With Hadley's quadrant, latitude could be determined within a minute, that is to say, to the third of a league. But such an approximate exactitude was not possible in deciding longitudes. When once the different phenomena of the variations of the magnetic needle, either of declination or inclination, should be fully understood, it would be easy; but how to obtain this knowledge? It was well known that in the Indian Sea, between Bourbon, Madagascar, and Rodriguez, a variation of four degrees in the declination of the needle was equivalent to a variation of five degrees in the longitude, but it was equally admitted that the declination of the magnetic needle was subject to variations, in the same localities, for which no cause could be assigned. Verdun de la Crenne, writing in 1778, says a declination of twelve degrees, from N. to W. twenty years ago, indicated a longitude of 61 degrees W. of Paris, in any given latitude. It is very probable that within the last twenty years the declination has varied two degrees, which makes the longitude deduced from it wrong by two and a half degrees, or nearly fifty nautical miles. If the right time is known on board, that is to say, the correct time by which the meridian could be computed at the moment of any given observation, and if at the same time, the exact time at the port from which the ship had started, or that if any known meridian could be ascertained, the difference of time would evidently give that of the meridians, at the rate of fifteen degrees per hour, or one degree per four minutes. The problem of the longitude could thus be reduced to a determination, at a given moment of the time at any given meridian. To achieve this it was necessary to have a watch or clock which should preserve a perfect isochronism, in defiance of the state of the sea or differences of temperature. Many attempts had been made. Besson in the sixteenth century, Huyghens in the seventeenth century, and again Sully, Harrison, Dutertre, Gallonde, Rivas, Le Roy, and Ferdinand Berthoud had attempted to solve the problem. The English and French Governments, moreover, convinced of the value of a perfect instrument, had offered a high reward for its invention. The Academy of Science had instituted a competition. In 1765 Le Roy sent in two watches for competition, whilst Berthould, who was in the king's service, was unable to do so. Le Roy's watches passed successfully through the various trials to which they were subjected on land. It remained to be proved whether they would be equally trustworthy at sea.