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    Re: Traditional navigation by slide rule
    From: Greg Rudzinski
    Date: 2016 Sep 26, 00:17 -0700


    I see by your example how to use the D scale and the ' mark on ST. What I did also was to pencil in the minutes on the slide from 34' down to 3.5'

    Greg Rudzinski

    From: Paul Hirose
    Date: 2016 Sep 25, 22:09 -0700

    On 2016-09-25 11:38, Greg Rudzinski wrote:
    > I have been doing sight reductions with a K&E 4070-3 and noticed that the ST 
    scale ends at 35'. I think an additional ST scale continuing from 35' would 
    be useful when doing the sine product (classic formula) when declinations or 
    latitudes are less than 35'.
    Don't overlook the ′ and ″ gauge marks on ST. For example, for the sine
    of 25′, set cursor to 25 on the D scale, set the ′ mark (near 2° on ST)
    to the cursor, read .00728 on D at the C index. (That was my slide rule
    result. Calculator says .007272.)
    Note that the ′ gauge mark coincides with ca. 3440 on C. That's the
    number of minutes per radian. So what you did was convert 25′ to
    radians. That's practically equal to its sine if the angle is small.
    The ″ gauge mark works in similar fashion. Its projection on C is the
    number of seconds per radian. If you can remember there are about 3400
    minutes or 200,000 seconds per radian, that's enough to correctly place
    the decimal point.
    A decitrig ST scale can extend down by decades with parallel adjustments
    of the decimal point in the angle and sine. For example, the 2.1°
    graduation can also stand for .21°, .021°, etc.
    This trick is possible but more difficult on a sexagesimal rule. Purely
    from the mathematical standpoint there's no problem. But the resulting
    angles are not as easy to see mentally. For instance, the 2°10′ (= 130′)
    graduation can also stand for 13′, 2°20′ for 14′, etc.
    Near the left end of the scale, the 40′ and 50′ graduations can stand
    for 4′ and 5′. The space between them is divided into ten parts, so each
    minor graduation would be .1′ or 6″.
    At the right end, 4° (= 240′) can stand for 24′, 4°10′ for 25′. The five
    graduations between them are .2′ each.
    Like the S scale, each black number on ST has a corresponding red
    number, though they're rarely marked. For example, black 4° corresponds
    to red 96. The same graduations could also stand for black 24′ and red
    When the cursor is on that graduation, on CI read 143.2, the tangent of
    89°36′. It's one way to get tangents arbitrarily close to 90°. But the
    trick is much easier on a decitrig rule.
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