Maths: Curious measures

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536...can you see the pattern here?  The value 65536 is the ratio between the smallest and the largest of the traditional English measures for liquid. Even before Leibniz proposed a binary system of counting, the English were using binary in a practical way.

They began with a measure called the mouthful, about 15 millilitres or half a fluid ounce. Two mouthfuls made a jigger or handful. Two handfuls made a jack, or jackpot, and two jackpots made a gill, or jill. When King Charles I needed more money, he placed a tax on the jackpot, and reduced its size, so there would be more of them. By its definition as two jackpots, the gill was also reduced in size, much to the annoyance of the common people.

The pail was another measure, about the size of a gill. Given that King Charles wore a crown, until he was beheaded a few years later, you may now be able to read the old rhyme about Jack and Jill with more understanding. Keep in mind, though, that the gill is eight mouthfuls.

Continuing, two gills made a cup, and there were two cups to a pint. Two pints made a quart, and two quarts filled a pottle, and we find this pair of measures in Henry IV part 2, V, iii:

SHALLOW. By the mass, you’ll crack a quart together—ha! Will you not, Master Bardolph?
BARDOLPH. Yea, sir, in a pottle-pot.

The pottle, then, is 128 mouthfuls. Twice a pottle was a gallon, while the double gallon was also called a peck, the double peck was a half bushel, and obviously two half bushels made a bushel, which was eight gallons, or about 35 litres. Two bushels filled a cask, and two casks made a barrel or chaldron. Doubling the barrel gave us a hogshead, but that is hardly enough to drown a man in, as Shakespeare knew.

Adrien Brouwer, Peasants Carousing

Still, it was enough to lose oneself in, according to Prince Hal, the future Henry V. In Henry IV, Part 1, the roistering young prince is asked where he has been, and he answers, “With three or four loggerheads amongst three or fourscore hogsheads.”

Just to help you keep count, the hogshead is 16,384 mouthfuls. Back to drowning a man, though: in Act I, scene iv of Richard III, the First Murderer, as he stabs the Duke of Clarence, says:

Take that, and that. If all this will not do,
I’ll drown you in the malmsey-butt within.

The butt was also called a double hogshead or a pipe, but in Shakespeare’s play The Tempest, Trincalo lands on Prospero’s island after clinging to a butt of sack. This sack was a strong wine. There was one more step in the barrel range, the tun, which is close to a ton or tonne in weight. When sailors in the Royal Navy had to heave tuns and butts full of water around in ships, this helped to make ruptures the most common injury in the peacetime British navy.

Of course, to older computer-savvy readers, the number 65536 has another significance. Aside from being the 16th power of 2, it is also the real numerical value of the 64 kilobytes and that was all that we primitive folk could fit in (or afford) in the early 1980s for our computers.

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