<p style='text-align: justify;'>An envelope containing a booklet of copies of reports from 1765 made to the Board of Longitude on the methods of George Witchell and Israel Lyons to compensate for the effects of refraction and parallax respectively upon observations for the lunar-distance method of finding longitude. During this same period, Witchell and Lyons were both hired as computers (calculators) for the first of the <i>Nautical Almanacs</i> overseen by Nevil Maskelyne and put out by the Board annually. Both were long respected members of the longitude, mathematical and Naval communities - with Witchell becoming an F.R.S. and becoming head mathematical master at the Royal Naval Academy in Portsmouth in 1767, and Lyons being a prodigious talent in mathematics and natural philosophy who was involved with a number of Board publications and was also one of its expedition astronomers.</p><p style='text-align: justify;'>The <a href='' onclick='store.loadPage();return false;'> instructions (RGO 4/292:1)</a> for George Witchell's method of compensating for the effect of refraction (an improved version of a method he had submitted to the Board in 1764) describe how the observer should consult the provided tables and perform certain calculations in order to remove the distorting effect in seconds of refraction upon the observed altitudes of the Moon and Sun or other observed star. The <a href='' onclick='store.loadPage(2);return false;'> instructions (RGO 4/292:1v)</a> for Israel Lyons's method of compensating for parallax describe a similar but more complex process, for which three <a href='' onclick='store.loadPage();return false;'> examples (RGO 4/292:2)</a> are provided.</p><p style='text-align: justify;'>John Howe, at the behest of the Board of Longitude, reported in an <a href='' onclick='store.loadPage();return false;'> undated letter (RGO 4/292:5)</a> presumably written in 1765 that Witchell's method was 'of very ready & convenient use for Mariners & of sufficient exactness when neither Luminary is nearer to the horizon than ten degrees', as long as certain changes were made to the accompanying tables. He judged that Lyons's method was 'sufficiently true and of ready use' as long as changes were made to these tables as well and additional precepts or directions were added. Howe <a href='' onclick='store.loadPage(12);return false;'> concluded (RGO 4/292:5v)</a> that the use of these two methods would be beneficial, and that it should not cost much to publish them, but agreed with Witchell's suggestion that a table compensating for both the parallax of the Sun and the variation of refraction would be of even greater benefit if calculated exactly rather than by approximations.</p><p style='text-align: justify;'>Matthew Raper<a href='' onclick='store.loadPage();return false;'> wrote (RGO 4/292:6)</a> from his manor Thorley Hall in <a href='/view/'> Thorley, Hertford ()</a>, on 9 July 1765 that, at the request of the Board, he had compared the two previously described methods and Witchell's suggestion for both parallax and refraction and concluded that the last, with some adjustments, was 'preferable, for the use of Seamen [...] both in respect to its facility, & (if scrupulously computed) its accuracy' due to addressing both problems at the same time. (This may be the method <a href='' onclick='store.loadPage();return false;'> described later (RGO 4/292:12)</a> in the booklet without attribution.) Roper then <a href='' onclick='store.loadPage(14);return false;'> made suggestions (RGO 4/292:6v)</a> for how this comprehensive table should be laid out, and sketched out an example. Related calculations and geometric sketches fill the pages from <a href='' onclick='store.loadPage();return false;'>RGO 4/292:8</a> to <a href='' onclick='store.loadPage();return false;'>RGO 4/292:11</a>, while tables for correcting for parallax are on pages <a href='' onclick='store.loadPage();return false;'>RGO 4/292:15</a> to <a href='' onclick='store.loadPage();return false;'>RGO 4/292:19</a>.