National Maritime Museum Manuscripts : Navigational workbook: rule for clearing a lunar distance

National Maritime Museum Manuscripts

<p>A collection of eight pages, written by Fisher, on the ‘Rule for Clearing a Lunar Distance’. This is one of the stages of the process of finding longitude by the lunar distance method.</p> <p>After the original lunar distance, the distance between the Moon and a particular celestial body, has been taken along with the heights of the two bodies above the horizon, the mariner or astronomer corrects the observation first for dip and the Moon’s semidiameter, the distance between the outer edge of the moon and its centre. Since the Moon varies in size each day, the <i>Nautical Almanac</i> lists the Moon and Sun’s semidiameter for each day. This is Step 1 [<a href='' onclick='store.loadPage(2);return false;'>2</a>] of Fisher’s instructions.</p> <p>The next set of corrections is where this workbook by Fisher is used; ‘clearing the lunar distance’ means correcting for the effects of parallax and atmospheric refraction on the observation. The Nautical Almanac gives lunar distances as if the mariner or astronomer were at the centre of a transparent Earth. Because the Moon is so much closer to the Earth than the stars are, the position of the observer on the surface of the Earth shifts the observed position of the Moon by up to an entire degree. The clearing correction for parallax and refraction is a trigonometric function of the original observations of lunar distance and the altitudes of the two bodies, after they have first been corrected for dip and distance between the edge and the centre of the bodies. This is steps 2, 3 and 4 [<a href='' onclick='store.loadPage(2);return false;'>2</a>] in Fisher’s instructions. Fisher also includes in this collection of papers an example of the calculation [<a href='' onclick='store.loadPage(3);return false;'>3</a>] for <a href='/search?keyword=Greenwich'>Greenwich</a> on April 3rd 1849 using the Moon and Venus.</p> <p>Perhaps the most interesting part of the document is the final note [<a href='' onclick='store.loadPage(7);return false;'>7</a>] that Fisher leaves after the example calculation. Fisher advises that the preliminary observations only need to be made to the nearest minute with the addition or subtraction of the requisite seconds continued into the reduction of the observations. This will allow the first stages of calculation to be made faster, as there won’t be the remaining seconds to consider, with, Fisher claims ‘no sacrifice to accuracy’. This helps to remind us of the different understandings and requirements of accuracy cultivated by mariners and astronomers. Mariners need their calculations to be as quick as possible in order to give a longitude reading for as close to their present position as possible; the ship would presumably keep moving whilst the observations were reduced meaning mariners would often work out the longitude for their position at the time they took their observation, not where they were when they finished the reduction. Reducing the time taken over these calculations was one of the priorities of those producing manuals and almanacs for the lunar distance method to counter this time lag. In contrast to this, astronomers were perhaps more willing to observe and then reduce their observations within a more luxurious timespan. Therefore they were perhaps less inclined to round up or down to the nearest minute in order to move through the calculation quickly or more simply, instead favouring the highest degree of accuracy possible for them to obtain.</p> <p>Sophie Waring<br />History and Philosophy of Science<br />University of Cambridge<br /> </p>

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