# Mensuration

When I was that knobbly-kneed, snotty-nosed, balaclava'd urchin to whom I may have referred previously, one was expected not only to read and write and tell the time, but to recite, flawlessly, the times-tables all the way up to thirteen thirteens. And furthermore, to understand, and manipulate, the mind-boggling complexities of the traditional English currency (pounds, shillings, pence, ha'pence and farthings), weights and measures, and all the paraphernalia of mixed-base arithmetic that was involved.

I firmly believe that the all-too-brief period of British ascendancy in the world was brought to an untimely demise by our reluctant acceptance of the decimal system. Our advantages of flexibility and sharp-wittedness were dissipated, and thus began that melancholy, long, withdrawing roar of the British lion.

Well, good riddance, you may say. But with it go the Graeco-Roman classics, the Judaeo-Christian ethics, and the Anglo-Saxon respect for the rule of law, plus our empiricism and pragmatism in science, politics and philosophy. The future is a boot stamping in our face for ever, as the new Eastern dawn begins.

Sorry, I got carried away. My real intent was to investigate those curious figures with which the area of Dr Robert's estate were defined: 23, 1, 31 acres. What could they have meant?

The acre, as any fule kno, is 4840 square yards, which is equal to 10 square chains, a chain (incidentally being the length of a cricket pitch) being 22 yards (so that a square chain is 22^{2} = 484 square yards).

A mile is 1760 yards, which is equal to 8 furlongs (as all horse-racing devotees recognise), each furlong being 220 yards, or 10 chains, so that a mile is 80 chains. A square mile is therefore 80^{2} = 6400 square chains, clearly equal to 640 acres.

So far, so easy. But now it ramps up.

A rod, pole or perch is 5 ½ yards, equal to ¼ chain. So a chain is 4 poles, and a square chain is 16 square poles.

Now it becomes Himalayan (and would be even more so if we adopted the old English ambiguity that the name of a rod, pole or perch could be the same for square as for linear dimensions). My own preference is that rod is linear measure and perch is square measure.

So 1 acre = 4840 sq yards = 10 sq chains = 160 sq poles (perches).

And 1/10 acre = 484 sq yards = 1 sq chain = 16 sq poles (perches).

These things are of course much more easily comprehended when tabulated, and you will notice that the second table slyly introduces the rood, equal to ¼ acre or 40 sq poles (perches):

mile | furlong | chain | pole | yard | link |

1 | 8 | 80 | 320 | 1760 | 8000 |

1 | 10 | 40 | 220 | 1000 | |

1 | 4 | 22 | 100 | ||

1 | 5½ | 25 | |||

1 | 4 6/11 |

sq mile | sq furlong | acre | rood | sq chain | sq pole | sq yard |

1 | 64 | 640 | 2560 | 6400 | 16000 | |

1 | 10 | 40 | 100 | 1600 | ||

1 | 4 | 10 | 160 | 4840 | ||

1 | 2½ | 40 | 1210 | |||

1 | 16 | 484 |

We thus understand the original measure of Dr Robert's residential plot:

- 23, 1, 31 acres = 23 acres 1 rood 31 perches = 23.44375 acres

Despite the rhodomontade with which this section started, I fully accept the computational advantages of a decimal system, or even the sexagesimal system (base 60, as used by the Babylonians), with the nautical mile as its base unit, which has major navigational advantages.

Unfortunately, the decimal metric system introduced by the French revolutionaries, though admittedly tied to the Earth's dimensions, mysteriously decided not to coordinate it with angular circular equatorial measure but to arbitrary elliptical circumpolar measure, not nearly so neat arithmetically.

But I guess it doesn't matter any more!