# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: The mil as a unit of angle.**

**From:**Robert Eno

**Date:**2003 Mar 12, 09:25 +0000

I still have an old "mil" compass from my very short-lived career in the army. Never could wrap my head around those units of measure. I've read about all kinds of efforts to replace the sexigesimal system for reckoning angles (as well as the quirky system that we use for reckoning the passage of time) and it appears, much to my delight, that these efforts have failed miserably. The sexigesimal system is here to stay. I know that it must stick in the craw of those metric zealots who wish to expunge our world of anything that does not conform to their neat, easily subdivided way of looking at things. I for one, rejoice at this roadblock to the metric juggernaut. I see it as a triumph of sorts for the real world and for the natural order of things, which is not easily subdivided and tends toward entropy. Vive la sexigesimal!!! (that wouldn't be considered politics would it?) Robert >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---.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. >================================================================ ------------------- Email sent using AnyEmail (http://netbula.com/anyemail/) Netbula LLC is not responsible for the content of this email