Sextant Read online

  Appointed professor of mathematics at the University of Göttingen in 1751, Mayer closely analyzed the available observational data and, with the help of Euler, prepared new tables of the moon’s motions that proved far more accurate than any previously available. His work first was already under discussion in England as early as 1754. In 1755 the Astronomer Royal, Dr. James Bradley, reported to the board on his examination of Mayer’s tables:

  In more than 230 comparisons which I have already made I did not find any difference so great as 1½' between the observed longitude of the Moon and that which I computed by the tables . . . it seems probable that, during this interval of time, the tables generally gave the Moon’s place true within one minute of a degree.

  A more general comparison may perhaps discover larger errors; but those which I have hitherto met with being so small, that even the biggest could occasion an error of but little more than half a degree of longitude, it may be hoped that the tables of the Moon’s motions are exact enough for the purpose of finding at sea the longitude of a ship, provided that the observations that are necessary to be made on shipboard can be taken with sufficient exactness.2

  With Mayer’s tables it seemed possible that a practical, astronomical method of determining the time accurately on board ship might at last be within reach. To make this lunar-distance method work successfully, however, a very accurate device for measuring angular distances was essential. The standard Hadley quadrant could measure angles only up to ninety degrees, and since the angular separation of the sun and moon often exceeded that amount, a larger instrument would plainly be helpful. Mayer himself had proposed the use of a circular device—the “reflecting circle”—but when Captain John Campbell of the Royal Navy was testing Mayer’s tables at sea in 1757 he found it inconvenient to use. Campbell then came up with the simple idea of enlarging Hadley’s quadrant, and so commissioned a leading instrument maker, John Bird, to make the very first sextant.3 Bird’s device was not only bigger but more accurate than the standard quadrants of the day: its frame was made of brass rather than wood, and it was equipped with a telescope instead of simple aperture sights. While the quadrant was, in general, capable only of measuring to the nearest minute of arc, the sextant, with the help of a tangent screw and vernier, could in principle give readings accurate to 10''.4 Using the new instrument at sea off Ushant in 1758 and 1759, Campbell found it was possible to obtain lunar distances on fifteen to sixteen days a month rather than just eight with a quadrant, and more important still, his observations with the new instrument yielded longitudes accurate to within 37 minutes—well within the terms of the Longitude Act’s provisions.5 With the development of the mechanical “dividing engine,” perfected by Jesse Ramsden in 1775, it became possible to graduate the scales of instruments like the sextant with much greater precision than was possible by hand. Not only was accuracy improved, but manufacturing costs were also much reduced. The Longitude Board accordingly rewarded Ramsden’s work with prizes amounting to more than £1,000.6 *

  The astronomer Nevil Maskelyne (1732–1811) was a central figure in the struggle to solve the longitude problem, and a controversial one. He sailed to St. Helena in 1761 in the hope of observing the Transit of Venus as part of an international effort to exploit this rare event, which occurs (twice, eight years apart) at intervals of more than one hundred years. The aim was to make simultaneous observations from widely separated parts of the world and to use the results to determine the distance of the earth from the sun. Poor weather frustratingly prevented him from making the crucial observation of the planet crossing the sun’s disc, but the two long voyages nevertheless proved useful. They gave him ample opportunity to familiarize himself with the general challenges of shipboard navigation, and also enabled him to test the lunar-distance method at sea using Mayer’s as yet unpublished tables. He took at least sixteen lunar-distance observations on the outward voyage in an East India Company vessel, and although bad weather prevented him taking any during the last eight days, he reported that his longitude error on arrival at St. Helena was only 1½ degrees—far less than that of some of the ship’s officers, who were presumably relying on DR.

  Maskelyne reported to the Royal Society that “a person who will take the pains necessary to make accurate observations and has at the same time leisure and ability to make the requisite calculations will be able to ascertain his Longitude by this method as near as will in general be required.”* On the return voyage to England, Maskelyne successfully encouraged some of the ship’s officers to learn and practice the lunar-distance method. In the light of this experience he concluded that longitude could always be found using the lunar method to “within a degree, or very little more”: he was to remain one of its most devoted champions.7 In 1763 he published the British Mariner’s Guide, which explained how to make lunar-distance observations and deduce the longitude from them, as well as containing the first English edition of Mayer’s tables.

  But observing lunars was, initially at least, a laborious and time-consuming process. Four people were ideally required—two to take simultaneous altitudes of the observed bodies, one to record the time intervals between the observations (for which an ordinary watch was sufficient), and one to observe the lunar distance itself—though an expert could, if necessary, manage on his own.8 Large and variable allowances had to be made for the effects of atmospheric refraction and parallax. This complex process was known as “clearing the distance,” and, over the years, at least forty different methods were proposed, though probably few of them were ever used.9 Having accurately measured the lunar distance, and “cleared” it, the navigator could use Mayer’s tables to determine the time at Greenwich. Coupled with observations for local time, the observer’s longitude could then readily be established. But the lunar-distance calculations were lengthy and, until precomputed values were published in the new Nautical Almanac (discussed on page 80), might take several hours to complete.

