Navigation was in a most primitive condition even as late as the middle of last century. Then the method of finding a ship's longitude at sea was the insufficient one of dead reckoning. In other words, the direction and speed of the ship were estimated as closely as possible, and so the position was carried on from day to day. The uncertainty of the method was very great, and many terrible stories might be told of the disastrous consequences which might, and often did, follow in the train of this method by guess-work. It will be sufficient, however, to cite the instance of Commodore Anson. He wanted to make the island of Juan Fernandez, where he hoped to obtain fresh water and provisions, and to recruit his crew, many of whom were suffering from that scourge of old-time navigators—scurvy. He got into its latitude easily enough, and ran eastward, believing himself to be west of the island. He was, however, really east of it, and therefore made the mainland of America. He had therefore to turn round and sail westwards, losing many days, during which the scurvy increased upon his crew, many of whom died from the terrible disease before he reached the desired island.

The necessity for finding out a ship's place when at sea had not been very keenly felt until the end of the fifteenth century. It was always possible for the sailor to ascertain his latitude pretty closely, either by observing the height of the pole-star at night or the height of the sun at noonday; and so long as voyages were chiefly confined to the Mediterranean Sea, and the navigators were content for the most part to coast from point to point, rarely losing sight of land, the urgency of solving the second problem—the longitude of the ship—was not so keenly felt. But immediately the discoveries of the great Portuguese and Spanish navigators brought a wider, bolder navigation into vogue, it became a matter of the first necessity.

To take, for example, the immortal voyage of Christopher Columbus. His purpose in setting out into the west was to discover a new way to India. The Venetians and Genoese practically possessed the overland route across the Isthmus of Suez and down the Red Sea. Vasco da Gama had opened out the route eastward round the Cape. Firmly convinced that the world was a globe, Columbus saw that a third route was possible, namely, one nearly due west; and when, therefore, he reached the Bahamas, after traversing some 66° of longitude, he believed that he was in the islands of the China Sea, some 230° from Spain. Those who followed him still laboured under the same impression, and when they reached the mainland of America, believed that they were close to the shores of India, which was still distant from them by half the circumference of the globe.

Little by little the intrepid sailors of the sixteenth century forced their way to a true knowledge of the size of the globe, and of the relative position of the great continents. But this knowledge was only attained after many disasters and terrible miseries; and though a new kind of navigation was established—the navigation of the open ocean, far away from any possible landmark, a navigation as different as could be conceived from the old method of coasting—yet it remained terribly risky and uncertain throughout the sixteenth century. Therefore many mathematicians endeavoured to solve the problem of determining the position of a ship when at sea. Their suggestions, however, remained entirely fruitless at the time, though in several instances they struck upon principles which are being employed at the present day.

The first country to profit by the discovery of America was Spain, and hence Spain was the first to feel keenly the pinch of the problem. In 1598, therefore, Philip III. offered a prize of 100,000 crowns to any one who would devise a method by which a captain of a vessel could determine his position when out of sight of land. Holland, which had recently started on its national existence, and which was challenging the colonial empire of Spain, followed very shortly after with the offer of a reward of 30,000 florins. Not very long after the offer of these rewards, a master mind did work out a simple method for determining the longitude, a method theoretically complete, though practically it proved inapplicable. This was Galileo, who, with his newly invented telescope, had discovered that Jupiter was attended by four satellites.

At first sight such a discovery, however interesting, would seem to have not the slightest bearing upon the sailor's craft, or upon the commercial progress of one nation or another. But Galileo quickly saw in it the promise of great practical usefulness. The question of the determination of the place of a ship when in the open ocean really resolved itself into this: How could the navigator ascertain at any time what was the true time, say at the port from which he sailed? As already pointed out, it was possible, by observing the height of the sun at noon, or of the pole-star at night, to infer the latitude of the ship. The longitude was the point of difficulty. Now, the longitude may be expressed as the difference between the local time of the place of observation and the local time at the place chosen as the standard meridian. The sailor could, indeed, obtain his own local time by observations of the height of the sun. The sun reached its greatest height at local noon, and a number of observations before and after noon would enable him to determine this with sufficient nicety.

But how was he to determine when he, perhaps, was half-way across the Atlantic, what was the local time at Genoa, Cadiz, Lisbon, Bristol, or Amsterdam, or whatever was the port from which he sailed? Galileo thought out a way by which the satellites of Jupiter could give him this information.

For as they circle round their primary, they pass in turn into its shadow, and are eclipsed by it. It needed, then, only that the satellites should be so carefully watched, that their motions, and, consequently, the times of their eclipses could be foretold. It would follow, then, that if the mariner had in his almanac the local time of the standard city at which a given satellite would enter into eclipse, and he were able to note from the deck of his vessel the disappearance of the tiny point, he would ascertain the difference between the local times of the two places, or, in other words, the difference of their longitudes.

The plan was simplicity itself, but there were difficulties in carrying it out, the greatest being the impossibility of satisfactorily making telescopic observations from the moving deck of a ship at sea. Nor were the observations sufficiently sharp to be of much help. The entry of a satellite into the shadow of Jupiter is in most cases a somewhat slow process, and the moment of complete disappearance would vary according to the size of the telescope, the keenness of the observer's sight, and the transparency of the air.