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    Re: Tables of Trig Functions and Logs of Trig Functions
    From: Gary LaPook
    Date: 2007 May 02, 16:42 -0700

    Gary LaPook wrote:
    I like to use my K&E  slide rule sometimes for sight reduction just to
    stay in practice. Obviously it lacks the precision of a digital
    calculator but you do get useful answers.
    George Huxtable wrote:
    >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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