I am looking for the use of the second (outer) dial numbered from 0 to 7 on the Silva Polaris compass. This second dial rotates independently of the inner dial.
It is used to measure distance. You turn it on its side and roll it along a path on the map. This means it has to correspond to a particular map scale (my first guess is 1:50,000, but that looks a bit off). For a different scale you could do a simple conversion.
Can you tell me what the arc length of one major division is? From the picture, it kinda looks like a little more than one inch (maybe 1.25" ?? ). I can get the associated scale from that (i.e. what is the arc length between 6 and 7)
A couple of additional items:
Angular units - Note that, for the full circle, it actually goes from 0 to 8. Each division is 1/8 of a circle. Each division is further divided into quarters, so the total number of subdivisions is 32, which is exactly how many points are in a compass. See Points_of_the_compass
Distance measurement - It doesn't really matter what the circumference or arc length is! If you know how many turns and fractions of a turn your measured map distance is, just reproduce the same distance down the side of the map's grid, or along its bar scale, and you have the scaled distance! You can also measure a map distance using a piece of string. You don't need to know the length of the string other than to lay it down along the map grid.