With a grid pattern to mark their position on the surface of the earth, and the means to plot a course, mariners confidently moved across the trackless, open ocean. And finally, with the development of the marine chronometer in 1761, navigators could also determine longitude. By the end of the fifteenth century, mariners could determine their latitude position from the sun as well as from the stars. Later, navigators were able to use Polaris at any time of the night without having to wait for it to reach its zenith. At first, only the meridian altitude of Polaris was used-that point when it reached its zenith in the sky. To the end of the fifteenth century, the celestial body most often used was Polaris, the North Star, for this was the easiest to use and required no tables of declination. Celestial navigation-determining one's position from observations of the sun or stars-provided greater flexibility. Christopher Columbus practiced latitude sailing on his 1492-1493 voyage, as did Vasco da Gama when he rounded Cape of Good Hope and reached Calicut, India in 1498. Latitude sailing enabled the mariner to reach his objective without having to know the longitude-it was only necessary to keep sailing at the same latitude until the destination was reached. This method required no elaborate tables of declination or complex mathematical calculations all that was needed was to keep that celestial body at the same declination, its angular height above the horizon. Another method is known as "latitude sailing" or "running down your easting (or westing)." Once the navigator reached a desired latitude, which he determined by sightings of a celestial body (Sun or the Pole Star), he maintained his course on that latitude by sailing due east or west. When conditions were right for taking celestial sightings, the dead reckoning course was updated and corrected. Continuous records were made of the direction traveled, provided by the magnetic compass, and distance as the result of time elapsed the time elapsed (measured by a sand-glass) multiplied by speed. The most basic method used by the navigator to plot the course on a chart is called "deduced" (or "dead") reckoning. As voyaging increased into the uncharted regions of the open ocean, the navigator had to know his exact position at sea, and, its corollary, be able to return whence he started in order to bring back information about his discoveries. Voyages were short and principally followed the coast ships were rarely out of sight of land for more than a few hours' time. Until the beginning of the sixteenth century, navigators had scant need to fix their precise position by latitude and longitude.