North and South America, and made it reasonable to suppose that any
one who sailed westward long enough from Spain would ultimately reach
Cathay and the Indies. Behaim's globe, which was completed in the year
1492, represented the farthest point that geographical knowledge had
reached previous to the discoveries of Columbus, and on it is shown the
island of Cipango or Japan.

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.

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