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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.
Francis
 

-----Original Message-----
From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of Frank Reed
Sent: 30 July 2018 06:01
To: francis@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

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