260 NAVIGATION controversies, and of subsequent improvements in time keepers, need not detain us here. In England the names of Arnold and Earnshaw are prominent, each of whom received, up to 1805, .3000 reward from the commis sioners of longitude. It was Arnold who introduced the name chronometer. 1 The French emulated the English efforts for the production of good timekeepers, and favour able trials were made between 17G8 and 1772 with watches by Le Roy and Berthoud. Meantime the steady progress of astronomy both by the multiplication and increased accuracy of observations, and by corresponding advances in the theory, had made it possible to construct greatly improved tables. In observa tions of the moon Greenwich still took the lead ; and it was here that Halley s successor Bradley made his two grand discoveries of aberration and nutation which have added so much to the precision of modern astronomy. Kepler s Rudolphine tables of 1627 and Street s tables of 1661, which had held their ground for almost a century, were rendered obsolete by the observations of Halley and his successor. At length, in 1753, in the second volume of the Commentarii of the Academy of Gottingen, Tobias Mayer printed his new solar and lunar tables, which were to have so great an influence on the history of navigation. Mayer afterwards constructed and submitted to the English Government in 1755 an improved body of MS. tables. Bradley found that the moon s place by these tables was generally correct within 1 , so that the error in a longitude found by them would not be much more than half a degree if the necessary observations could be taken accurately on shipboard. Thus the lunar problem seemed to have at length become a practical one for mariners, and in England it was taken up with great energy by N. Maskelyne " the father," as he has been called, " of lunar observa tions." In 1761 Maskelyne was sent to St Helena to observe the transit of Venus. On his voyage out and home he used Mayer s printed tables for lunar determinations of the longitude, and from St Helena he wrote a letter to the Royal Society (Phil. Trans., vol. Hi. p. 558, 1762), in which he described his observations made with Hadley s quadrant of 20 inches radius, made by Bird, and the glasses ground by Dollond. He took the observations both ways to avoid the errors. The arc and index were of brass, the frame mahogany ; the vernier was subdivided to minutes. The telescope was 6 inches long, magnified four times, and inverted. Very few seamen in that day possessed so good an instrument. He considered that ship s time should be ascertained within twelve hours, as a good common watch will scarcely vary above a minute in that time. This shows that he must have intended the altitude of sun or star to be calculated which would lead to new errors. He considered that his observations would each give the longitude within 1J degrees. On February llth he took ten; the extremes were a little over one degree apart. On his return to England Maskelyne prepared the British Mariner s Guide (1763), in which he undertakes to furnish complete and easy instructions for finding the longitude at sea or on shore, within a degree, by observing the distance between the moon and sun, or a star, by Hadley s quadrant. How far that promise was fulfilled, and the practicability of the instructions, are points worth consideration, as the book took a prominent place for some years. The errors which he said were inseparable from the dead-reckoning " even in the hands of the ablest and most skilful navigators," amount ing at times to 15 degrees, appear to be overestimated. 1 A letter by Dalrymple in The Times (February 13, 1806) gives some interesting details showing ho>v slowly chronometers came into general use. On the other hand, the lunar equations, which were from Mayer s tables, would, he believed, always determine the longitude within a degree, and generally to half a degree, if applied to careful observations. He recommends the two altitudes and distance being taken simultaneously when practicable. The probable error in a meridian altitude he estimated at one or two minutes, and in a lunar distance two minutes (equal to one degree of longitude). He then gave clear rules for finding the moon s position and distance by ten equations, too laborious for seamen to undertake. Admitting the requisite calculations for finding the moon s place to be difficult, he desired to see the moon s longitude and latitude computed for every twelve hours, and hence her distance from the sun and from a proper star on each side of her carefully calculated for every six hours, and published beforehand. In 1765 Maskelyne became astronomer-royal, and was able to give effect to his own suggestion by organizing the publication of the Nautical Almanac. The same Act of 1765 which gave Harrison his first 10,000 gave the commissioners authority and funds for this undertaking. Mayer s tables, with his MS. improvements up to his death in 1762, were bought from his widow for 3000; 300 was granted to the famous mathematician Euler, on whose theory of the moon Mayer s later tables were formed; and the first Almanac, that for 1767, was pub lished in the previous year, at the cost and under the authority of the commissioners of longitude. This was not the first almanac in the country, perhaps by a hundred, as that name was applied to small periodical works, frequently of a frivolous character, though the later and better description gave the sun s declination and moon s meridional passage approximately. In 1696 the French nautical almanac for the following year appeared, an improvement on what had been before issued by private persons, but it did not attempt to give lunar distances. 2 In the English Nautical Almanac for 1767 we find every thing necessary to render it worthy of confidence, and to satisfy every requirement at sea. The great achieve ment was that of giving the distance from the moon s centre to the sun, when suitable, and to about seven fixed stars, every three hours. The mariner has only to find the apparent time at ship, and clear his own measured distance from the effects of parallax and refraction (for which at the end of the book are given Lyon s and Dan- thorn s methods), and then by simple proportion, or pro portional logarithms, find the time at Greenwich. The calculations respecting the sun and moon were made from Mayer s last manuscript tables under the inspection of Maskelyne, and were so continued till 1804. 3 The calcu lations respecting the planets are from Halley s tables, 2 The French nautical almanac is still published under the title of Connaissance des Temps. It appeared under letters patent from the king, dated 24th March 1679 seventeen years before the first issue. The following is a literal translation of its advertisement: "This little book is a collection of holy days and festivals in each month. The rising and setting of the moon when it is visible, and of the sun every day. The aspects of the planets as with respect to each other, the moon, and the fixed stars. The lunations and eclipses. The difference of longitude between the meridian of Paris and the principal towns in France. The time of the sun s entrance into the twelve signs of the zodiac. The true place of the planets every fifth day, and of the moon every day of the year, in longitude and latitude. The moon s meridian passage, for finding the time of high water, as well as for the use of dials by moonlight. A table of refraction. The equation of time [this table is strangely arranged, as though the clock were to be reset on the first of every month, and the explanation speaks of the premier mobile ]. The time of twilight at Paris. The sun s right ascension to hours and minutes. The sun s declination at noon each day to seconds. The whole accompanied by necessary in structions. " 3 Mayer s tables were printed at London under Maskelyne s super intendence in 1770.
