NAVIGATION would look through F and C at the horizon, shifting the former up or down till the ray from the sun coincided with the horizon. The space from E to F would represent the altitude, and the remaining part F to K the zenith distance. The English quadrant which this was to supersede differed in having about half the arc from E towards N, and, instead of the pinule being fixed at E, it was on a smaller arc represented by the dotted line cQ, and movable. It was placed on an even number of degrees, considerably less than the altitude ; the remainder was measured on the larger arc, as described. 1 Hadley s instrument, on the other hand, described to the Koyal Society in May 1731 (Phil. Trans., Nos. 420 and 421), embodies Newton s idea of bringing the reflexion of one object to coincide with the other. He calls it an octant, as the arc is actually 45, or the eighth part of a circle ; but, in consequence of the angles of incidence and reflexion both being changed by a movement of the index, it measures an angle of 90, and is graduated accordingly; the same instrument has therefore been called a quadrant. It was very slowly adopted, and no doubt there were numerous mechanical difficulties of centring, graduat ing, &c., to be overcome before it reached perfection. 2 In August 1732, in pursuance of an order from the Admiralty, observations were made with Hadley s quadrant on board the " Chatham " yacht of 60 tons, below Sheerness, in rough weather, by persons except the master attendant unaccustomed to the motion ; still the results were very satisfactory. Two years later Hadley published (Phil. Trans., 1733) the description of an instrument for taking altitudes when the horizon is not visible. The sketch represents a curved tube or spirit- level, attached to the radius of the quadrant. From the year 1714 the history of navigation in England is closely associated with that of the " commissioners for the discovery of longitude at sea," a body constituted by Act 13 Anne c. 14 (commonly called 12 Anne c. 15), with power to grant sums not exceeding 2000 to assist experi ments and reward minor discoveries, and also to judge on applications for much greater rewards which were offered to open competition. For a method of determining the longitude within 60 geographical miles, to be tested by a voyage to the West Indie s and back, the sum of 10,000 was offered; within 40 miles, 15,000; within 30, 20,000. 10,000 was also to be given for a method that came within 80 miles near the shores of greatest danger. No action seems to have been taken before 1737 , the first grant made was in that year, and the last in 1815, but the board continued to exist till 1828, having disbursed in the course of its existence 101,000 in all. 8 In the interval a number of other Acts had l>een passed either dealing with the powers, constitution, and funds of the commissioners or encouraging nautical discovery ; thus the Act 18 George II. (1745) offered 20,000 for the dis covery by a British ship of the North-West Passage, and the Act 16 George III. (1776) offered the same reward for a passage to the Pacific either north-west or north-east, and 5000 to any one who should approach by sea within one degree of the North Pole. All these Acts were swept away in 1828, when the longitude problem had ceased to attract 1 In 1731 M. Bouguer was awarded another prize by the Royal Academy of Sciences for his method of finding the variation of the compass at sea. - Davis s quadrant was in common use till 1740 ; it is described in Robertson s Navigation (1755), and improvements on it are proposed in Phil. Trans., 1731 and 1734. 3 This total comprises the large sums awarded to Harrison and to the widow of Mayer, the cost of surveys and expeditions in various parts of the globe, large outlays on the Nautical Almanac and on subsidiary calculations and tables, rewards for new methods and solu tions of problems, and many minor grants to watchmakers or for im provements in instruments. Thus Ramsden received in 1775 and later about 1600 for Ms improvements in graduation, and Massey in 1804 got 200 for his log (see LOG). A good deal of money was wasted, and large sums were paid to certain commissioners for attendance. competitors, and voyages of discovery were nearly over. The suggestions and applications sent in to the commis sioners were naturally very numerous and often very trifling ; but they sometimes furnish useful illustrations of the state of navigation. Thus, in a memorial by Captain H. Lanoue (1736), which seems to be designed to commend a substitute for the log (a box with something, not fully explained, let into the sea), he records a number of recent casualties, which shows how carelessly the largest ships were then navigated. Several men-of-war off Plymouth in 1691 were wrecked through mistaking the Deadman for Berry Head. Admiral Wheeler s squadron in 1694, leaving the Mediterranean, ran on Gibraltar when they thought they had passed the Strait. Sir Cloudesley Shovel s squadron, in 1707, was lost on the rocks off Scilly, by erring in their latitude. Several transports, in 1711, were lost near the river St Lawrence, having erred 15 leagues in the reckoning during twenty-four hours. Lord Belhaven was lost on the Lizard in 1722, the same day on which he sailed from Plymouth. One of the first points to which the attention of the commissioners was directed was the survey of the coasts of Great Britain, which was pressed on them by Whiston in 1737. He was appointed surveyor of coasts and head lands, and in 1741 received a grant for instruments. An Act passed in 1740 enabled the commissioners to spend money on the survey of the coasts of Great Britain and the " plantations." At a later date they bore part of the expenses of Cook s scientific voyages, and of the publica tion of their results. Indeed it is to them that we owe all that was done by England for surveys of coasts, both at home and abroad, prior to the establishment of the hydro- graphic department of the Admiralty in 1795. But their chief work lay in the encouragement they gave on the one hand to the improvement of timepieces, and on the other to the perfecting of astronomical tables and methods, the latter issuing in the publication of the Nautical Almanac. Before we pass on to these two important topics we may with advantage take a view of the state of practical navi gation in the middle of last century as shown in two of the principal treatises then current. Robertson s Elements of Navigation passed through six editions between 1755 and 1796. It contains good teaching on arithmetic, geometry, spherics, astronomy, geography, winds and tides, also a small useful table for correcting the middle time between the equal altitudes of the sun, all good, as is also the remark that "the greater the moon s meridian altitude the greater the tides will be." He states that Lacaille recommends equal altitudes being observed and worked separately, in order to find the time from noon, and the mean of the results taken as the truth. There is a sound article on chronology, the ancient and modern modes of reckoning time. A long list of latitudes, longitudes, and times of high water finishes vol. i. The second volume is said by the author to treat of naviga tion mechanical and theoretical ; by the former he means seaman ship. He gives instructions for all imaginary kinds of sailings, for marine surveying and making Mercator s chart. There are two good traverse tables, one to quarter points, the other to every 15 minutes of the arc ; the distance to each is 120 miles. There is a table of meridional parts to minutes, which is more minute than customary. Book ix., upon what is now called "the day s work," or dead- reckoning, appears to embrace all that is necessary. A great many methods, we are told, were then used for measuring a ship s rate of sailing, but among the English the log and line with a half -minute glass were generally used. Bouguer and Lacaille proposed a log with a diver to avoid the drift motion (1753 and 1760). Robertson s rule of computing the equation of equal altitudes is as good as any used at the present day. He gives also a description of an equal- altitude instrument, having three horizontal wires, probably such a v one as was used at Portsmouth for testing Harrison s timekeeper. The mechanical difficulties must have been great in preserving a perpendicular stem and a truly horizontal sweep for the telescope. It gave place to the improved sextant and artificial horizon. The second edition of Robertson s work in 1764 contains an excellent dissertation on the rise and progress of modern navigation by Dr James Wilson, which has been greatly used by all subsequent writers. Don Jorge Juan s Compendia de Navcgacion, for the use of mid-
