West of the Account

At 11:26:45 by the watch, the distance from the Moon’s eastern edge to the star Spica measured 51 degrees and 38 minutes. At 11:32:35, it was 51 degrees and 40 minutes. At 11:41:45, it had reached 51 degrees and 44 minutes.

These were observations made by Nevil Maskelyne and the officers of the East India ship Warwick, returning from St Helena on 9 May 1762. By the following morning they would see the Isles of Scilly, off Cornwall at the western approach to the English Channel. Before that landfall, the moving Moon offered a way to check how far east or west their ship had travelled.

Maskelyne later made this set of observations the worked example in The British Mariner’s Guide. Published in 1763, the book follows the readings through the calculations needed to turn them into a correction to the ship’s position. The answer came out fourteen minutes farther west. Those were minutes of longitude—fractions of a degree around the Earth, rather than minutes on the watch.

Bringing two objects together

The instrument Maskelyne names is Hadley’s quadrant. It belongs to a family also called octants, whose two names describe different things. An octant’s curved edge occupies one eighth of a circle, or 45 degrees. Through double reflection it can measure an angle twice as large: a full quadrant, or 90 degrees.

The observer looks through a sight towards one object while bringing the reflected image of another into the same field of view. One mirror moves with the index arm; a second, fixed mirror combines the reflected view with the direct one. Turning the arm moves the image. When the two objects have been brought into the required contact, the arm’s position on the scale gives their angular separation.

For a height above the sea horizon, this means bringing the Sun’s edge down to the horizon. Both remain visible together as the ship moves, making contact easier to judge than a measurement which requires the observer to hold a separate reference steadily upright. For a lunar distance, the observer brings a star and the appropriate edge of the Moon together instead. The instrument can be held at the angle needed to join the pair; the measurement need not be vertical.

An angle is a useful beginning, but it does not identify the ship’s longitude on its own. The Moon moves against the background of the stars. If its position can be predicted for a reference meridian, an observed separation can tell the navigator the time there. That can then be compared with local time at the ship. As the Earth turns through 360 degrees in twenty-four hours, an hour of time difference corresponds to fifteen degrees of longitude.

Maskelyne had gone to St Helena for another astronomical undertaking. The Royal Society sent him to observe the 1761 transit of Venus, part of an international effort to measure the solar system. The sea journey also let him test lunar navigation, using the lunar tables of Tobias Mayer. His voyage journal compares astronomical determinations with the ship’s reckoning and records the conditions in which observations were possible.

The observations on the way home were shared work. In his printed account, Maskelyne credits the ship’s officers as well as himself. A set required more than the Moon–star distances: it also needed the altitudes of the bodies and observations from which local time could be established. The watch tied these events together. It was not being asked to preserve Greenwich time throughout an ocean voyage.

A wider arc

The choice of instrument affected which pairs of objects could be measured. A 90-degree range was ample for many altitudes above the horizon, but the Moon could be farther from a useful star or the Sun than an octant could reach. Lunar navigation encouraged a wider arc.

In the 1750s, Captain John Campbell tested a reflecting circle designed by Mayer. A complete circle offered the necessary range, but Campbell found it awkward at sea. He turned to the London instrument maker John Bird for a more manageable form with an arc of 60 degrees. Double reflection gave this sextant a measuring range of 120 degrees.

The larger range did not change the central optical task. It allowed more sky to be brought within it. Precision also depended on the divided scale, the adjustment of the mirrors, the frame’s steadiness and the observer’s judgement of contact. Increasing the range could not remove an error in any of those parts.

A closer look · 3:51 · English · automatic captions

Making the sight

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Correcting the sky

On 9 May, Maskelyne’s chosen star was Spica, which his book calls the Virgin’s Spike. The Moon was past full. Its illuminated eastern edge was the edge farthest from the star, and that was the contact the observers measured. The choice of edge mattered: the tables described the Moon’s centre, while the hand instrument was being set against its visible rim.

The three readings therefore needed a correction for the Moon’s apparent radius. They also needed the instrument’s own adjustment error—three and a half angular minutes to be added in this case. An angular minute is one sixtieth of a degree. Even at this first stage, the size of the correction was comparable with the change between successive readings.

The sky as seen from the deck required further work. Refraction in the atmosphere lifts the apparent positions of celestial bodies, with a larger effect near the horizon. And the observer stood on the surface of the Earth, while the calculations required positions referred to its centre. This displacement, called parallax, especially affects the comparatively nearby Moon. Its apparent place changes much more than a distant star’s does when the viewpoint moves across the Earth.

The altitudes recorded alongside the lunar distances allowed these effects to be calculated. The sight of the sea horizon itself required an allowance for the observer’s height above the water. Maskelyne’s instructions distinguish each of these operations; subtracting the Moon’s radius was not enough to turn a deck observation into the distance required by the tables.

Nor could the watch reading simply be treated as local astronomical time. Maskelyne used observations of the Sun, with the ship’s latitude and the Sun’s declination, to establish the relation between the watch and local apparent time. An afternoon observation was followed by another the next morning to regulate the comparison more securely. The three Moon–star readings were combined at a mean time, so that the moving Moon and the moving ship could be compared consistently.

All this is the work between the visible contact and the navigational result. The printed example passes through trigonometry and logarithms, correcting the separation and calculating the Moon’s position before comparing it with the predicted place. A fine instrument could supply a better starting measurement. It could not do this subsequent arithmetic for the observer.

Fourteen minutes west

The ship already had a position by dead reckoning: an account carried forward from earlier positions through estimated courses and distances travelled. At the time of the lunar observation, that account put Warwick at 6 degrees 54 minutes west of Greenwich.

Maskelyne’s calculation put the ship fourteen angular minutes west of the account. Adding them gave 7 degrees 8 minutes west. His book also applies the correction to the preceding and following noons, carrying the ship’s movement forward or back to the moment required.

The modest correction had an explanation. The reckoning had already been corrected by a lunar observation the previous night. This was a continuing check on the account as the ship approached land.

At sunrise the observers saw the Scilly islands, estimated to be six leagues away. At nine in the morning they took a bearing of the lighthouse on St Agnes and estimated its distance at five leagues. These sightings supplied a way to compare the lunar result with known land.

The comparisons did not produce a single tidy answer. The longitude inferred for the middle of the islands differed from the result for the lighthouse. Maskelyne pointed to the spread of the islands, the difficulty of judging which part appeared central from offshore, estimated distances and the ship’s passage through tidal waters. He judged the results to lie within eighteen or twenty minutes of longitude of the best charts, about twelve miles at that latitude.

The lighthouse gave him another quantity to check. With a noon observation for latitude and a bearing of St Agnes, he calculated a latitude for the light ten minutes farther north than the position in Whiston’s chart of the Channel.