Derivation of the "Ranga"

[Valandil]

In an Appendix to "The Disaster of the Gladden Fields" in the "Unfinished Tales" collection, Tolkien gives the basic Numenorean measure of the "ranga" - and says that it was approximately equal to 38". He further tells us that the term "man-high" was a general statement about someone reaching full stature - and that this was considered two rangar - which would be 76" or 6'-4" (I think that's about 193 cm, for you in the metric world). He also say that 5000 rangar made one league - very nearly equivalent to our own "league" of three miles - and gives the exact 5277 yards + 2' + 4" - compared to 5280 yards for our own league. So - a Numenorean league was just 6'-8" short of our own three mile long league.

He also gives a statement about how the ranga was determined - and it has to do with a man's step.

Now - consider this: the history of the "mile" is that it was 1000 paces - both a left and a right step - of Roman soldiers on the march.

I suppose that Tolkien actually worked backwards to arrive at his "ranga". Since a league is just a little over 5000 yards, I suppose he divided that distance by exactly 5000 to work up his "ranga".

Here's what happens if you do that:

1 league = 3 miles x 5280 ft/mile x 12 in/ft = 190,080 inches.

190,080 / 5000 = 38.016 inches

So - he just rounded to 38" even.

By doing this, he's able to come up with a "man-based" measuring scale, which would seem reasonable in the Middle-earth setting - and also use a larger scale with a very near equivalent to our own (with a pacing system similar to the history of the mile). Not to mention that his "ranga" is just about exactly half way between the English system "yard" (36") and the metric system "meter" (~ 39.4"?) - so we can all relate to it.

Plausible?

[CAB]

I think it is very plausible Valandil. It seems to me that he probably placed the priority on the “roundness” of the numbers (5000 paces) and the nearness of the two different leagues, while compromising a bit with the size of the “yard”. The impression I get is that he would have made the Numenorean ranga larger if the math had worked out that way. For instance he said that two rangar could only be considered “man-high” after the Numenoreans had diminished in stature and that one ranga was actually less than a full-stride. For me, this also suggests that the position of the ranga between the yard and meter wasn’t really a consideration.

I wonder if Tolkien did any work on the smaller measurements. For instance, if fathoms and feet were also based on Numenorean bodies (it makes sense that they would be) then some of the structures described in Middle Earth would actually be much larger than they at first seem.