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.

The first mishap occurred on Monday, August 6th, when the Pinta carried away her rudder.  The Pinta, it will be remembered, was commanded by Martin Alonso Pinzon, and was owned by Gomaz Rascon and Christoval Quintero, who had been at the bottom of some of the troubles ashore; and it was thought highly probable that these two rascals had something to do with the mishap, which they had engineered in the hope that their vessel would be left behind at the Canaries.  Martin Alonso, however, proved a man of resource, and rigged up a sort of steering gear with ropes.  There was a choppy sea, and Columbus could not bring his own vessel near enough to render any assistance, though he doubtless bawled his directions to Pinzon, and looked with a troubled eye on the commotion going on on board the Pinta.  On the next day the jury-rigged rudder carried away again, and was again repaired, but it was decided to try and make the island of Lanzarote in the Canaries, and to get another caravel to replace the Pinta.  All through the next day the Santa Maria and the Nina had to shorten sail in order not to leave the damaged Pinta behind; the three captains had a discussion and difference of opinion as to where they were; but Columbus, who was a genius at dead-reckoning, proved to be right in his surmise, and they came in sight of the Canaries on Thursday morning, August 9th.

Columbus left Pinzon on the Grand Canary with orders to try to obtain a caravel there, while he sailed on to Gomera, which he reached on Sunday night, with a similar purpose.  As he was unsuccessful he sent a message by a boat that was going back to tell Pinzon to beach the Pinta and repair her rudder; and having spent more days in fruitless search for a vessel, he started back to join Pinzon on August 23rd.  During the night he passed the Peak of Teneriffe, which was then in eruption.  The repairs to the