# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Lunar Distance in Wikipedia**

**From:**George Huxtable

**Date:**2007 Oct 30, 01:20 -0000

Referring to Frank Reed's earlier message- | > By 1800, there were | > many practical methods for clearing lunars available which reduced the total | > time for the calculation (from beginning to end, including calculating local | > apparent time) to twenty minutes or even less. Mike Daly asked- | Is there a good reference for this? Something suitable for Wikipedia? | I'm reworking some of the history stuff for navigation and would like to | specify the time reducing from hours to minutes from Maskelyne's first | voyage to the regular use of lunars in the early 19th c. The working-time reduced instantly when the precomputed tables for lunar distance appeared in the 1767 issue of the Nautical Almanac (long before the early 19th c.!) After that, there may have been a bit more speeding-up, in streamlining of the "clearing" process, but it was only marginal. Until that date, it was necessary to predict the position of the Moon in ecliptic lat and long, from a complex calculation involving looking up many harmonic constituents from tables which had been provided by Mayer, then calculate the position of the Sun (for example) in a similar but less complex way, and then get the great circle distance between those positions. You can follow such a procedure in Maskelyne's "British Mariner's Guide",(first ed. 1763), a procedure for which he claims to give "complete and easy instructions". Complete they may have been, but far from easy. I am not surprised that they took several hours. What amazes me is that anyone could get the right answer after all that longhand arithmetic. Just try it for yourself. That gave the lunar distance, which really was needed twice, to provide bracketing values, to interpolate between, to get the Greenwich time. And still you had to observe the lunar distance, and "clear" it, before you could compare it with the predicted value. Once the lunar distance had been precomputed in the Almanac, those steps, except that last, had been done for you. When Cook set off on his first circumnavigation in 1768, Nautical Almanacs hadn't been produced far enough in advance to cover the four years of the voyage, and his astronomer had to revert to the old method of long calculation. The astronomer, Green, didn't survive the voyage, and the celestial observations were written-up many years later by William Wales, in his "Astronomical observations ... " of 1788, which I don't have easy access to. Cook had this to say, quoted in the Beaglehole edition of his Journals, vol 1, page 392. " it is only by such means that this method of finding the Longitude at Sea can be put into universal practice- a method we have generally found can be depended on to within half a degree; which is a degree of accuracy sufficient for all Nautical purposes. Would Sea officers once apply themselves to the makeing and calculating these observations they would not find them so very difficult as they at first imagine, especially with the help of the Nautical Almanac and Astronomical Ephemeris, by the help of which the calculations for finding the Longitude take up little more time that that of an Azimuth for finding theVariation of the compass; but unless the Ephemeris is published for some time to come more that either one or two Years it can never be of general use in long Voyages, and in short Voyages is not so much wanting; without it the Calculations are laborious and discouraging to beginners and such as are not well Vers'd in these kind of caalculations." Cook was echoing Maskelyne's claim, in his preface to the 1767 Almanac, which read- "The Tables of the Moon had been brought by the late Professor Mayer of Gottingen to a sufficient exactness to determine the Longitude at Sea, within a Degree, as appeared by the Trials of several Persons who made Use of them. The Difficulty and Length of the necessary Calculations seemed the only Obstacle to hinder them from becoming of general Use: To remove which this Ephemeris was made; the Mariner being hereby relieved from the Necessity of calculating the Moon's Place from the Tables, and afterwards computing the Distance to Seconds by Logarithms, which are the Principal and very delicate Part of the Calculus; so that the finding the Longitude by the Help of the Ephemeris is now in a Manner reduced to a Computation of the Time, an Operation equal to that of an Azimuth, and the Correction of the Distance on account of Refraction and Parallax, which is also rendered very easy by either of the Two Methods invented by Mr Lyons and Mr Dunthorne, and published among the Tables required to be used with the Ephemeris." In his final point there, Maskelyne drew attention to the two methods of clearing the lunar distance provided in his "Tables Requisite ...", which were intended for use with the Almanac, and which became a bast-seller. In my own view Maskelyne's claims were entirely justified. I can't provide references to contemporary estimates of the time navigators took over a Lunar before and after the step-change when the Almanac appeared, but in my own view, a reduction from "several hours" to twenty minutes or less seems entirely reasonable. George. contact George Huxtable at george---.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 unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---