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    Re: Tables of Trig Functions and Logs of Trig Functions
    From: George Huxtable
    Date: 2007 May 2, 21:44 +0100

    Robert Eno wrote-
    | Essentially, for the same reason why I persist in using a sextant: the
    | challenge of doing it the hard way. Oddly enough, I find it rather
    | therapeutic to perform the odd sight reduction the old way using the trig
    | and log tables. It also hones my basic understanding of the mathematics
    | behind the calculations. It also gives me another level of independence of
    | electronic gadgetry should the latter fail me absolutely some day. Don't
    | misunderstand me: I still use a scientific calculator (and if I am
    | particularly impatient, my Celesticomp V) but for every round of sights
    | I take, I reduce at least one or two using the tables: the hard way.
    Comment from George-
    I agree with that, in every respect but one, where Robert writes "It also
    hones my basic understanding of the mathematics behind the calculations."
    And for this reason: because the basic simple spherical trig expressions
    have been bent, twisted, and manipulated, quite beyond recognition, in order
    to avoid additions and subtractions, once the navigator has "gone into
    logs". This results in him going blindly through the set procedures "by
    rote", without much chance of understanding the steps involved, and simply
    accepting the result that comes out of that process.
    And so (in my view) doing all that trig manipulation by a pocket calculator
    provides a breath of fresh air. Now that logs are no longer called for, the
    basic trig expressions can be worked through, bit by bit, just as they come
    out of the textbook. It's easy to see what contributions the individual
    terms in the expressions are making. It's easy to try out simplifications
    and short-cuts, such as taking the sine of an angle near 90 to be exactly 1;
    that sort of thing, when you can see what you're actually doing.
    As I see it, having to use logs and lookup tables (and in their time, there
    was really no alternative) set back the understanding of what navigators
    were actually doing. Now we can enjoy the privilege of doing the
    mathematical manipulations absolutely straight, and far more accurately than
    we will ever need. How our navigational forbears, as recently as thirty-odd
    years ago, would have relished that opportunity!
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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