NAVIGATION and those of Jupiter s satellites from tables made by Wargentin and published by Lalande in 1759, except the fourth satellite. It will be seen by the following outline of contents that the first Almanac contained all the principal points of information which the seaman required ; and greater accuracy at that time was not desirable, or at least would not have been appreciated. Page 1 of each month gave the Sundays and holidays, four phases of the moon, and positions of sun, moon, and planets in the signs of the zodiac ; page 2, sun s longitude, right ascension in time, declination, and equation for noon each day ; page 3, sun s semidiameter, time of passing the meridian, hourly motion of the sun, logarithm of sun s distance, and place of the moon s node, for every sixth day ; also eclipses of Jupiter s satellites, time of immersion ; page 4, the positions of the four principal planets for every sixth day ; page 5, the configuration of Jupiter s satellites at 11 P.M. of every day; page 6, the moon s longitude and latitude for noon and midnight of every day; page 7, the moon s age, passage over the meridian, right ascension, and declination at noon and midnight ; page 8, the moon s semidiameter, horizontal parallax, and logistic logarithm each at noon and midnight ; pages 9 to 12, the moon s centre from the sun and seven stars for every three hours, while within about 116 degrees. Then follow tables of refraction, moon s parallax in altitude, a catalogue of stars, with their right ascension and declination, table for the "dip" of the sea horizon, and several other useful things, many of which are omitted in modern Nautical Almanacs, as they are included in and more properly belong to the permanent rules and require ments of navigation. Various useful rules and tables were appended to early volumes of the Almanac. Thus the volume for 1771 contains a method and table for determining the latitude by two altitudes and the elapsed time first published by Cornelius Downes of Amsterdam in 1740. 1 At the end of the Almanac for 1772 Maskelyne and Whichell gave three special tables for clearing the lunar distance ; still their rule is neither short nor easily remembered. An improvement of Dunthorn s solution is also given, and a problem in Mercator s sailing by Halley solved by Israel Lyons, 2 viz., the latitude of the point of departure given, distance sailed, and change of longitude, required the course steered. In the edition for 1773 a new table for equations of equal altitudes is given by "W. Whale. In those for 1797 and 1800 tables are added by John Brinkley for rendering the calculations for double altitudes easier. From 1777 to 1788 inclusive, the moon s place was calculated from improved tables by Charles Mason, founded on observations by Bradley, which were pub lished in the Nautical Almanac for 1774. The difference then only amounted to 1" in longitude, the apogee 56", and the ascending node 45". From 1789 to 1804 the tables were further corrected by Mason, and calculated to tenths of a second. The distances between the moon and the stars were still further corrected by the use of Taylor s logarithms to seconds, and their places by Bradley s observations in 1756 and Maskelyne s in 1809. The places of the planets at that time were from Lalande s Astronomy (the 3d edition was published in 1792), more recently from vol. iii. of Professor Vince s Astronomy. The places of the moon since the beginning of 1821 were calculated from Burckhardt s tables. They are now taken from Hansen s tables, completed with the aid of the English Government in 1857. The eclipses of Jupiter s satellites for 1824 and following years were from De- 1 This method, for which the author received 50 from the com missioners of longitude in 1768, used logarithmic solar tables of Downes s own invention. As he also used the latitude by dead reckon ing, the calculation involved repetition and was long. Dr Pemberton, in a paper read to the Royal Society (Nov. 20, 1760), showed that the pro blem could be worked without the new logarithmic solar tables ; but he also uses the dead reckoning. The problem was not new ; Nunez had solved it on the globe ; and solutions by the globe, disks of talc, or the like, which are useful only as illustrations, have since been repeated from time to time down to our own age. One such by R. Graham (1734) is given in Phil. Trans., xxxviii. 435, with much boasting. The first discussion of double altitudes in which the motion of the ship between the observations was taken into account was in a pamphlet by N. F. Duillier in 1728. 2 Lyons received 1 for his solution of this problem from the com missioners in 1769 ; and in 1772 he and Dunthorn each got 50 for their improvements in "clearing the distance." lambre s new tables. In 1827 the positions of sixty of the principal stars were given for every tenth day, from the tables of Maskelyne and Dr Pearson. Since 1824 the work has been printed three and latterly four years in ad vance. The price was 5s. till 1855; but the Almanacs for that and subsequent years have been issued at 2s. 6d. A book of Tables Requisite to be Used with the Nautical Ephemeris was published by Maskelyne at the same time as the first Almanac, and ten thousand copies were quickly sold. A second edition, prepared by W. Wales, appeared in 1781, an octavo of 237 pages, in the preface of which it is stated, with apparent truth, that it contains everything necessary for computing the latitude and longi tude by observation. There are in all twenty-three tables, the traverse table and table of meridional parts alone being deficient as compared with modern works of the kind ; dead- reckoning Maskelyne did not touch. He gave practical methods for working several problems ; the lunar especi ally is an improvement on those by Lyons and Dun- thorn, though a rule there given for clearing the dis tance, called Dunthorn s improved method, is remarkably short. The half sum of three logarithms gives an arc, and the half sum of other two gives half the true distance. The objection is the use of special logarithms. Maskelyne s rule for finding the latitudes by two altitudes and the elapsed time is also good, but with the same objection. The third edition of the Tables was issued in 1802. It has been said that Maskelyne neglected the planets ; be that as it may, he established the positions of sixty of the principal stars, and completed many other things. He had but one assistant, whereas there are now eight, and the Nautical Almanac is under another department. As the necessary calculations for clearing the lunar distance from the effects of parallax and refraction were considered difficult to seamen, many efforts were made to shorten the process. Among others Whichell, master of the Royal Naval Academy, Portsmouth, conceived a plan whereby it could be taken from a table by inspec tion. In October 1765 the commissioners of longitude awarded him 100 to enable him to complete and print 1000 copies of his table. On the following April they gave him 200 more. The work was continued on the same plan by Shepherd, the Plumian professor of astronomy, Cambridge, with some additions by the astronomer-royal. The total cost of the ponderous 4to volume up to the time of publication in June 1772 was 3100, after which 200 more was paid to the Rev. Thomas Parkinson and Israel Lyons for examining the errata. It is a very large and expensive volume, very ill-adapted for ship s use. Considerable sums were paid by the commissioners from time to time for other tables to facilitate navigation not always very judiciously. It is sufficient to mention here the tables of Michael Taylor and the still esteemed tables of Mendoza, published in 1815. Here also may be mentioned a useful table by Stevens (1780) for finding the latitude by the altitude of the pole star, and Crosswell s tables for facilitating the computation of lunars partly new and partly after Maskelyne. These appear to be the first tables in which half the logarithmic sine, &c., is given, to save the trouble of halving a sum of four or more logarithms. The plan of the Nautical Almanac was soon imitated by other nations. In France the Academic Royale de Marine had all the lunar distances translated from the British Nautical Almanac for 1773 and following years, retaining the Greenwich time for the three-hourly distances. The tables were considered excellent, and national pride was satisfied by their having been formed on the plan proposed by Lacaille. They did not imitate the mode given for clearing the distance, considering their own better. Though the Spaniards were leaders in the art of navi gation during the 16th and 17th centuries, it was not till November 4, 1791, that their first nautical almanac was printed at Madrid, having been previously calculated at Cadiz for the year 1792. They acknowledge borrowing from the English and French. The lunar distances were reduced from Greenwich meridian to that of Cadiz, by subtracting 25 m 9 s . It is in larger and better print than the French almanac. In the book for 1803 the meridiaa
