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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
decimal-degrees..

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.

George.

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