Saturday, October 1, 2011

Numbers, Jumbled

In Chapter 7, "Mapping the World", of The Philosophical Breakfast Club, a book I abused a few days ago, the author discusses a cadastral survey projected for the Commutation of Tithes. She throws in quite a few numbers, without relating them:
  • A full survey would cost about 1.5 million pounds (9 pence/acre for survey, 3 pence/acre for valuation).
  • The maps would be at a scale of 26.7 inches/mile.
  • Some large parishes required tens of square meters at this scale.
  • Had all of England and Wales been mapped to this scale, the maps would have occupied 6.5 acres.
Now, I grew up with a decimal currency, but can see that the first point gives us 30 million acres to be mapped. I also grew up knowing that there are 5,280 feet to the mile, which suggests to me that the "26.7" is a misprint for "26.4", and that the scale envisioned was 1:2400. The third point is more or less inconsequent, at least to those who do not easily convert between square meters and acres. The final one gives us a further check on the scale of the survey: 1 to 2400 linear is about 1 to 5.8 million square, so we get about 38 million acres on the maps. Given that England and Wales lack the man-made geometry of a state like Wyoming, one would expect rectangular maps to include untitheable water or other areas, so the figure is plausible.

However, the figure of 6.5 acres does cast doubt on the remark that
... the tithe maps as envisioned by Jones and Dawson would allow a viewer to take in, with a single look, a complete understanding of the whole extent of the rural land of England and Wales.
What can you tell with a single look over six and a half acres--acres of maps, that is, not of open country?

I don't especially mind doing the arithmetic. I do mind that the numbers seem to have been piled up to impress rather than to inform--else why not connect the numbers and provide some context?

I conclude by providing one piece of context gratis: the standard 7.5 minute quadrangle of the United States Geological Survey uses a scale of 1:24,000. Working out comparisons I leave as an exercise for the reader.

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