Viscosity in the Swing

Under “Discrepancies, gas viscosity, 1866” - that is where this entry belongs, and I record the reasoning so that whoever finds the loose leaf will not mistake it for waste.

At the Cavendish last spring, the swinging-disk apparatus gave me a result the whole kinetic theory had predicted against. The viscosity of air, measured by the damping of oscillations at pressures from one atmosphere down to a small fraction of an inch of mercury, refused to diminish as the density diminished. The damping remained, so far as my instrument could resolve it, constant. Every naive derivation - including one I had myself written with confidence - required the friction to fall in proportion to the density, since fewer molecules should mean less to carry the momentum across.

The resolution, when the arithmetic forced it upon me, is that the mean free path grows exactly as the density falls. The molecule carries its momentum farther before surrendering it; the two effects cancel; the product is independent of density. The transport is not a flow through the medium but a propagation across it - each molecule a little wave train traversing the interval between collisions, and the collision interval stretching precisely to compensate the thinning crowd. Two terms, opposite in sign, equal in magnitude: the interference is exact, and the cancellation is the discovery, not the failure of the measurement.

File it thus: not under “instrumental error,” though the tidy ledger would prefer that shelf, but under “predictions overturned by their own premises.” The naive prediction assumed the collision interval fixed; the theory, properly extended, dissolves the disagreement and becomes a stronger theory for having survived it. A discrepancy of this kind is not noise in the signal but the signal announcing a missing term in the equation. Mark the class clearly, because the same filing rule will recur: whenever a measurement contradicts an expectation derived from the same equations it purports to test, suspect first that the expectation was the crude limiting case and the measurement the true solution.

The next measurement worth making is at the lowest attainable pressures, where the mean free path approaches the dimensions of the vessel itself - there the cancellation should break down, and the viscosity should at last depend on the box.

Peter, fetch the larger pump from the basement before term begins; I want the vessel evacuated far enough that the walls, not the neighbouring molecules, set the limit.