## 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 10º 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: