For mercury vapour the value of γ has been shown by Kundt to be 1·33 or 1⅓, and hence β is equal to 1. Thus all the energy of a particle of mercury vapour is translational, and its behaviour in this respect is consistent with the assumption that a particle of mercury vapour is a smooth sphere.
The two results of this theory which seemed to lend themselves most readily to experimental verification were (1) that the viscosity of a gas is independent of its density, and (2) that it is proportional to the square root of the absolute temperature. The next piece of work connected with the theory was an attempt to test these consequences, and a description of the experiments was published in the “Philosophical Transactions” for 1865, in a paper on the “Viscosity or Internal Friction of Air and other Gases,” and forms the Bakerian lecture for that year.
The first result was completely proved. It is shewn that the value of the coefficient[51] of viscosity “is the same for air at 0·5 inch and at 30 inches pressure, provided that the temperature remains the same.”
It was clear also that the viscosity depended on the temperature, and the results of the experiments seemed to show that it was nearly proportional to the absolute temperature. Thus for two temperatures, 185° Fah. and 51° Fah., the ratio of the two coefficients found was 1·2624; the ratio of the two temperatures, each measured from absolute zero, is 1·2605.
This result, then, does not agree with the hypothesis that a gas consists of spherical molecules acting only on each other by a kind of impact, for, if this were so, the coefficient would, as we have seen, depend on the square root of the absolute temperature. But Maxwell’s result, connecting viscosity with the first power of the absolute temperature, has not been confirmed by other investigators. According to it we should have as the relation between μ, the coefficient of viscosity at t° and μ₀, that at zero the equation—
μ = μ₀ (1 + .00365 t).
The most recent results of Professor Holman (Philosophical Magazine, Vol. xxi., p. 212) give—
μ = μ₀ (1 + .00275 t - .00000034 t²).
And results similar to this are given by O. E. Meyer, Puluj, and Obermeyer. Maxwell’s coefficient ·00365 is too large, but ·00182, the coefficient obtained by supposing the viscosity proportional to the square root of the temperature, would be too small.
It still remains true, therefore, that the laws of the viscosity of gases cannot be explained by the hypothesis of the impact of hard spheres; but some deductions drawn by Maxwell in his next paper from his supposed law of proportionality to the first power of the absolute temperature require modification.