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Halley's lunars, back in 1698-1700
From: George Huxtable
Date: 2004 May 5, 17:46 +0100
From: George Huxtable
Date: 2004 May 5, 17:46 +0100
I've been in touch with a correspondent in Scotland who has been doing some serious work on Edmond Halley (1656-1742), and look forward to its eventual publication. He kindly reminded me of Halley's "lunar" observations, that were made on his two voyages around the Atlantic, in the British Navy 89-ton pink "Paramore", as early as 1698-69 and 1699-70. Although I had a copy on my shelves of Norman J W Thrower's account "The three voyages of Edmond Halley in the Paramore 1698-1701", (Hakluyt Society 1981), I had only glanced through it, and had not appreciated the significance of the navigational details. Now, I have, and it seems to be a remarkable story. I recommend anyone interested in the history of navigation to give it a read. Halley, of course, was famous for predicting the reappearance, long after his death, of the comet that bears his name. Astronmers know him as the author of the first catalogue of Southern stars, observed from the South Atlantic island of St Helena in his 20s. But his real hobby-horse was in proposing, long before the days of the famous longitude prize, that if magnetic variation could be accurately mapped worldwide, it could provide a tool for determining longitude. In the end, of course, that goal was illusory. To that end, he persuaded the Admiralty to fit out and man a small vessel under his command, for surveying magnetic variation over the Atlantic Ocean. It was, I think, the first time (and probably the last) that such a command was given to someone who was not a Navy Officer, but a scientist. He sufferd from disciplinary troubles with his officers and crew; perhaps they resented being commanded by an outsider, throughout his three voyages. The third was to study the tides of the English Channel. Because his Atlantic voyages were magnetic surveys, rather than a simple passage from A to B, Halley had to estimate his positions, along his path, as best he could. Latitudes were no problem, of course. For longitudes, his main tool was dead reckoning, by log, line, and sandglass, compass and traverse table. On the rare occasions of a Moon eclipse, he timed that. He carried some sort of timekeeper, better than an hourglass, on board, because he occasionally refers to "at 3h 15m in the morning". Balance-wheel watches existed then, but were in no way chronometers, though they would do for maintaining apparent time from one day to the next. When he arrived on land, he observed Jupiter satellites with a telescope to get Greenwich time. What interested me, though, and what may interest Nav-l members, was his use of lunars, for determining time at sea. Remember, Hadley's (or Godfrey's) quadrant (= octant) was 30 years away yet. The only instrument Halley had for measuring angles across the sky, for a lunar, was the cross-staff, good to a degree or so. So how did Halley measure his lunar distances with sufficient accuracy? He didn't measure his lunars. He timed them instead, directly. For that, all he needed was his telescope. Here's how the trick was done. Remember, Halley had spent two years observing and cataloging Southern stars at St Helena, and had done the same at his observatory in Britain. He knew just what star was where, and no doubt had with him a good catalogue of their precise (for that date) positions, especially the zodiacal stars. When the Moon follows its wandering path across the sky, it never departs from the ecliptic by more than 5 degrees or so. Thoere's no shortage of stars in the sky. Sometimes the Moon will pass right over one, blotting it out. That an occultation, but it wasn't what Halley was looking for. What he was looking for was a star that the Moon passed really close to, grazing it if possible: a close conjunction, with the Moon passing above or below it. Then he drew a line in the sky (either in his mind, or using a cross-wire in his telescope) that passed through the two "horns" of the Moon, and therefore passed through the Moon's centre also. That line swept through the sky slowly, as the Moon moved through the stars. Halley would note the time when that line swept past a star he could identify, with a position that he knew. And that was all there was to it. The job was done! If the Moon followed the ecliptic exactly, then the line between the horns would be exactly at right-angles to its path. Being off, by up to 5 degrees, the line between the horns could be skewed around by a few degrees. That's why a close conjunction was called for. He wouldn't want to extrapolate that