sat on deck with his back against the mainmast and with his left hand held up the instrument by the ring at the top.  The long arm was moved round until the two sights fixed upon it were on with the sun.  The point where the other arm then cut the circle gave the altitude.  In conjunction with this instrument were used the tables of solar declination compiled by Regiomontanus, and covering the sun’s declination between the years 1475 and 1566.

The compass in Columbus’s day existed, so far as all essentials are concerned, as it exists to-day.  Although it lacked the refinements introduced by Lord Kelvin it was swung in double-cradles, and had the thirty-two points painted upon a card.  The discovery of the compass, and even of the lodestone, are things wrapt in obscurity; but the lodestone had been known since at least the eleventh century, and the compass certainly since the thirteenth.  With the compass were used the sea charts, which were simply maps on a rather larger and more exact scale than the land maps of the period.  There were no soundings or currents marked on the old charts, which were drawn on a plane projection; and they can have been of little—­practical use to navigators except in the case of coasts which were elaborately charted on a large scale.  The chart of Columbus, in so far as it was concerned with the ocean westward of the Azores, can of course have contained nothing except the conjectured islands or lands which he hoped to find; possibly the land seen by the shipwrecked pilot may have been marked on it, and his failure to find that land may have been the reason why, as we shall see, he changed his course to the southward on the 7th of October.  It must be remembered that Columbus’s conception of the world was that of the Portuguese Mappemonde of 1490, a sketch of which is here reproduced.  This conception of the world excluded the Pacific Ocean and the continent of 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