  Mayer’s tables were in due course significantly refined,10 and it eventually proved possible for a skillful observer using a good sextant to find the Greenwich time using lunars to within one or two minutes—a far narrower margin than that promised by Maskelyne. Such levels of accuracy were adequate for most navigational purposes, but for the making of charts a higher degree of precision was desirable. By taking a long series of observations from temporary observatories set up onshore and averaging the results, the effects of observational errors could be greatly reduced. Navigators on voyages of discovery would apply this technique whenever possible and might perform a hundred or more sets of lunar observations in order to establish accurate fixed points on which to base their charts. Observations of Jupiter’s moons as well as eclipses of the sun and moon were also employed when opportunities offered.

  MASKELYNE HAS SOMETIMES been painted as the villain who denied Harrison his just deserts, but while his influence over the board (of which he became an ex officio member following his appointment as Astronomer Royal in 1765) was no doubt powerful, the decision to withhold the full reward certainly did not rest with him alone. Relations between Harrison and the Longitude Board began to deteriorate after the first trials in Jamaica, but soon Maskelyne became the focus of his anger and suspicion. On his arrival in Barbados, Harrison’s son William, representing his elderly father, who had stayed at home in England, asserted that the astronomer was not a proper person to conduct the observations necessary to test H4’s performance. He claimed that Maskelyne, as a well-known advocate of the rival lunar-distance method, was himself a candidate for the Longitude prize and therefore an interested party.11

  Maskelyne was, it is true, a devotee of the lunar method, but he did not stand to gain financially from the experiment since it was Mayer’s method he was testing, not his own. In any case, there is no evidence that Maskelyne ever took advantage of his official position to enrich himself. Nor did he allow his own views to color his judgment of H4’s performance: he later acknowledged in an unpublished autobiographic
al note that “Harrison’s watch was found to give the Longitude of the island [Barbados] with great exactness.”12 That he was among those who proposed William Harrison for the great honor of fellowship of the Royal Society shortly after their return from Barbados13 does not suggest that he was hostile toward either him or his father, even if his attitude tended to be condescending.

  However, in 1767, following extensive tests conducted at Greenwich, Maskelyne reported to the Longitude Board on the performance of H4 in terms that infuriated Harrison:

  . . . Mr. Harrison’s Watch cannot be depended upon to keep the Longitude within a Degree in a West India Voyage of six weeks; nor to keep the Longitude within half a degree for more than a few days; and perhaps not so long, if the Cold be very intense; nevertheless . . . it is a useful and valuable invention, and, in conjunction with observations of the Distance of the Moon from the Sun and fixed Stars, may be of considerable advantage to Navigation.14

  Harrison dismissed Maskelyne’s findings out of hand and did not hesitate to publish his complaints. Though Harrison’s criticisms of the trials are largely unconvincing, it is fair to say that Maskelyne’s own conduct was stiff-necked. While the report Maskelyne produced for the board was perfectly accurate in a technical sense, he made no allowance for the fact that H4 was gaining at a fairly steady rate, at least at the start of the trials. Had he done so, H4 would have passed four out of six of them. Harrison, however, had failed to draw Maskelyne’s attention to this problem, and his sulky and uncooperative behavior did nothing to help his case.15 Nevertheless, even if Maskelyne questioned the reliability of the new watch, it is clear from his testimony to the Longitude Board that he recognized its potential value.

  The Longitude Board may perhaps have treated Harrison ungenerously, but this does not mean—as Harrison himself passionately believed—that they were biased in favor of astronomical methods. Having made such a large investment in Harrison’s work, they had no reason to turn their backs on it, and their assessment of Mayer’s achievements was, in fact, even harsher. Though the efficacy of his tables had been clearly demonstrated, they did not reward him immediately. Interpreting the terms of the Longitude Act at least as strictly as they had in Harrison’s case, the board argued that the lunar method was too complicated to be of practical use at sea. In 1765 they declared—with nice symmetry—that while Harrison’s chronometer method was “practicable but not generally useful,” Mayer’s tables were “useful but not practicable.” Harrison was therefore deemed to merit an amount not exceeding half the maximum award while Mayer’s widow (he had died in 1762 at the age of thirty-nine) was entitled to at most half the minimum award. She eventually received £3,000 while a mere £300 went to Euler.16 Harrison, who got £10,000, did very well by comparison.

  ONE OF THE greatest achievements of Maskelyne’s long and distinguished career, and the one for which he is best remembered, was the development of the Nautical Almanac. This was first published—under his personal supervision—in 1766, though it went on sale only in January 1767. Produced continuously ever since, its popularity among mariners all over the world helps to explain why Greenwich was ultimately selected as the prime meridian. Maskelyne subcontracted the tedious and repetitive calculations needed to produce the Nautical Almanac to numerous human “computers” around the country, working in their own homes. The most important calculations were duplicated by separate “computers,” and then checked by an independent “comparer.”