line far, if a star was away from the Moon. What Halley had measured, to reasonable accuracy, was the moment when the Moon's centre had the same ecliptic longitude as the star did. All that he needed to do was to compare his observation with the predicted motion of the Moon, to discover the Greenwich time of the event. Because the Moon and star were so close, correction for refraction didn't arise. If the measurement could be made at a time when the line between the horns was vertical (somewhere near the Moon's meridian passage) then not even Moon parallax was important, as parallax moves it only in altitude, and so wouldn't affect the timing of such an event. Halley was making these lunar observations as a matter of scientific interest, to test out the method. Also he was using the results for navigational purposes, to discover (for example) how near he had got to the coast of Brazil. In that case he showed that his dead reckoning was many degrees short of where he found he had got to. But the real purpose was to help him to plot the positions for his magnetic surveying. Presumably, for that purpose (unlike for navigation) there was no need for a result to be available in real-time. Remember, at that date lunar orbit theory was very much in its infancy. Moon position predictions could not be relied on to any great accuracy. But obtaining his survey positions was a job that could wait until he returned to Greenwich., when he could discover what Moon positions had actually been recorded there, on the same night as his own observation was made. If that day had happened to be cloudy at Greenwich, no doubt he could interpolate between others, or ask of another observatory. If he used that technique (which was the way land-surveyors of the period would obtain their longitudes from Jupiter satellites) he would then become quite independent of the inadequacy of predictions Please note: in the description of Halley's measurement technique above, there's a lot of surmising, from me, about the details. Halley's own descriptions are tantalisingly terse. I will quote an example, of the log entry for that observation off Brazil, on (nautical day) 4 Dec 1699, which is about as full as Halley ever gets. "Latitude by observation 20deg 58' Wind and Weather as before we Stear away S W b S p Compass which makes a S 43 W Course correct Distance 79 Miles Diff: of Long 57 minutes Long a' London 31deg 13'West Last night the Amplitude was 34 1/2 and this Morning 15 1/2 very good observation, theSea being verySmooth and the Ship quiet True Variation Stated from both is 9deg 30'West in 20deg 30' This Morning the Moon aplyed to a Starr in Virgo of the 4 Mag: whose Longitude is [approx. equal to] 0deg 39' Laty 1deg 25' The Moon did exactly Touch this Starr with her Southern Limb at 3h 15' in the Morning, and at 3h 20' 20" the Southern horn was just 2 Minutes past the Starr haveing carefully examin'd this observation and Compared with former observations made in England I conclude I am in True Longitude from London at the time of this observation 36deg 15' and at this Noon 36deg 35'. That is according to the Account I have of it, about 5 Degrees East of Cape Frio." Note that Halley makes a step-change in his presumed long. at noon, from his DR value of W 31deg 13' to a new value, based on his lunar, of W 36deg 35', a change of 5deg 20' or nearly 500 miles! He used that longitude for further dead-reckoning, from then on. Halley didn't sight land until several days later, so unfortunately we have no good confirmation of the accuracy (or otherwise) of his lunar longitude. Cotter in "History of Nautical Astronomy", notes that as early as 1615 Baffin measured a Sun-Moon distance using a cross-staff for altitudes combined with azimuth observations. The ship was beset in ice at the time, so its stability may have helped. Being far North, both Sun and Moon were presumably very low in the sky, which may have made azimuth measurement more feasible. However, it seems unlikely that such a crude technique could possibly provide a useful measurement of lunar distance. However, it's something of a surprise to me, that neither in Cotter nor in Andrewes (ed.) "The Quest for Longitude", does there seem to be any mention of the 1698-1700 lunar observations made by Halley, although his many other contributions to navigation are fully credited. He appears to qualify as the first navigator to use lunars at sea in a practical way. This note is an attempt to redress the balance. George. ================================================================ contact George Huxtable by email at george@huxtable.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================