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 two at Greenwich Observatory, to be 3h 54m 20s west of Greenwich. In February 1765 the commissioners of longitude expressed an opinion that the trial was satisfactory, but required the principles to be disclosed and other watches made. Half the great reward was paid to Harrison under act of parliament in this year, and he and his son gave full descriptions and drawings, upon oath, to seven persons appointed by the commissioners of longitude. The other half of the great reward was promised to Harrison when he had made other timekeepers to the satisfaction of the commissioners, and provided he gave up everything to them within six months. The second half was not paid till 1773, after trials had been made with five watches. These trials were partly made at Greenwich by Maskelyne, who, as we shall see, was a great advocate of lunars, and was not ready to admit more than a subsidiary value to the watch. A bitter controversy arose, and Harrison in 1767 published book in which he charges Maskelyne with exposing his watch to unfair treatment. The feud between the astronomer-royal and the watchmakers continued long after this date.

Even after Harrison had received his £20,000, doubts were felt as to the certainty of his achievement, and fresh rewards were offered in 1774 both for timekeepers and for improved lunar tables or other methods. But the tests proposed for timekeepers were very discouraging, and the watchmakers complained that this was due to Maskelyne. A fierce attack on the astronomer’s treatment of himself and other watchmakers was made by Thomas Mudge in 1792, in A Narrative of Facts, addressed to the first lord of the Admiralty, and Maskelyne’s reply does not convey the conviction that full justice was done to timekeepers. Maskelyne at this date still says that he would prefer an occultation of a bright star by the moon and a number of correspondent observations of transits of the moon compared with those of fixed stars, made by two astronomers at remote places, to any timekeeper. The details of these controversies, and of subsequent improvements in timekeepers, need not detain us here. In England the names of John Arnold and Thomas Earnshaw as watchmakers are prominent, each of whom received, up to 1805, £3000 reward from the commissioners of longitude. It was Arnold who introduced the name chronometer. The French emulated the English efforts for the production of good timekeepers, and favourable trials were made between 1768 and 1772 with watches by Le Roy and F. Berthoud.

The marvellous accuracy with which the modern chronometer is constructed is doubtless greatly stimulated by the annual competition at Greenwich, from which the Admiralty purchase for the British navy. These chronometers are all fitted with secondary compensation balances, and it is therefore unusual in the navy to apply any temperature correction to the rate. The perfection obtainable in compensation may be illustrated by the performance of a chronometer at the Royal Observatory in 1886, which at a mean temperature of 50° F. had a weekly rate of 1·6 secs. losing; and on being further tested at a mean temperature of 92° F., it only changed its weekly rate to 2·9 secs. losing. In the mercantile marine cheaper chronometers without secondary compensation are more commonly used, and temperature corrections applied, calculated from a formula originally proposed by Hartnup, formerly of the Liverpool Observatory. Great success attends this mode of procedure, as illustrated by the following facts. From the discussion of the records of performance of the chronometers of the Pacific Steam Navigation Company during twenty-six voyages from London to Valparaiso and back, by giving equal weight to each of the three chronometers carried by each ship, the mean error of longitude for an average voyage of 101 days was less than three minutes of arc. As a single instance, in the s.s. Orellana, on applying temperature rates during a voyage of 63 days, the mean accumulated error of the three chronometers was only 2·3 sec. of time.

While chronometers were thus rapidly approaching their present perfection 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 observations 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 Göttingen, 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 improved 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 lunar would not be much more than half a degree if the necessary observations could be taken accurately at sea. 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 Nevil Maskelyne—“the father,” as he has been called, “of lunar observations.”

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., 1762), in which he described his observations made with Hadley’s quadrant of 20 in. radius, constructed by John Bird, and the glasses ground by Dollond. He took the observations both ways to avoid errors. The arc and index were of brass, the frame mahogany; the vernier was subdivided to minutes. The telescope was 6 in. 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 before or after observing the lunar distance, as a good common watch will scarcely vary above a minute in that time. This shows that he must have intended the altitudes to be calculated—which would lead to new errors. He considered that his observations would give the longitude within 1 degrees. On the 11th of February he took ten observations; 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,” amounting at times to 15 degrees, appear to be overestimated. On the other hand, the equations to determine the moon’s position at time of observation 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 of observation in a meridian altitude he estimated at one or two minutes, and in a lunar distance at two minutes. 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 mathematician L. Euler, on whose theory of the moon Mayer’s later tables were formed; and the first Nautical Almanac, that for 1767, was published in the previous year, at the cost and under the authority of the commissioners of longitude. 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