  The purpose of the Almanac was—quite simply—to give the navigator all the information necessary to find his position at sea, with or without a chronometer. In addition to the standard data that were already available in the French Connoissance des Temps, Maskelyne included precomputed lunar distances from the sun at three-hourly intervals (when the two bodies were at the right distance from each other), based on the Greenwich meridian.17 On the days when the angle between sun and moon was either too great or too small, lunar distances to selected stars were tabulated. These new tables greatly reduced the burden of calculating lunar distances, which might now take as little as half an hour. Maskelyne also published separately the Requisite Tables, which included all the information that the navigator needed to clear the distance, as well as a variety of other useful data that did not have to be revised annually.

  Fig 7: A page of lunar distances from the first Nautical Almanac. The small crescent stands for the moon and the dotted circle for the sun.

  With the help of these two publications the offshore navigator could now measure his longitude quickly and comparatively easily, provided he had a good Hadley quadrant (costing about £5) or, better still, a sextant (costing more like £15), and a decent watch. One or (preferably) several chronometers would make life easier still, but they would cost at least 40 guineas (£42) each—this at a time when a Royal Navy lieutenant’s maximum annual salary was only £84.18 Ships’ officers in the East India Company had already begun to take up the use of lunars following Maskelyne’s example on his excursion to St. Helena, and they warmly embraced the new publications. The Royal Navy, for its part, soon began to supply the Almanac and Requisite Tables to their ships, and in 1769 masters of all naval vessels visiting Portsmouth were ordered to obtain instruction from the Royal Naval Academy in the use of the Hadley quadrant and Almanac. This instruction was not well received and very few masters seem to have acted on it, but it is clear that a revolution in navigation had begun.19

  Before the Almanac became available, only a handful of navigators had succeeded in measuring their longitude when out of sight of land, and according to Maskelyne’s biographer its first publication was “the most important date in the history of the art of navigation, certainly since the invention of the reflecting quadrant thirty-six years earlier, perhaps since the beginnings of latitude navigation back in the fifteenth century.”20

  THE LONG-STANDING RIVALRY between the advocates of the two different approaches to finding the longitude—which goes back to the clashes between Harrison and the Longitude Board—has never entirely subsided, but it reflects a failure to grasp their crucial interdependence. No prudent navigator before the mid-nineteenth century would have dreamed of relying exclusively on a chronometer (or even several of them) to find his position during a long ocean voyage. However convenient to use, chronometers were delicate, temperamental devices, and far from perfectly accurate. Even if they ran regularly, any errors would steadily accumulate. On the other hand, if they did not run regularly they were of little use. In either case, the navigator crucially needed some independent means of determining the time to establish their rates.

  As late as 1839, Norie’s Complete Epitome of Practical Navigation—a standard manual—was offering the following advice:

  several ingenious artists . . . have brought chronometers to an astonishing degree of perfection, whereby they have become a valuable acquisition to the navigator, in determining the difference in longitude made in short periods: however, considering the delicacy of their construction, and the various accidents to which they are liable, an implicit confidence ought not to be placed on them alone, particularly in long voyages; but recourse should be had to astronomical observations, whenever opportunities present themselves.21

  Another leading navigational authority, Henry Raper, who fully recognized the value of chronometers and strongly recommended their use,22 also commented on their unreliability. In The Practice of Navigation and Nautical Astronomy, first published in 1840, he observed:

  Chronometers are generally found to perform best at the beginning of a voyage; many subsequently become useless from irregularity, and some fail altogether. They are liable, also, to change their rates suddenly, and then to resume the former rates in a few days.23

  Lunars certainly had their shortcomings. They were tricky to observe, laborious to calculate, and often unobtainable. However, they had the crucial merit of providing a reliable and independent means of finding the time wherever the navigator happened to be. A chronometer, on the ot
her hand, was always available (so long as it worked), and it enabled the navigator to keep track of the time during the intervals between lunar observations. In practice, the two methods were entirely complementary, and they were to be used in tandem for at least seventy years. It was only with the invention of the electric telegraph and the laying of submarine telegraph cables that lunars ceased to be essential.

  Chapter 8

  Captain Cook Charts the Pacific

  Day 9: Wind W by S force 4–5. Not a very good day. Various mishaps: failure of engine circulating water when trying to charge batteries; the binnacle light wouldn’t go on; and the washing up liquid drained away—so we now have to wash up in plain seawater. Pretty tired from night watches, which Colin and I share. Lucky Alexa is excused.

  We put our clocks forward an hour at 1700. Time passes so very slowly. Anything at all complicated seems to be much harder when you’re tired, especially when the boat is bouncing around. It took me more than half an hour to do the calculations for the noon fix, which finally came out as 43°16' N, 41°51' W, making a day’s run of 105 miles. A really good supper—sardine pilaf made by Alexa. Still under No. 2 stays’l. This evening Colin showed me how to do a Polaris sight.

  The heroic age of scientific hydrography began in the late 1760s, when the major naval powers—Britain, France, and Spain—began to send out expeditions to explore and chart the world employing the latest navigational technology.