As guardians of public funds the Board were understandably anxious not to expose themselves to charges of waste. But their reluctance to reward Harrison in full was also influenced by the belief – which Newton had shared – that the only reliable solution to the longitude problem must be astronomical not mechanical. After all, watches could go wrong, and seemed very likely to do so in a damp and bumpy ship at sea – especially if the temperature varied a good deal, as it would on a voyage from Europe to the tropics. How would the navigator be able to tell if the watch started to misbehave? Who was going to fix it if it stopped? How could any errors be corrected?
These were perfectly fair questions, and as experience subsequently showed many chronometers did indeed perform poorly, often running irregularly or stopping altogether for no obvious reason. Even their own makers did not understand exactly what they were doing: they were artists as much as engineers, and they relied heavily on trial and error. The sun, moon and stars, by contrast, were the very embodiment of perfection – and indeed the basis of time itself. Until the invention of the ‘atomic clock’ in the mid-twentieth century, the movements of the sun and stars remained the fundamental indices of time. Harrison’s watch may well have seemed inelegant to the more mathematically minded members of the Longitude Board – a questionable, brute-force solution to a problem they regarded as essentially astronomical in nature.
Harrison’s great achievement was the invention of a radically new watch movement that could keep time accurately – not just in stable conditions on land, but also in the wildly variable environment of a ship at sea. He was certainly a difficult and irascible man, as was his son, but he was highly ingenious and extremely determined, and in 1773, following a powerful speech in the House of Commons by Edmund Burke, and a sympathetic intervention by King George III himself, Parliament (rather than the unbending Longitude Board) awarded him a further £8,750.17 fn7 The practical marine chronometers (as these ‘time-keepers’ were eventually to be known) that relied on Harrison’s pioneering work were not, however, mere duplicates of H4. They owed much to the inventive skills of other watchmakers like Pierre Le Roy and Ferdinand Berthoud in Paris and Larcum Kendall, John Arnold and Thomas Earnshaw in London.18
The chronometer we carried aboard Saecwen was a descendant of those developed in the last decades of the eighteenth century and probably differed little from them. It sat luxuriously in a pretty mahogany box with brassbound corners, secured by strong elastic cords in a safe corner of the cabin near the mast. Lifting the lid, a circular brass case was revealed, with a plain but elegant dial and thin, spear-shaped hands, the whole mechanism supported in a gimballed cradle that isolated it quite effectively from the motion of the boat. Colin alone undertook the delicate task of winding it, a ritual performed at the same time each day in order to maintain an even tension in the mainspring. The chronometer’s lovely, silky tick was like a breathless heartbeat. With the sextant, it was a thing of beauty.
The ‘PZX’ Triangle
The ‘PZX’ triangle is at the heart of celestial navigation and can be used to solve a variety of navigational problems.
The angle XPZ is the key to finding the ‘local time at ship’. P is the North Pole, X the ‘geographical position’ of the sun, and Z the position of the ship. The arc XA is the declination of the sun (tabulated in the Nautical Almanac); the arc ZB is the ship’s latitude (typically obtained from a ‘mer alt’). We can calculate the lengths of sides PX and PZ: PX is 90 degrees minus the sun’s declination, while PZ is 90 degrees minus the ship’s latitude. The third side, ZX, is equivalent to the ‘zenith distance’ of the sun, which is obtained by subtracting its altitude (observed with the sextant) from 90 degrees.
Using spherical trigonometry we can now derive the angle XPZ, which is the sun’s Local Hour Angle or LHA – in this case a measure of the time elapsed since the sun crossed the ship’s meridian. The time that has passed since the sun crossed the Greenwich Meridian (revealed by the chronometer) is its Greenwich Hour Angle or GHA. By subtracting the LHA from the GHA the navigator can obtain the required ‘local time’ and thereby the ship’s longitude. Similar calculations can be performed using other celestial bodies.
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Using our chronometer (duly set to Greenwich time) I learned from Colin a rough-and-ready method of determining Saecwen’s longitude. When the weather was clear I would time the moment of sunrise or sunset and compare the results with the times of these events tabulated in the Nautical Almanac. If, for example, the disc of the sun appeared over the eastern horizon at 0600 GMT according to the chronometer while the tabulated time of the same event at Greenwich was 0400, it followed that we were two hours or 30 degrees west of Greenwich. The results I obtained were – at best – accurate to about half a degree either way. In principle the same technique could be used to obtain the longitude by comparing the local and Greenwich times of a heavenly body’s transit across our meridian.
In practice, however, it is difficult to determine the exact moment of sunrise or sunset because atmospheric refraction, which is strongest at low angles, has the effect of ‘lifting’ the sun’s disc so that it remains visible for some time after it has actually dipped below the horizon. The timing of a meridian passage at sea is also problematical as heavenly bodies pause for a significant interval at the height of their arc. One way of doing so is to take two, timed ‘equal altitude’ observations of the relevant body on either side of the meridian and to halve the time difference between them. A major drawback of this method is that clouds may obscure the crucial second sight. It also requires a reasonably accurate clock. And precision is vital: an error of just one minute in the measurement of either local or Greenwich time can result in a positional error of as much as 15 miles.
How then is the navigator to obtain an accurate longitude, even if he or she has an accurate clock? Knowing the exact time at the reference meridian by itself is no help. There has to be something with which that time can be compared. The solution lay in discovering the local time at ship from sextant observations – usually altitudes of the sun in the morning or afternoon, though other heavenly bodies could be used. Mathematicians developed a variety of techniques for achieving this objective, all of which involved solving what came to be known as the ‘PZX’ triangle – see diagram above. These methods – which, as we shall see, relied on knowing the ship’s latitude – remained at the heart of celestial navigation until the emergence of the ‘new navigation’ in the 1870s.
Day 8: Up again at 0400 and got a sunrise longitude fix of about 45° W at 0515. The same weather – force 5 from WSW with a fair bit of sunshine interspersed with low cloud and rain showers. Much rolling and rattling of crockery and cutlery. Not much speed – only 4 knots.
One week at sea. I tried to measure how far we had gone but failed to realize that on the small-scale North Atlantic chart the latitude scale is not uniform so I got it wildly wrong. Colin filled in the track chart. We have done 830-odd miles but there’s a long way to go.