</p><p style='text-align: justify;'>Raper, an F.R.S. with a private observatory designed by the well-known engineer John Smeaton, was one of the luminaries who signed a testimonial in 1764 supporting Nevil Maskelyne as candidate to be the next Astronomer Royal. He was also a close friend of and executor for Howe of <a href='/view/'> Hanslop in Buckinghamshire ()</a>, whose will is PROB 11/951 at the National Archives in Kew. Howe was related to Richard Viscount Howe, a member of the Board of Admiralty who also began attending Board meetings in 1766 as Treasurer of the Navy. Other RGO volumes including those of <a href='/view/MS-RGO-00014-00005'> official Board minutes (RGO 14/5)</a> reveal Raper's and Howe's expertise being consulted on a number of matters over the years, for example when they <a href='/view/MS-RGO-00014-00005/22'> were asked (RGO 14/5:18)</a> in June 1762 their opinion of the 'Accuracy & Correspondency' of observations <a href='/view/MS-RGO-00014-00005/20'> recently made (RGO 14/5:16)</a> of the Jovian moons at Portsmouth and Jamaica as part of the process of trialling John Harrison's marine timekeeper H4 [<a target='_blank' class='externalLink' href='http://collections.rmg.co.uk/collections/objects/79142.html'><img title="Link to RMG" alt='RMG icon' class='nmm_icon' src='/images/general/nmm_small.png'/></a>]. In recognition of this frequent service, the men were sometimes given presents, as when it was decided on <a href='/view/MS-RGO-00014-00005/76'> 10 January 1767 (RGO 14/5:72)</a> that they and Gael Morris and Captain Campbell were to be given free copies of Tobias Mayer's tables, the latest ephemeris, and the published drawings of John Harrison's 'H4' timekeeper.</p><p style='text-align: justify;'>Other volumes also reveal the timing and decision-making process behind considering, evaluating and publishing Witchell's and Lyons's methods of correction for the lunar-distance method. On <a href='/view/MS-RGO-00014-00005/38'> 18 September 1764 (RGO 14/5:34)</a>, the Earl of Egmont laid before the Board a lunar-distance proposal from George Witchell with a General Table and Ephemerides, which was referred to Howe, Raper and Gael Morris. On <a href='/view/MS-RGO-00014-00005/41'> 19 January 1765 (RGO 14/5:37)</a>, the three men's opinions were read aloud, but the Board did not reach a resolution in response. On the ensuing <a href='/view/MS-RGO-00014-00005/49'> 28 May (RGO 14/5:45)</a>, Witchell's improved method and Lyons's method were introduced and referred to Raper, John Rowley, Gael Morris and John Bevis (the last man being <a href='/view/MS-RGO-00014-00005/52'> omitted (RGO 14/5:48)</a> two days later). Both mathematicians were also asked for estimates of the cost of making and publishing their tables. On <a href='/view/MS-RGO-00014-00005/56'> 18 July (RGO 14/5:52)</a>, the three experts' reports were read and, after discussion with George Witchell, he was given £100 to compute, correct and print 1,000 copies of his 'General Tables of Refraction & Parallax with the Additions proposed by Mess.rs Raper & Howe' for the Board before the publication of the Ephemeris for the year 1767. Lyons was likewise employed to prepare his own tables, to be inserted at the end of the Ephemeris. On <a href='/view/MS-RGO-00014-00005/73'> 24 May 1766 (RGO 14/5:69)</a>, the Board decided that Witchell was working too slowly and had provided too costly a printing estimate and sought someone else to take over his work, deeming the £300 he had been given to date sufficient as a reward for his innovation and efforts. On <a href='/view/MS-RGO-00014-00005/74'> 10 January 1767 (RGO 14/5:70)</a>, Anthony Shepherd was assigned to oversee computers finishing the tables for publication. Much later in 1782, Witchell <a href='/view/MS-RGO-00014-00002/'> wrote (RGO 14/2:212)</a> to the new Secretary of the Board, Henry Parker, of these events and of how the tables were finally published in 1772.</p><p style='text-align: justify;'>Alexi Baker<br />History and Philosophy of Science<br />University of Cambridge<br /></p>
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