By far the most important element in the navigation of Columbus, in so far as estimating his position was concerned, was what is known as "dead-reckoning" that is to say, the computation of the distance travelled by the ship through the water. At present this distance is measured by a patent log, which in its commonest form is a propeller-shaped instrument trailed through the water at the end of a long wire or cord the inboard end of which is attached to a registering clock. On being dragged through the water the propeller spins round and the twisting action is communicated by the cord to the clock-work machinery which counts the miles. In the case of powerful steamers and in ordinary weather dead-reckoning is very accurately calculated by the number of revolutions of the propellers recorded in the engine-room; and a device not unlike this was known to the Romans in the time of the Republic. They attached small wheels about four feet in diameter to the sides of their ships; the passage of the water turned the wheels, and a very simple gearing was arranged which threw a pebble into a tallypot at each revolution. This device, however, seems to have been abandoned or forgotten in Columbus's day, when there was no more exact method of estimating dead-reckoning than the primitive one of spitting over the side in calm weather, or at other times throwing some object into the water and estimating the rate of progress by its speed in passing the ship's side. The hour-glass, which was used to get the multiple for long distances, was of course the only portable time measurer available for Columbus. These, with a rough knowledge of astronomy, and the taking of the altitude of the polar star, were the only known means for ascertaining the position of his ship at sea.