The Universe of Discourse

Fri, 17 Feb 2006

More on the frequency of vibrations in 1666 and other matters
In a series of earlier posts (1 2 3) I discussed Robert Hooke's measurement of the frequency of G above middle C: he determined that it was 272 beats per second. There are two questions here: first, how did he do that, and second, why is his answer so badly wrong? (Modern definitions make it about 384 hertz; 17th-century definitions differ, and vary among themselves, but not by so much as that.)

The article Mr. Birchensha's Ear, by Benjamin Wardhaugh, provides the answers. In 1664, Hooke and the Royal Society set up a vibrating brass wire 136 feet long. It could be seen to vibrate once per second. Hooke divided it in half, and it vibrated twice per second. He truncated it to one foot, and the assembled musicians pronounced the sound to be a G below middle C. Since a wire one foot long vibrates 136 times as fast as one 136 feet long, we have the answer.

And the error? Partly just slop in the dividing and the estimation of the original frequency. Wardhaugh says:

In fact, the frequency is badly wrong (G has a frequency of 196 Hz), probably because Hooke was careless about the length of the pendulum that measured the time. In private he is meticulously precise, but maybe the details don't matter so much for Society showpieces.
Pepys wasn't there, which is why he had to learn about it from Hooke in 1666.

The rest of the article is well worth reading:

Passers-by jeer at the useless toy: the pointlessness of the Royal Society's activities is already threatening to become proverbial. (Shadwell later wrote a comedy in which 'the Virtuoso' weighed air, swam on dry land and read by the light of a decaying fish. Poor Hooke went to see it and 'people almost pointed'.)
The Royal Society is well-known to be the inspiration for the Grand Academy of Laputa in Gulliver's Travels, one of whose members "had been eight years upon a project for extracting sunbeams out of cucumbers...".

Reading the contents of Derham's 1726 collection of Hooke's papers on Wednesday, I was struck by the title "Hooke's Experiments on Floating of Lead". I was gearing up to write a blog post about how no real scientific paper has ever reminded me quite so much of the Grand Academy. But I abandoned the idea when I remembered that there is nothing unusual or surprising about being reminded of the grand Academy by a Royal Society paper. Also, the title only sounds silly until you learn that the paper itself is about the manner in which solid lead floats on molten lead.

Final note: while searching for the title of the floating-lead paper (which I left at home today) I learned something else interesting. In South Philadelphia there is a playground attached to an antique "shot tower". I had had no idea what a shot tower was, and I had supposed it was a place for storing shot and gunpowder. But why build a tower? It turns out it is the place where lead shot is manufactured. You melt up a cauldron of lead at the top, then dump it through a copper sieve and let it fall into a tub of water at the bottom. On the way down, the molten lead turns into round shot. You sort it for size and roundness, re-melt the ones that aren't round, and you have your shot.

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