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Following on from Brooke and Marvin's contributions, the underlying
point here is the basic bit of high-school math:

Tan(A) = A  (as a very close approximation) ...  provided that A is
measured in radians and provided that it is small.

Hence Brooke's

> In military artillery one mil is equivalent to 1 yard offset at 1,000 yards range.


(incorporating his correction) makes the artillery mil essentially the
same as Marvin's definition of the mil as a milliradian.

The U.S. military decision to approximate the mil as 1/6400 of a circle
and the Russian use of 1/6000 (as explained in the Web page cited by
Marvin) are also understandable in the same terms: The numerical
equality between angles in milliradians and corresponding linear offsets
at specified ranges only works for small angles of arc. If you never
measure more than a few mils to a precision of the nearest mil, you will
get the same numerical result whether you are counting in units of one
6000th, one 6400th or one 6283.1853...th of a circle.

But woe betide the navigator who tries to calculate the reciprocal of a
bearing in mils without knowing which kind of mil his instruments are
calibrated in! I think I will stick to points. By comparison, they seem
altogether simpler.


Trevor Kenchington


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Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
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Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

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