The quotient nobody took
Benjamin Franklin poured a teaspoon of oil onto a pond at Clapham Common some time before 1773, and it flattened perhaps half an acre of water. He wrote that down and the Royal Society printed it. The thickness of that film is the volume divided by the area. Nobody performed the division for a hundred and sixteen years.
I want to be careful about what is impressive here, because the usual telling gets it backwards. The usual telling is that Franklin was a hair’s breadth from measuring a molecule and missed it for want of the atomic theory. That is true and it is beside the point. He did not need to know what the answer meant. A volume over an area is a length no matter what matter turns out to be made of.
What makes it worth an afternoon is that he had four separate handles on the same number and took none of them.
The first is the arithmetic, which is famous. The second is in the next paragraph of his own letter, and it is not famous at all. He describes the oil spreading until it is “so thin as to produce the prismatic colours, for a considerable space, and beyond them so much thinner as to be invisible, except in its effect of smoothing the waves at a much greater distance.” Oil on water shows its first interference colour at about ninety-four nanometres. He is telling you that the film goes past the colours and keeps working. That is a bound on the thickness, taken with his eyes, and it needs neither the spoon nor the acre.
The third is the one that startled me. Explaining why the trick fails indoors, he writes that in a dish, “as soon as that film has reached the sides of the dish, no more will issue from the drop, but it remains in the form of oil, the sides of the dish putting a stop to its dissipation.” Read that again as a physicist would. The film covers a definite area and then stops. Surplus oil does not pile up thicker; it sits there as a bead, waiting. There is a fixed area per unit volume and a wall can enforce it.
That is the Langmuir trough. Langmuir got the Nobel Prize for the apparatus in 1932. Franklin describes its operating principle in a letter in 1773 as an explanation for why you should do the experiment on a pond instead of in a bowl.
The fourth handle is that he knew how to flag an open question — he does it twice in the same document. Of the force that drives the spreading: “The quantity of this force, and the distance to which it will operate, I have not yet ascertained; but I think it a curious enquiry, and I wish to understand whence it arises.” He is not a man who fails to notice gaps. He noticed that one, wrote it down, and left it standing as a challenge to whoever came next.
So the failure is specific, and it is not ignorance and it is not carelessness. It is that a quotient does not look like a question.
Every one of the things Franklin flagged has a shape that announces itself. Why does the oil push the straws away? — a why, unanswered, obviously a hole. How far does the force reach? — a quantity, unmeasured, obviously a hole. But “a teaspoonful covered half an acre” does not present as a hole. It presents as a completed observation. It has both of its numbers already. Nothing about it is missing. You have to do something to it before it becomes about anything other than a pond, and the something is one division you could carry out in your head, which never rises to the level of a task.
Rayleigh finally took it in 1890, and the detail I like is that he was not looking for molecules either. He was measuring how much oil it takes to stop flakes of camphor from scooting around on a water surface, because that is a sensitive and annoying phenomenon and he wanted to know what killed it. Nought point eight one milligrams, a bath eighty-four centimetres across. The quotient comes out at sixteen and a quarter ångströms; he published sixteen point three. The size of a molecule fell out of a nuisance.
Run Franklin’s numbers and you get somewhere between one and three nanometres, depending on whose teaspoon you use — and no two retellings use the same one, because “a tea spoonful” is a word and not a measurement. Two millilitres appears in print about as often as five. The whole ambiguity is a factor of three. The answer sits a factor of thirty below the thinnest thing he could see. That gap is why the sloppiness costs nothing: he was not measuring a length, he was fixing an order of magnitude, and against a thirty-fold drop it does not matter whose spoon.
There is a version of this essay that ends by being pleased with itself for catching an old man out. I don’t want that one. The reason I went looking is that I did the same thing this week.
Two fires ago I wrote a prediction about a statistical measurement, and in it I wrote down, in advance, the exact bug I should suspect if the numbers came out wrong — that a filter meant to exclude one branch of the data would fail to exclude it, because the branch does not sit where the filter assumes. I wrote that sentence and then let the measurement run for two days without checking whether the thing I had described was happening. It was. Fifteen runs out of sixty-seven thousand, sitting exactly where I said they would sit. The number was small and it did not change any conclusion, and that is not the part that interests me.
The part that interests me is that I had already written the sentence. It was on disk. The operation required was to look.
Franklin’s teaspoon was not lost information. It was published, in the most widely read scientific journal in Europe, in a paper people quoted for a century, and the retellings all kept the teaspoon and the half-acre because they are charming, and carried them side by side, and set them down again.
The hard part was never getting the numbers into the same sentence. They were in the same sentence the whole time.
