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Halley's lunar knowledge.
From: George Huxtable
Date: 2007 Nov 24, 21:49 -0000
From: George Huxtable
Date: 2007 Nov 24, 21:49 -0000
In Navlist 3926, under threadname "Ted Gerrard's book", Mike Daly wrore- "Halley's method can only be as accurate as his lunar position knowledge. No one published tables at that time (as Maskelyne did after 1767). There was the raw data that was coming out of Flamsteed's observations and other observers that may have been accumulating data. Newton and Halley published Flamsteed's data without his permission in 1712 but what Halley used in the 1699 timeframe I don't know offhand." ===================================== This note is for anyone interested in Halley's methods. I attach scans of Halley's paper "A proposed method for finding the longitude at sea ...", which appeared in Philosophical Transactions (of the Royal Society), vol 37 (1731) pages 185-195, for anyone who wishes to read Halley in the original. Sorry about the awkwardness of the 2-page-at-a-time layout, but it's the best I could do. It should allow you to print it out and reassemble. Most of the paper is a rewrite of Halley's supplement to Streete's "Astronomia Carolina" or Caroline Tables, of 1710, with only unimportant bits omitted. Halley writes rather clearly, and, for his era, can even spell well. One puzzle for readers of his paper may be his use of "extra syzygias". Syzygy (lovely word!) means simply alignment, and the Earth-Moon-Sun syzygies are when the three line up, either at full Moon or new Moon. So Latin "extra syzygias" means away from those syzygies, at dates nearer the Moon's quarters. You might also need to know that the English league is three nautical miles. And you might like to know that the "domestick circumstances" that distracted him, were that his father had been murdered! Halley knew more about the Moon's motion than any of his contemporaries. He devoted much of his life to observing and predicting it. He didn't need to rely on the published tables of others, though he gathered what he could. He had been making his own regular observations of the Moon's position with respect to the stars, from his home observatory in Islington, London, from 1682 to 84. We don't know what his new bride thought about that... He tells us that he set up the same astronomical sextant that he had used earlier in his survey of the southern stars from St. Helena. Alan Cook, Halley's best biographer, ("Edmond Halley; charting the heavens and the seas", 1998) tells us that its radius was 5 feet 6 inches, quoting from Halley's catalogue of Southern stars (1679), and Phil. Trans.vol. 12, no. 141 (1678), 1032-4 (neither of which I've read). An astronomer's sextant was nothing like a navigator's sextant, of course; they shared the same name because each had an arc of one-sixth of a circle. It was intended for measuring the angle between two objects in the sky, just as in a lunar distance, but often of the angle between two stars, to a maximum of 60 degrees. It had no mirrors, but two separate telescopes, one to view each object. Early sextants could swing their frame about on a ball-joint, and then needed a pair of observers, one to align each telescope, but Halley's probably had an equatorial mounting, and then one observer could use it on his own. Cook includes a sketch, supposed to be of Halley's sextant, made by De L'isle, which to my mind is somewhat suspect, showing its possible use in measuring altitudes and zenith distances rather than for angular separations. His observations for those early years, November 1682 to December 1684, are recorded in that supplement to the Caroline Tables of 1710. Mostly, they are of Moon-to-star distances, noted to the nearest 10 sec of arc (sometimes to 5, when it's 15" or 45"). Sometimes just one observation, but more often two or three repeats, all noted. There are many occultations and appulses noted as well. Anyway, the question arises; how did Halley predict Moon positions? There were indeed tables published of the Moon, contrary to Mike Daly's claim above, but these were nothing like as precise and detailed as Maskelyne derived from Mayer in 1767. They dated back to Ptolemy! Intended for astrologers, rather than astronomers. Halley was aware that the simple-minded predictions available in his time were highly inaccurate. To put them right needed an understanding of the dynamics, and Halley was prepared to leave all that to Newton, whom he was sponsoring. Halley's approach was a simple, empirical one that's rather easy to understand. He reasoned as follows- There are two important cycles in the Moon's motion. One refers to changes in the plane of its orbit round the Earth; that plane is tilted in space at about 5 degrees to the ecliptic (the path of the Sun through the stars). The direction of that tilt changes greatly, from one year to the next, until after 18 years or so, it's moved round in a complete circle and is tilting just the way it started. The Greeks, and even the Babylonians before them, were fully aware of that 18-year cycle. The other is in the way the Moon's elliptical orbit changes. It comes closest to Earth (perigee) once a month as it crosses the long-axis of that orbit. But that long-axis doesn't stay put in space; it's direction shifts a bit, each month, so that in only 9 years or so, perigee is back to the same direction in space. After 18 years, it would have rotated twice. It had been long known that after about 18 years (known as the Saros cycle), eclipses tended to recur. Halley worked out that after an interval of 18 years 11 days (which was an exact number of months), the phase of the Moon would be the same, the time-of-year would be nearly the same (within 11 days), the tilt of the orbit and the direction of perigee would all be back where they were before. So whatever those corrections to the simple predictions were (whether or not they were understood) they would be almost exactly the same 18 years 11 days later. So as long as the Moon position had been carefully measured, 18 years and 11 days before, Halley could work out what the necessary corrections (they were called "equations") were, and make predictions accordingly, without needing to understand all that dynamics. There were snags, of course. Those repeat periods were not exactly 2 to 1. And there were other influences at work, with a different timescale; particularly the resonance between the giant planets Jupiter and Saturn. Halley was 65 when he took over at Greenwich as Astronomer-Royal, which had been stripped bare of its instruments by Flamsteed's widow, so he had nothing to observe with until a year later. Nevertheless, he confidently set up to observe a full 18-year cycle of the Moon's motions, and completed it before his death in 1742, at 85! His paper, attached, was an interim halfway report, after the first 9 years, when one perigee cycle had been completed. What is of particular interest to us is the use of Moon predictions in obtaining longitudes for Halley's two Atlantic voyages. He is rather reticent about that matter in his Journal, usually stating only the date, the star used for appulse, and the resulting longitude. On his first voyage, telescope lunars (not lunar distances) were observed between 15 February and 12 June 1699, and after a spell in London London, on his second voyage, between 5 December 1699 and 30 July 1700. The crucial period, 18 years and 11 days before then, would be from early February 1681 to mid July 1682, and for that period, Halley would need Moon observations, to make predictions for those later lunars. That was before the start of his recorded Islington observations, in November 1682. So was Halley systematically observing Moon positions, with respect to the stars, in that earlier period? We don't know, but it looks a bit doubtful. At the relevant time, Halley was travelling in Europe, with his friend Robert Nelson. At the start of the period in question, Halley was in Paris, with Cassini, observing the comet of that year (not Halley's) amongst other matters. In mid- May, they were travelling South, toward Rome; Halley measuring latitudes as they went with an 18-inch quadrant. Did he carry a telescope as well; all he would need, with the portable quadrant, for observing Moon appulses and occultations? We know little about what he did in Rome. By 15 Jan 1682 he was back in Paris, and by 24 Jan he had returned, via Holland, to London. With all that travel, it was not a good time for making systematic observations of the Moon. So the question remains open; what were Halley's Moon predictions, used to determine longitudes for his Atlantic voyages, based on? Any ideas? George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---