The Angry Corrie 15: Oct-Nov 1993

On Agginesss

Professor Perkin Warbeck writes...

Much though I applaud Settler and Sinn's geometric rigour (TAC14, p13), I beg to dispute their definition of munroness - the volume integral of the hill's surface. Clearly we are at a crucial time in this whole debate and munroness once defined will be hard to change. It is thus imperative that the definition encapsulates all that one would look for in a munro. Clearly Settler and Sinn's definition would give an extensive lumpen plateau of 3100 feet more weight than an airy curving spire of 3800 feet or a castellated pinnacled ridge bobbing up and down about the 3000 foot contour. This is unsatisfactory.

I propose at his time to define the Coefficient of Agginess. Clearly from the name, the paradigm case is the Aggy Ridge. A definition of agginess would be required to give the Eponymous Ridge a high score compared with, say, Kinder Scout in the so-called "Peak District". Turning to the differential calculus, I found that the first derivative of the hill's profile gives an indication of agginess. Fig 1 (a) shows the profile of the summit of Kinder and Fig 1 (b) shows the first derivative of the profile.

I have used the Leibniz notation and shall brook no debate over the new fangled f-dash notation.Fig2(a) shows the portion of the Aggy Ridge 100 m on either side of the Chancellor and 2(b) its first derivative. The scale in the figures only refers to the top part, the derivative being dimensionless.

Clearly agginess is reflected in the spikes in the first derivative - both positive and negative. Ironically, Kinder Scout gets most of its agginess from the trig point, but we shall leave that be for the moment. I therefore suggest that the Coefficient of Agginess (() be defined as the sum of the absolute value of each individual spike in the first derivative. Like the derivative it is dimensionless. The figures show a cross-section through the ridge in one direction. In practice thirty-six 10 radial samples would be used with a sampling grid of five metres. Any feature smaller - eg a trig point - does not represent true agginess. This yields the new equation for x-coordinate of the Munro Centre:

and similarly for y. The TAC "Deep Agg " supercomputer has duly crunched its way through all the OS maps, derived (for all the Munros and plugged them into the summation. The coordinates of the Munro Centre, strangely, appear to be within 100m of the summit of Beinn an Lochain. This is within the experimental error caused by our sampling approximations (110m). We can only conclude therefore that contrary to HM the Broon's recent pontifications, Beinn an Lochain is indeed a Munro and must immediately be re-accorded status. Which of course means that it should be plugged into the summation. When that is done, the new Munro Centre is found to be the South Peak of the Cobbler. A conundrum then presents itself: (i) The south Peak is not even the summit of a hill; (ii) Its height is too far below 3000 feet to be an error of measurement. We await suggestions as to the meaning of all this. All we know is that there are now 279 Munros, with Beinn an Lochain and the South Peak of the Cobbler as the two new ones. As for the Summit of the Cobbler, it now has the most curious status of all hills - as befits its high Coefficient of Agginess.

which brings us neatly onto...A Grand Unified Scottish Hill Theory

TAC 15 Index