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    Re: Practical Haversine Use
    From: Tony Oz
    Date: 2021 Nov 16, 09:15 -0800

    Hello!

    To refresh my long-forgotten ability to use logarithm tables I recreated the four-place one I used at school - by W.M.Bradis. (beware of typos in the scanned edition! my recreation is more reliable :D )

    Then I tried to solve the division step of some all-Haversine azimuth calculation - which involved the divident == 0,2410 and the divisor == 0,3271.

    0,2410 = 2,410·10-1; 0,3271 = 3,271·10-1

    These "minus one" powers of ten mean that the logarithms of both numbers will have the "bar one" prefixes further denoted as "/1".

    log(0,2410) = /1,3820; log(0,3271) = /1,5146

    Now the subtraction step:

    /1,3820

    -

    /1,5146

    ______

    /1,8674

    The resulting "bar one" prefix is born when I borrow from the minuend's characterisic digit - the "minus one", making it "minus two", then subtrahend's "bar one" changes its' sign and becomes "plus one": -2 + 1= -1, thus the "bar one" in the result.

    Note that the fractional part is exactly the mantissa of the result, ready to be reverse-looked-up in the table - for exponentiation.

    Now exponentiating the resulting mantissa (the 0,8674) I get 7,369. The "bar one" characteristic means that the result actually is 7,369·10-1, or 0,7369.

    This is how I did calculations until electronic calculators and computers made me lazy and stupid...

    I wonder how the "10+" logarithms would work in this example?

    Warm regards,
    Tony
    60°N 30°E

    File:
    4-place_Log10_v1b.ods
       
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