of the observer’s body in a sea-way, soon displaced in good measure the astrolabe on shipboard. This was the cross-staff, or jackstaff, which in several modified forms for a long time served mariners as a convenient help in ascertaining the altitude of the celestial bodies. Precisely when it was first introduced is not certain; but the earliest description of it which has been found is that of Werner in 1514. Davis, the Arctic navigator, made an improvement on it; and his invention was called a backstaff.