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    Re: Longitude Without Time - 1977 Luce Article
    From: Francis Upchurch
    Date: 2018 Jul 30, 21:16 +0100

    I agree with Frank,
    I'm emotionally obsessed with all things lunar and have tried every method. (hobby, not really logical)
    My preferred method is classic lunars using Thompson type clearance methods 
    using slide rules. (again, purely my hobby rather than anything logical)
    I find LD sextant measurements easier and more accurate than Alts. Alts with 
    bouncy horizons less accurate . LD measurements much more accurate.
    The easy maths with the Thompson type methods makes the Altitude methods irrelevant.
    Thanks Frank for finally explaining why ordinary slide rules are adequate for 
    reducing these "cosine corner" type of methods . Now I understand! My Fuller 
    probably well above what is required, but I love it anyway and it does 
    everything else. The Bygrave does the great circle distance for the 3 hourly 
    LD table, although I usually cheat and use Frank's excellent website to 
    generate my own pre 1912 NA 3 hourly LD tables. Either way all easy and lunar 
    Alts not necessary. Proper lunars any time for me. 
    Meanwhile, my Invicta mechanical watch is so accurate that I can do classic 
    LOPs without any electronics, lunars or anything. Can do Cook's second voyage 
    type games. Job done.
    Very accurate,  non electronic celnav methods now easy for me, no lunars required, except for hobby.
    -----Original Message-----
    From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of Frank Reed
    Sent: 30 July 2018 06:01
    To: francis{at}pharmout.co.uk
    Subject: [NavList] Re: Longitude Without Time - 1977 Luce Article
    Mark Coady, you wrote:
    "By Chichester's day, while Bowditch and others and dropped lunars from their 
    later editions, it seems that lunars had been simplified to the point where 
    they weren't such an intimidating exercise?  Various corner cosine methods, 
    etc. had been worked out and made life a bit easier."
    A lot easier! In fact, all of that had been done by the late 18th century. The 
    series methods (involving those factors of proportion which I have called 
    "corner cosines") were available and popular right at the beginning of the 
    lunars "era", such as it was. So what had changed by Chichester's day or John 
    Letcher's later day, and why didn't they simply use one of those nice easy, 
    accurate lunars methods?
    In Letcher's case, he did describe one of those nice, easy accurate methods 
    for working real lunars! He advocated a method in his book which he appears 
    to have assembled himself, presumably after some basic study of historical 
    lunars methods. Letcher's method is a simple variant on the series or "corner 
    cosines" approach, and if a copy of his book had been thrown into a time 
    vortex and ended up in 1835, a Bowditch or Thomson would have recognized it 
    immediately. Letcher then went on in his book to advocate this "time by lunar 
    altitudes" method which so many people re-discovered/re-invented over the 
    centuries. And he advocates it for the same reason that most of them do: on 
    the face of it, it seems easier to teach to potential students who would 
    presumably be familiar already with the nitty-gritty of calculations for 
    altitudes. That's only true up to a point, only in certain contexts with 
    particular "rules of the game", and it ignores the fact that lunar altitudes 
    methods require special techniques (that will have to be taught separately!) 
    if they're going to achieve anything like the accuracy of a "real" lunar. For 
    example, it's important to know that lunar altitudes for GMT are only really 
    viable when the "horns" of the Moon are relatively horizontal. 
    For other navigators who re-discovered or wrote about the concept of using 
    lunar altitudes as a check on the Greenwich Time, it's also important to 
    remember that real lunars had vanished into history much earlier than the 
    almanac tables might suggest. It's true that you could find tables of lunar 
    distances in nautical almanacs in the first decade of the 20th century, but 
    for practical maritime use, they were fifty years in the past with only rare 
    exceptions in the second half of the 19th century. Lunars were the stuff of 
    legend by 1925. Sure, you might know an "old salt" who said he had once taken 
    a lunar decades earlier and bragged about it, but that was the end of it.
    If you were a navigator trying to use the Moon for GMT in the 1930s, nearly 
    all of the potential resources were in ancient books whose very navigational 
    jargon was already becoming dificult to decipher. And how many navigators had 
    access to a library of old books in the first place? As Lecky wrote in 
    "Wrinkles", lunars were "as dead as Julius Caesar" in 1883 (and the methods 
    might as well have been written up in Caesar's Latin, they had become so 
    inscrutable by then). Furthermore, as lunars faded into history, the last 
    methods recommended and the last published resources tended frequently toward 
    the theoretical, heavily mathematical, and difficult end of the spectrum. 
    Practical mariners were not expected to be prime users of lunars. The 
    remaining user groups might conceivably include teams working in the high 
    Arctic trying to achieve inordinately accurate longitudes, so fussy 
    corrections for temperature and the oblateness of the globe were emphasized. 
    Mathematical exactness was emphasized over practicality in many resources in 
    the closing decades of the 19th century and into the early 20th (not always 
    --the British Abridged Nautical Almanac included a nice practical emergency 
    method that targeted practical navigators).
    Mark, you wrote:
    "When I did Frank's lunar class I learned that lunars were no longer a source 
    of mathamatical pain and suffering, and that their discontinuation was not so 
    much the result mathamatical gyrations as the result of the common 
    availability of timepieces of high accuracy. I found the Bowditch-Thompson 
    method or others cookbook enough not to be intimidating."
    Quite so. Bowditch-Thompson is genuinely easy, like most of the series (or 
    "corner cosine") approaches to clearing lunars. And it's the same methodology 
    that Francis Upchurch has grown to love, too. And as he has discovered, the 
    required accuracy of the computations, when done using a series method (like 
    Thompson's original, Bowditch-Thompson, or Lyons, or Turner, or a whole list 
    of others) is really quite low, contrary to nearly all expectations of 
    lunars, and it's quite possible to work them up on a basic handheld 
    calculator, or with basic log tables, or on a common cheap slide rule (the 
    Moon's "corner cosine" only tells us the fraction of the Moon's altitude 
    correction that acts along the lunar arc and since that altitude correction 
    is going to be on the order of one degree and given to the nearest tenth of a 
    minute of arc --so one part in 600--, we only need the corner cosine accurate 
    to a tenth of a percent, which is within the range of computational accuracy 
    of common slide rules or paper calculations with common log tables --which 
    was overwhelmingly the normal tool historically).
    It should be remembered though that using real lunars without access to a 
    computing device did still have one roadblock through most of the 20th 
    century --there were no tabulated lunar distances in the almanacs. Today this 
    is no problem. It's just a great circle distance problem. Given the GHA and 
    Dec of the Moon and the GHA and Dec of the other body at any hour of time, we 
    can roll our own lunar distance tables just as easily as calculating the 
    distance on a great circle from the Empire State Building in NYC to the 
    Eiffel Tower in Paris. Without those tables, "GMT by lunar altitude" has one 
    other mark in its favor.
    Frank Reed
    [plain text auto-generated]
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