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    More on Lunars
    From: Henry Halboth
    Date: 2008 Jul 8, 22:04 -0700

    Hi all,
    I apologize to the List for my delay in responding to Frank’s reply to my 
    original postings under the above subject; unfortunately, I simply do not 
    have the time to compose properly reasoned replies to much of what is posted 
    these days and spend much of my time lurking. However, as Lunars have again 
    been featured, it may be appropriate to now respond, as follows ...
    In NavList 3269 I opined that Lunars generally had received a bad name as far 
    as accuracy is concerned primarily for two reasons.
    I stated in 3269
    1.  The relative inaccuracy of early instruments. Let's remember that the 
    octant, as originally produced was not fitted with a tangent screw and gear 
    for easy and positive measurement of small arc increments. Although the 
    vernier appeared rather early on, it was the incorporation of the tangent 
    screw that allowed more positive fine adjustment. I also certainly cannot 
    believe that some of the earlier instruments made of wood with ivory arcs, 
    although works of art, could be relied on as respects accuracy over a wide 
    range of condition to be met at sea.
    Frank responded in 3272, in part 
    Certainly, instrument accuracy was always a big issue and still is for lunars. 
    I agree with that. Regarding your specific comments on octants, I know of no 
    one who shot lunars with a wooden octant in the era. A metal sextant --with 
    tangent screw, telescope, and assorted shades-- were all recommended right 
    from the very beginning of the lunars era. Even in 1763, Maskelyne spells out 
    these requirements in detail. There's clear evidence 
    that navigators carried two types of instruments: octants, like you've 
    described above, for daily latitude observations (almost always Noon Sun) and 
    sextants for lunars. Of course, if there WERE any navigators who declined the 
    advice to get a proper sextant, and this advice was in practically every 
    navigation manual and guide to shooting lunars, they would definitely have 
    been disappointed with the results. Wooden octants arecomparable in accuracy 
    to modern plastic sextants (e.g. Davis).
    Then he went on to post in 3789, in part ...
    Here's an article published in 1847 discussing the uses of lunars and  
    chronometers. The principal lunar story actually refers to events in 1825.  
    Apparently, this navigator had good success taking lunar observations with a  
    "quadrant" which in that era would have meant an ordinary wooden octant.
    I now respond further ...
    It was not my intent to imply that octants were employed in Lunar observations 
    to the exclusion of any other instrument type, and merely cited their 
    construction as an example of the potential for inaccuracies. Frank knows as 
    well as I do that there were also wooden sextants manufactured – how many I 
    don’t know, but enough have wound up in collections and museums to give us a 
    good sample. Even if a metal sextant was the 18/19th century navigator’s 
    instrument, what was the arc made of – early instrument makers were known to 
    sometimes use common bone, ivory, or brass for the arc before silver became 
    the commonly accepted material for this purpose; Spencer, Browning & Co., 
    London (1849 – 1870), and others,  marketed  brass sextants with an ivory 
    arc, and I have personally handled a metal 19th century sextant possessing an 
    ivory arc which had become so contracted as to render the instrument useless 
    for any purpose. Certainly, it is possible to
     reference log books containing worked up Lunars, but unless that logbook also 
    specifies and describes the instrument used in some detail you really don’t 
    know what was used, do you now. Assumptions not based on hard evidence do not 
    make historical fact. Also, what degree of accuracy can be ascribed to such 
    records of Lunar calculations at sea as have come down to us by way logbooks; 
    unless associated with a landfall, or comparable navigational event, you 
    again simply don’t know.
    John Bird, London astronomer and scientific instrument maker, manufactured 
    both brass and wood instruments; in 1759, he produced a mahogany framed 
    sextant with an ivory arc – an example is in the Scheepvaart Museum, 
    Amsterdam; he is reputed, but not so proven, to have made a large wood framed 
    sextant in 1771 for Captain Cook to use on his 2nd voyage – this instrument, 
    or an example thereof, is presently in the Science Museum, London. H. 
    Limbach, of Hull, England, produced an ebony framed Sextant with brass index, 
    ivory arc, and ivory vernier, and there are on display other signed wood 
    framed sextants "equipped with, tangent screw, telescope, and assorted 
    shades”, at least into the 1830s. I cannot say what these wood framed 
    sextants were used for or how accurate they may have been – neither can I say 
    that they were not used for Lunars. Scientific expeditions, supported by 
    Governments appear to have been well funded and supplied with the best
     instruments available; not so the average Merchant Vessel, aboard which 
    officers were generally required to provide their own instruments, and I 
    seriously doubt that they universally provided themselves with the assortment 
    recommended by some navigational texts, regardless of how valid such 
    recommendations may be. As respects the United States, the best of 
    instruments were not always available; witness the US Exploring Expedition, 
    of 1838 – 1842, which found it necessary to send an emissary to Europe in 
    search of suitable instruments to outfit its vessels. I am pleased to find 
    that Frank, in 3789, has found an 1825 navigator who apparently ... “had good 
    success taking lunar observations with a  "quadrant" which in that era would 
    have meant an ordinary wooden octant.”   ... I think there may have been many 
    I also stated in 3269
    2.  The mathematical methods of clearing the distance, especially the so 
    called approximate methods were a wonderment of complication, in some 
    instances requiring the application of numerous corrections which in 
    themselves sometimes defied reason. Most of the epitomes I have read did not 
    apply to reason, but simply listed rules to follow. In my view, at least, a 
    relatively simple explanation of the problem related to a trigonometrical 
    format would have better served the mariner. The entire subject of spherical 
    trigonometry does not appear as complicated as some of the approximate 
    Frank responded  in 3272........
