The Universe of Discourse
           
Tue, 14 Feb 2006

The wings of flies

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The Diary of Samuel Pepys
The Diary of Samuel Pepys
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I was leafing through The Diary of Samuel Pepys recently. Pepys, in case you hadn't heard, was an official of the Royal Navy in England in the 17th century. He kept a meticulous diary, in which he recorded all sorts of trivia about what he did, who he saw, what he liked and didn't, what he ate and drank, and so on. It gives a wonderfully clear picture of life in London at the time. (The diary is available online; the version linked to the right is selections only. If you want to buy a paper copy of the complete diary, get it used, or it will be absurdly expensive. I got my copy at a library sale.)

The diary is a good book for browsing. Someday I'd like to read a long stretch of it and try to get a sense of the history and continuity of what's going on. But in the meantime, it's still good for browsing. Every few pages you run into something fascinating. Here's what I ran into today:

August 8th, 1666. Discoursed with Mr. Hooke, whom I met in the streete, about the nature of sounds, and he did make me understand the nature of musicall sounds made by strings, mighty prettily; and told me that having come to a certain number of vibrations proper to make any tone, he is able to tell how many strokes a fly makes with her wings (those flies that hum in their flying) by the note that it answers to in musique, during their flying.

Mr. Hooke, I hardly need tell you, is Robert Hooke, a groundbreaking scientist, and secretary of the (then newly-formed) Royal Society. (Pepys was later a member of the Society, and, still later, its president.) Hooke is responsible for Hooke's law, which states that the force exerted by a spring is proportional to the distance by which it has been extended or compressed from its natural length. He is also responsible for the use of the word "cell" to describe living cells.

This passage struck me first because it seemed so simple and clever to determine the rate at which a fly's wings beat by comparing the sound with that of a vibrating string. But as I thought about it more, it grew more puzzling. How do you know that a certain string, a middle C, say, is vibrating 256 times per second? How can you measure that with only 17th-century technology?

My first thought was that you can attach a bristle to the string, and then draw a piece of smoked glass under the bristle as the string vibrates; the bristle will leave a track on the glass. I seem to recall having heard of this being done at some time, but I can't remember the details. I'm also not sure that it could be done accurately enough. If you can pull a foot of glass past the bristle in one second, and the string is a middle C, then the bristle will trace a sinusoid whose peaks are about 1/21 inch apart, which is enough to measure. It seems plausible that something like this might be made to work with 17th-century technology. I think the sticking point would be moving the glass at a uniform speed. I don't think they had accurately machined screws yet.

So far the only other thing I have been able to think of is that since the relationship between the mass, tension, length, and pitch of a vibrating string was already known, Hooke measured some slow, massive vibrating rope, and then measured the tension, mass, and length of the string and extrapolated the vibrational rate from that. Perhaps there was a more direct method, but I don't know what it was.

These days you would just hold up a microphone that was plugged into an oscilliscope, or shine an adjustable strobe light on the fly. But you had to be pretty clever to carry out useful physics experiments in 1666.

That's one of the things that always amazes me about historical physics. The equipment was so crappy, it seems almost miraculous that they figured out anything at all. Consider the Greeks, who figured out that the moon shines by the reflected light of the sun. Presumably this idea originated in the observation that the lit side of the moon always faces the sun. But that's not all they did. They observed that the shape of the illuminated area was consistent with the shape you would see if part of a sphere was illuminated from without. Who the heck noticed that? They could presumably make spheres out of clay, but they didn't have any reliable, steady, directed light source. Candles flicker. So who got the idea to look at partially illuminated spherical wads of clay, and then went to the trouble of setting up the light source so they could examine the shape of the illuminated area?


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