The Angry Corrie 14: Aug-Sep 1993
Paper (ii): The Quest for the SMC
Further to the articles by Rob Pearson (TAC10), Professor M Bob (TAC12) and Professor David Summers (TAC13) regarding the Scottish Munro Centre and the legendary "Lost Munro", having further refined the mathematics I have come up with the valid solution.
The problem lies in Prof M Bob's definition of "Munroness": he only takes account of the HEIGHT of each hill, when he should also include its MASS. In so doing, a hill such as Ben Alder should carry more "weight" than, say, Geal Charn although they are of similar height. This can be seen in the following diagrams. For simplicity the Munros have been divided into three groups according to SHAPE: ie Concave, Convex and Constant Gradient.
For each hill the effective mass is found by INTEGRATION of the function of the slope f(X) over the range 0 (the centre) to a point D where the hill meets sea level (or would if continued at the same angle to sea level). Viz:
Evaluating this function for the X and Y co-ordinates in fact puts the Lost Munro almost equidistant between Ingleborough, Whernside and Pen-y-Ghent. This may seem unlikely, but does lend credence to the theory that in ancient times Scotland included much of Albion as far south as Yorkshire. This theory is amply supported by my colleague - a linguistic anthropologist - viz: "Aye" is standard in Yorkshire dialect, and "h" is not used as a letter in either area except to aspirate in the Gaelic. (Isn't aspirate what dentists make the nurse do to you? - Ed.)
It seems likely that this Lost Munro has been eroded to buggery by millions of pairs of Brasher Hillmasters (TM), thus lending support to NOT giving Loch Lomond area national park status. I hope this resolves the issue once and for all whilst not offending too many individuals. (Hopefully not - copy-seeking Ed - and anyone else think the diagrams look like tent designs?)