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    Re: Easy Lunars
    From: George Huxtable
    Date: 2004 Apr 30, 13:33 +0100

    Among other comments, Doug reacted to my statement-
    >>Of course, to work this on a calculator, all the degrees-and-minutes
    >>quantities have first to be converted to decimal degrees.
    as follows-
    >Some scientific calculators have the * ' " base60 function that can
    >accomplish all the algebraic steps in base60 thus reducing further another
    >step.Certain models of Casio and T.I. scientific calculators of this ability
    >cost around $25-30.00.Bouc-coup computing power for very little dinero.Easy
    >to use also.
    Reply from George-
    Yes, but be careful. Test all such routines thoroughly to make sure they do
    what you expect.
    For example, take the Casio family of programmable calculators, FX700, 730,
    and 795. Getting on a bit now, they are, but I have got accustomed to the
    way those machines work over twenty-odd years.
    These aren't operating in base 60, as are the ones Doug is discussing, but
    they offer conversion functions to translate from degrees, minutes, and
    seconds to decimal degrees, and vice versa.
    Take the function DMS$(), which converts an angle in decimal degrees,
    within the brackets, into a character string of whole-degrees,
    whole-minutes, and decimal seconds, separated by the appropriate symbols.
    It works fine, for both positive and negative angles. Trouble with that one
    is that few modern navigators wish to be troubled with arc-seconds, and
    prefer to express their angles as degrees and minutes (with decimal
    minutes). And there's no way to specify that preferred format. Of course,
    you can always invent a little routine to do that job just the way you want
    it, and ignore the DMS$() function..
    A more-insidious problem occurs with the converse function DEG(d,m,s),
    which converts quantities d, m, and s, separated by commas, into decimal
    degrees. The seconds, or minutes-and-seconds, terms can be omitted with
    their preceding commas, and a, b, and c can be expressed as decimal numbers
    if preferred, so it becomes easy to convert, say 15deg 27.1' into decimal
    minutes. All that is fine.
    The problem arises when you wish to convert negative angles, as often is
    necessary in astronav. For example, Southern declinations are often
    expressed as negative. If you precede the degrees term with a negative
    sign, then that's fine, it becomes a negative angle when translated. The
    trouble is that even though the d term was negative, that doesn't ensure
    that m and s are also negative. So converting -1deg 15' by using DEG(-1,
    15) converts to (-1degree + 15/60 degrees), or 0.75 degrees: not what was
    wanted, at all. To get it right, for negative angles, you must precede each
    term d, m and s with a - sign (such as DEG(-1, -15)) or else treat all
    angles as positive but then multiply the end result by (-1).
    I can see why they do it that way, because each term, d, m, and s is
    allowed to be the result of a separate mathematical expression, and so
    their signs may legitimately differ. This property can be handy when
    summing or subtracting sets of hexadecimal angles to get a result in
    The above problem presents no real difficulties once you become aware of
    it, but discovering it for the first time can be a real pain.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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