|The Universe of Discourse|
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Fri, 03 Mar 2006
In skimming over it, I noticed that Wilkins' language contained words for units of measure: "line", "inch", "foot", "standard", "pearch", "furlong", "mile", "league", and "degree". I thought oh, this was another example of a foolish Englishman mistaking his own provincial notions for universals. Wilkins' language has words for Judaism, Christianity, Islam; everything else is under the category of paganism and false gods, and I thought that the introduction of words for inches and feet was another case like that one. But when I read the details, I realized that Wilkins had been smarter than that.
Wilkins recognizes that what is needed is a truly universal measurement standard. He discusses a number of ways of doing this and rejects them. One of these is the idea of basing the standard on the circumference of the earth, but he thinks this is too difficult and inconvenient to be practical.
But he settles on a method that he says was suggested by Christopher Wren, which is to base the length standard on the time standard (as is done today) and let the standard length be the length of a pendulum with a known period. Pendulums are extremely reliable time standards, and their period depends only their length and on the local effect of gravity. Gravity varies only a very little bit over the surface of the earth. So it was a reasonable thing to try.
Wilkins directed that a pendulum be set up with the heaviest, densest possible spherical bob at the end of lightest, most flexible possible cord, and the the length of the cord be adjusted until the period of the pendulum was as close to one second as possible. So far so good. But here is where I am stumped. Wilkins did not simply take the standard length as the length from the fulcrum to the center of the bob. Instead:
...which being done, there are given these two Lengths, viz. of the String, and of the Radius of the Ball, to which a third Proportional must be found out; which must be as the length of the String from the point of Suspension to the Centre of the Ball is to the Radius of the Ball, so must the said Radius be to this third which being so found, let two fifths of this third Proportional be set off from the Centre downwards, and that will give the Measure desired.Wilkins is saying, effectively: let d be the distance from the point of suspension to the center of the bob, and r be the radius of the bob, and let x be such that d/r = r/x. Then d+(0.4)x is the standard unit of measurement.
Huh? Why 0.4? Why does r come into it? Why not just use d? Huh?
These guys weren't stupid, and there must be something going on here that I don't understand. Can any of the physics experts out there help me figure out what is going on here?
Anyway, the main point of this note is to point out an extraordinary coincidence. Wilkins says that if you follow his instructions above, the standard unit of measurement "will prove to be . . . 39 Inches and a quarter". In other words, almost exactly one meter.
I bet someone out there is thinking that this explains the oddity of the 0.4 and the other stuff I don't understand: Wilkins was adjusting his definition to make his standard unit come out to exactly one meter, just as we do today. (The modern meter is defined as the distance traveled by light in 1/299,792,458 of a second. Why 299,792,458? Because that's how long it happens to take light to travel one meter.) But no, that isn't it. Remember, Wilkins is writing this in 1668. The meter wasn't invented for another 110 years.
[ Addendum 20070915: There is a followup article, which explains the mysterious (0.4)x in the formula for the standard length. ]
Having defined the meter, which he called the "Standard", Wilkins then went on to define smaller and larger units, each differing from the standard by a factor that was a power of 10. So when Wilkins puts words for "inch" and "foot" into his universal language, he isn't putting in words for the common inch and foot, but rather the units that are respectively 1/100 and 1/10 the size of the Standard. His "inch" is actually a centimeter, and his "mile" is a kilometer, to within a fraction of a percent.
Wilkins also defined units of volume and weight measure. A cubic Standard was called a "bushel", and he had a "quart" (1/100 bushel, approximately 10 liters) and a "pint" (approximately one liter). For weight he defined the "hundred" as the weight of a bushel of distilled rainwater; this almost precisely the same as the original definition of the gram. A "pound" is then 1/100 hundred, or about ten kilograms. I don't understand why Wilkins' names are all off by a factor of ten; you'd think he would have wanted to make the quart be a millibushel, which would have been very close to a common quart, and the pound be the weight of a cubic foot of water (about a kilogram) instead of ten cubic feet of water (ten kilograms). But I've read this section over several times, and I'm pretty sure I didn't misunderstand.
Wilkins also based a decimal currency on his units of volume: a "talent" of gold or silver was a cubic standard. Talents were then divided by tens into hundreds, pounds, angels, shillings, pennies, and farthings. A silver penny was therefore 10-5 cubic Standard of silver. Once again, his scale seems off. A cubic Standard of silver weighs about 10.4 metric tonnes. Wilkins' silver penny is about is nearly ten cubic centimeters of metal, weighing 104 grams (about 3.5 troy ounces), and his farthing is 10.4 grams. A gold penny is about 191 grams, or more than six ounces of gold. For all its flaws, however, this is the earliest proposal I am aware of for a fully decimal system of weights and measures, predating the metric system, as I said, by about 110 years.