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    Mike Pepperday's S-Table
    From: Stan K
    Date: 2014 Jun 5, 21:39 -0400
    Over the years several people have tried to figure out the derivation of the numbers in Mike Pepperday's S-Table.  I have been in touch with Mike, and he has given me permission to reveal his "trade secret".

    I sent him the following message:

    On 31 May 2014 02:20, <slk1000@aol.com> wrote:

    I am the author of Celestial Tools, a computer program I wrote for the United States Power Squadrons (USPS) to help students with their work. (Latest beta available at www.celestialtools.webs.com.) One of the tools, SR Methods, includes the Law of Cosines, NASR, 249, 229, 214, 211, 208, etc., though only the Law of Cosines and NASR are currently taught by USPS.  The others were added for the sake of people on NavList, an online community of traditional navigation enthusiasts, who still enjoy reducing sights by older methods.  Someone on NavList suggested I add your S Table, which I was familiar with, having a 1991 Yachtsman's Edition Nautical Almanac.  Apparently your S Table has a larger following than I thought, and is being sold by Amazon, Celestaire, and others.  So I started thinking about it and found something I felt was unusual.  Where other Ageton-type methods use a nice round multiplier of a factor of 10, your table seems to use a number that I cannot begin to guess where it came from.  If analyzed correctly,

                                                                                            S(x) = 94.2934*log10[cosecant(x)]      (thanks to Rodger Farley of Teacup Navigation).

    I realize that the multiplier can be anything that would make the logs easier to work with, but 94.2934 is making my head spin.  If it is not some kind of trade secret, please let me know how it was selected.


    Stan Klein

    I got a very nice response from Mike Pepperday.  In a million years I would never have figured why he selected the multiplier he did.

    -----Original Message-----
    From: Mike Pepperday <mike.pepperday@gmail.com>
    To: slk1000 <slk1000@aol.com>
    Sent: Sat, May 31, 2014 6:30 pm
    Subject: Re: S Table question

    Hi Stan,
    Every three or four years someone asks me that question.
    The reason was indeed a sort of trade secret. I had a plan to produce the table in another form—a simple idea that no one else seems to have thought of. Since that's now in the past I will reveal all.

    If you look at the first page of the table, you'll see that the last number (for 4 degrees 59 minutes) has six digits and the next number has five digits. Compare with Bayless where six digits go over the page to 5 deg 40. This makes the first column of the second page wider and hence the second page slightly wider. My modification makes the second page the same width as the rest of the pages.

    And the point? The big trade secret is the plan to put the whole table on a single sheet. The second to ninth pages, being all the same size, allow the sheet to be folded nicely—like a map. The effect is that there are four pages (or four panels) to an "opening" which means that just two openings show the whole table other than the first page. Two openings for a sight reduction table. With a couple of other minor tricks it is pretty slick.

    There is a perpetual sun almanac on the reverse along with instructions and booking/calculation forms. (I improved the reduction form since the version you have.) It was also to include stars and Aries though I never got around to including this on my mock-ups. This would give complete almanac and sight reduction on a single sheet. There is a half-size version for those with good eyesight—sight reduction in your shirt pocket.

    As you may or may not know, I developed the Merlin navigation computers. I sold the Merlin business in 1991 but pursued the S-Table as a possible emergency method. I lost interest not only because of the GPS but because I concluded, with reluctance, that it wasn't possible. For the sailor who has not used celestial for years (ever since learning it at night school or whatever) it is just too complicated.

    Ten years ago in a fit of enthusiasm I manufactured several tables using a photocopier and glue. I have just one of these "single page" S-Tables left. Do you want it? I think you would like it. It is only ordinary paper so it has to be handled with care but it works and if you tell me a postal address I will give it to you. It is full size.

    To keep my hand in, every few years I dig out the carton of S-Table stuff, take a couple of forms, fill in some sights as if I had booked them, and proceed to compute them using the table. Now that I have the carton open, this is a good moment to refresh...


    BTW, the "single page" S-Table is on its way.  If there is any interest, I'll see what I can do about making copies.


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