    Here, I DO disagree. The great majority of the lunars that you will find 
    worked out in 19th century logbooks are series methods (erroneously known 
    sometimes as "approximate" methods). The steps involved in working them were 
    no more complicated than working an ordinary time sight --something which 
    nearly every navigator could do with ease. The amount of work was about three 
    times greater, but the steps and mathematical skills were not greater. I've 
    seen many examples of lunar observations worked out on spare pages in old 
    logbooks, and not once have I seen any of the straight triangle methods, ike 
    Borda's, in use. They used the series methods, like Bowditch's Principal 
    Method, Thompson's method (adopted into Bowditch in 1837 just before his 
    death), Witchell's method, variants of Lyons' method, Bowditch's Original 
    Method (known in Europe as the method of Mendoza Rios, although never claimed 
    by MR himself) and so on. There's no doubt that other direct
     methods, including Dunthorne's and Borda's and Krafft's were in fact used, 
    but they were less popular. The choice of method was not considered a "big 
    deal" in the day. Many navigators seem to have learned a couple of different 
    methods if for no other reason than for intellectual amusement. 
    I now respond further ...
    My dictionary defines approximate: 1) as an adjective = “ nearly exact, not 
    perfectly accurate or correct”, and 2) as a verb = “to come near to; approach 
    closely to”. So really what is the discussion about. Is it now claimed that 
    the methods mentioned in 3272, including the “straight triangle methods” are 
    perfectly accurate or correct – if not, they are and have been properly 
    called "approximate". I have long felt that Lunars should be perhaps 
    categorized as “Scientific” or “Commercial”, as well as by period. Certainly, 
    some excellent observations were returned by early Government expeditions; 
    these were,however, well funded, supplied with the best instruments and 
    astronomical tables available, and frequently included astronomers in their 
    complement of scientific personnel.
    Accuracy in the clearing of a Lunar Distance requires, in addition to other 
    factors normally considered, attention to the Moon’s parallax in azimuth, the 
    spheroidal shape of the earth, and the true shape of the Sun/Moon disks as 
    affected by refraction. These factors were apparently early on not thought 
    necessary of consideration in practical usage and of relatively small 
    magnitude – given Maskelyne’s own expectations of instrumental accuracy to 
    only 1-minute of arc, as well as Longitude accuracy of from 15 to 30-minutes 
    of arc, and including log entries posted on this List wherein Lunar 
    observations are recorded to only the nearest minute of arc, an effort to 
    improve accuracy by a few seconds of arc here an there may well have been 
    extraneous. Regardless, as instruments improved, tables became more accurate, 
    and scientific minds became tuned to the problem, more attention was 
    obviously invited to these lesser corrections - unfortunately, by this 
     time Lunars were already partially on the way out.
    While acknowledging the method of Friedrich Wilhelm Bessel (1784 – 1846), a 
    German astronomer and mathematician of the highest repute, as being then the 
    only truly rigorous method of clearing a Lunar Distance, William Chauvenet, 
    in his 1868 paper entitled “Navy Scientific Papers No. 1 – Astronomy: 
    Comprising Suggestions to US Naval  Officers”, details a more modern and 
    balanced view of Lunars. This paper, once discussed on this List extensively, 
    details and quantifies the errors to which Lunars were subject previously by 
    reason of tabular inaccuracies prior to 1855, neglect of certain corrections, 
    instrumental error, and observational error. I will not extend this writing 
    by further quoting from this paper, but will strongly recommend it to budding 
    Lunarians and for review by the pundits of this List for it lays bare the 
    inadequacies, at least in the authors opinion, of the older methods. He also 
    published a set of tables to facilitate the use of
      an “approximate” (his words) method, devised by him, to clear the distance 
    with a mean error of not more than 2-seconds. Chauvenet’s method seems to 
    have impressed the US Hydrographic Office, as the 1888 edition of HO 9 
    (Bowditch) includes its use, to the exclusion of others. 
    In a paper presented before the Royal Society of Victoria in 1889, E. V. 
    White, FRAS, reported a mean of 42 Sun/Moon Lunars, observed by him at a 
    place of known Longitude between August 27 and October 2, 1887 and cleared by 
    Chauvenet’s method, to have exceeded the true Longitude by 4.8 seconds in 
    time; the probable error of a single observation is said to have been +/- 21 
    seconds in time. Mr. White also has a number of less than favorable remarks 
    to make regarding the accuracy of sextants encountered over his some 40 years 
    prior experience in their use.
    I certainly agree with George's philosophy regarding Lunars, as set forth in 
    5647, and perhaps carry it a step further. Lunars have evolved, from a rather 
    crude beginning to an ever more scientific approach. The solution to the 
    Lunar Problem is based on sound principle, and perhaps still awaits the more 
    perfect means of measurement - experiments were at one time in progress 
    utilizing the photographic plate and apparently with some success. Who knows; 
    someday, somebody may come up with a startling breakthrough. In the meantime 
    Navigation List archive: www.fer3.com/arc
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