The Angry Corrie 12: Apr-May 1993


Boring Squares, Trig Points, White Holes... Where will it ever end? Not here, for sure...

In reading Rob Pearson's letter in TAC 10, where he tries to locate the "Munro Centre", I noticed two fatal flaws in his reasoning. Firstly his use of the directions North, South, East and West is wholly inappropriate. These concepts are derived from the axis around which the earth spins. A hill's being a Munro does not depend on its movement through space but upon its being in Scotland. Their positions can only be considered relative to each other. Secondly he has taken no account of the relative displacements nor of the Munroness of particular hills. On top of Meall a'Bhuiridh there may well be equal numbers of hills North and South but they are at different distances in different directions and some are Munroier than others. A more appropriate means of calculation would be to take a weighted mean displacement of all Munros, analogous to the calculation of the centre of mass of an extended system. The measure of a hill's Munroness would have to be its height.

The position of a hill can be defined relative to an arbitrary set of Cartesian coordinates - the OS grid system is convenient. (Here we are using the Flat Earth Approximation as it is inherent in Munro's own thinking: he measured a hill's height from sealevel, not from the centre of the earth (see John Biggar for details).)

Hence:

and similarly for the y-coordinate.

So taking NM 000 000 as an origin and working with the 1981 Tables (due to the danger of right-wing political bias in the most recent edition), I found the Munro Centre to be NN 383 876 (workings provided on request).

At this point the exercise moved from the academic to the gravely serious. This is a point 700m up on the North side of Beinn a'Chaorainn, 300m away from a large cairn. The cairn must mark something. It's not a summit. It's too far away from a track to be where his Grace shot the stag. The coincidence is too much; it must have been made to mark the Munro Centre - but it's in the wrong place. Hastily I calculated the error bounds on my figures - they only came to less then a tenth of a grid square: not enough to include the cairn. Replacing Beinn Teallach with Beinn an Lochain didn't make nearly enough difference. What did the builders of the cairn know that I didn't? Is there another Munro?

Well I didn't get a physics degree without knowing how to frig my results (see John Biggar for details). The hunt was on. Its height was easy to determine, both Brown and Hopping Bear agreeing that the known Munros are numbered 1 to 277 with no gaps. Therefore it's number 278. Therefore it has to be 914m. (You ask "What if there are two?" I reply "How could anyone lose two 3000ft mountains?!") Then simply plug the desired result into the equation and out comes the necessary data. The lost Munro is at NM 651 256.

Feverishly I opened the map. Loch Uisg on Mull. A coastal loch where a Munro should be? Glaciation my foot! A super quarry scar more like! Beware! yesterday Beinn Uisg, tomorrow Beinn a'Bheither!!

Professor M. Bob


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