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    Re: The mil as a unit of angle.
    From: George Huxtable
    Date: 2003 Mar 12, 12:05 +0000

    Wow! What a can-of-worms I have unwittingly opened up by my innocent
    question about the mil as a unit of angle. Here's what I have learned so
    far from this correspondence:
    Instead of a single unit of angle it seems that the mil comes in so many
    different flavours that few users are going to agree between them what they
    are measuring.
    We can all agree that to subtend an angle of 1 yard at 1,000 yards (or to
    most of the world, 1 metre at a kilometre, which is the same thing) the
    angle is 1 milliradian. There must be, as near as dammit, 6283 of these
    milliradians in a complete rotation. Even that is only an approximation:
    the number is 2000 x pi, which works out as 6283.1853... and you can go on
    adding decimal places as you think fit. So in no way is this a "round
    number", and if you had to add up a number of angles, which summed to be
    several rotations, doing the arithmetic to arrive at the resulting angular
    position would be complicated and inexact.
    And as Trevor Kenchington notes, a simple task such as finding a reciprocal
    angle would be difficult and error-prone. Clearly, the milliradian is a bad
    unit for practical purposes.
    So, it appears, the milliradian has been "adapted" to increase its
    usefulness, and it this form has been renammed the "mil". Clearly, if this
    unit differs from a milliradian, it can't bear the name milliradian, but
    must be called something else. If it's been given the name "mil", that must
    surely imply a thousandth of something. But a thousandth of what? Here we
    seem to have a unit which a prefix only as its name. Seems odd, doesn't it?
    It appears that there is not just one definition of the "mil".
    Marvin Sebourn warns us to distinguish between "standard" and "military" mils.
    Myrt Webb says-"The mil is 1/6400th of a circle and 1 mil subtends an arc
    of 1 meter at 1000 meters." but both of Myrt's statements in that sentence
    cannot be precisely true, together.
    Trevor Kenchington tells us that the Russians use 6000 mils to the circle.
    Doug Royer initially supplied a figure of 64,000, but I suspect he may be
    out by a factor of 10.
    What a recipe for confusion! By comparison, even our longstanding 360
    dogrees, divided into sixtieths (which I hate) is at least accepted by all.
    However, the French have had a try at introducing the "grad", which has 400
    to the circle. The argument for this is that the kilometre is so defined
    that 100 km. along the Earth's surface subtends an angle at the centre of 1
    grad. Grads are always subdivided decimally, not in 60ths. I have Michelin
    road maps of France that are gridded in grads, though I understand some
    more recent editions have switched to degrees.
    Just to make confusion worse confounded, the word the Germans use when they
    mean degrees is the "grad", of which there are, like our degrees, 360 to
    the circle, and not 400 as in the French grad.
    What a mess!
    George Huxtable.
    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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