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    Re: Modified Martelli Table V
    From: Hewitt Schlereth
    Date: 2013 Jan 3, 17:46 -0800

    Frank, I really appreciate your taking the time to so fully explicate the 
    underpinnings of Martelli in particular and time sights in general. I often 
    carried Weems Secant TS as a backup. Practiced it a few times ashore, but 
    fortunately my calculator never let me down asea. FWIW, and if memory serves, 
    I find Martelli less tedious and am very happy to have him in a contemporary 
    form thanks to Greg, Robert and Hanno.
    Sent from my iPad
    On Jan 3, 2013, at 11:39 AM, "Frank Reed"  wrote:
    > Hewitt, 
    > Just to reiterate, FUNDAMENTALLY all of the Martelli tables are in Bowditch 
    and other navigation manuals. His Table I is a table of log cosines (plus a 
    constant). His Table II is a table of natural cosines (plus a constant). His 
    Table III is a table of natural sines (negated, plus a constant). His table 
    IV is a table of common logarithms (negated, plus a constant ...or 
    equivalently, a table of "proportional logarithms" plus a constant). His 
    Table V is a table of log haversines (negated, plus a constant ...or many 
    other equivalent descriptions). These are all simple tables which could have 
    been combined into a slim volume by anyone. But who would buy such a volume 
    if they're already in Bowditch or Norie? Ahh, but mix in a little Italian 
    magic and peddle it to gullible British mariners, and now you've got a 
    product that sells! A big advantage of short, highly-specialized methods like 
    Martelli's is that the tables can be truncated to save pages and to make 
    lookups easier. For example, the range for his tables I, II, and III, is 0 to 
    90 degrees. That's more convenient than making tables that cover 0 to 360 
    degrees (it doesn't save pages --it saves the navigator from having to learn 
    multiple entry tables). But then again, that means that they are much less 
    useful for any other problem.
    > Incidentally, I think I've got a "good" reason now for his odd choice of 
    sexagesimal (units, minutes, seconds) output from his log tables. It's easier 
    to look up logs in sexagesimal tables because you can head each page with a 
    certain number of "units" (call them hours or degrees, it makes no 
    difference) and then head the columns with a certain number of "minutes" and 
    then each row is labeled with "seconds". And as it happens a small book can 
    easily display 60 rows per page. This saves space in the table of common 
    logarithms (Table IV) though at the big expense of making those logarithms 
    useless for any other problem. And since logarithms were so useful to a 
    navigator, any navigator carrying Martelli's tables with their obfuscated 
    logarithms would necessarily also have to carry a redundant normal table of 
    logarithms (probably in a larger volume, like Bowditch or Norie).
    > -FER
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