page forty-eight

The Gauge

Forty-seven rooms, and everything in them could be seen before it was measured. Today's number sends you, an officer of the Excise, into a cellar in a Georgian town with three casks to charge. You may not open them. You have a gauging rod, a dip rod and the gauging book, and the duty is owed on what is inside.

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The cellar
The cask, lying on its stillage

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Sight along the staves

The drawing shows only the swell of the stave above the height of the heads, stretched until it fills the box, so that a bend you could never see from the doorway is plain. Hold each of the gauging book's four patterns against it and choose the one it follows.

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The day's entries
Cellar
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The arrow keys walk to other days. Every day is a different town, trader, liquor and set of casks.

What is real here and what is not

The gallons, the four varieties and their formulas, and the geometry are real. The traders, their casks and the cooper's hand are the day's number.

  1. 01

    Two gallons

    Until the imperial gallon arrived in 1824, England measured liquor by two different gallons. Beer and ale went by the ale gallon of 282 cubic inches; wine and spirits by the wine gallon of 231. A hogshead of beer and a hogshead of wine are therefore not the same size, and the officer has to know which he is in front of before he divides.

  2. 02

    Four varieties

    No cask is a cylinder. The gauging books sorted them into four shapes by how their staves bend: the middle of a spheroid, the middle of a parabolic spindle, two paraboloids or two cones set base to base. Each has an exact formula in the bung diameter, the head diameter and the length. Real casks fall between them, which is why the officer sights along the staves before he chooses.

  3. 03

    Lying ullage

    A broached cask on its side is only part full, and the dip rod gives the depth of liquor at the bung. The plain rule takes the wet share of the bung's circle as the wet share of the cask. It is wrong, because near the heads the circle is smaller and the same surface cuts off more of it. The book here works the ullage section by section along the variety you chose, and the resurvey shows how far the plain rule would have gone astray.

  4. 04

    What the page simplifies

    The rods here read the inside of the cask to a tenth of an inch, and the two heads are averaged. Officers actually measured outside and made allowances for the thickness of the wood, and they used the sliding rule and printed tables where the page does the arithmetic for you. The diagonal rod's scale here is marked for one standard cask, so it shows how a quick reading fails on an odd one.

Forty-eight rooms, and one number doing all the work. Today it lets a cooper bend the staves however he liked and puts the duty on what nobody can see.