Dead reckoning consisted in charting a route and periodically measuring the ship's position and the distance traveled from a known position. The reckoning data were plotted every day on a sea chart showing the position reached and the point of departure for the following day. The route's direction was easily checked by means of the compass, an essential instrument that had radically transformed navigation methods since the twelfth century. By contrast, reckoning the distance sailed was a more complex task, because it required measuring the ship's speed in a time interval and multiplying that figure by the time elapsed since the previous measurement. The result was always very approximative, for two reasons. First, because the ship's speed was never constant, as it depended on the winds, currents, and the state of the sea. Second, because the flow of time was measured with unreliable instruments such as the water clock and sandglass. The flow of water, in the water clock, or of sand, in the sandglass, was influenced by the instrument's stability, the temperature, and the air humidity. In addition, both the water clock and the sandglass needed to be kept under continuous observation. They had to be turned every half hour, and had to be calibrated daily with the nocturnal astrolabe, an instrument that enabled navigators to determine midnight by observing the stars. The use of astronomical tables made it possible, when conditions permitted, to calibrate the timekeeping devices at dawn, noon and sunset. To measure speed, navigators used chip logs, recording the value every half hour on a wooden board displaying rhumb lines and the route direction. Every four hours, the measured values would be added up, and, at the end of the day, the route and distance would be plotted onto the sea charts.