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Note on the Reduction of Mr. Crookes’s Experiments on the Decrement of the Arc of 
Vibration of a Mica Plate oscillating within a Bulb containing more or less 
Rarefied Gas. 
By Professor G. G. Stokes, Sec. R.S. 
Received and Read February 17, 1881. 
In the course of his long series of researches “ On Repulsion resulting from Radiation,” 
Mr. Crookes had frequently occasion to observe the deflections of a light bar or 
lamina of some substance delicately suspended and oscillating by torsion. When such 
a bar was set in vibration, the vibrations tended more or less rapidly to subside, in 
consequence, no doubt, of the viscosity of the gas enclosed in the apparatus. At first 
it seemed as if the rate of subsidence tended to reach a constant value which remained 
the same at all higher exhaustions. But as methods of exhaustion were improved, 
and the gases were so rarefied that the effect of a candle in causing repulsion distinctly 
fell off, the rate of subsidence of the oscillations was found greatly to fall off too. This 
falling off at extreme exhaustions seemed to present a very interesting field of study 
in connexion with the molecular condition of gases. The inquiry would naturally 
involve the observation of the nearly constant rate obtained at somewhat lower 
exhaustions; and the same apparatus would serve for experiments on the rate of 
subsidence at higher densities, up to that corresponding to atmospheric pressure. 
A comparison of the rates of subsidence in different gases at great but not extreme 
exhaustions was further interesting as a new means of determining the ratios of the 
viscosities of different gases. In fact, at high exhaustions the motion of the gas tends 
to a condition of ideal simplicity from which a comparison of the viscosities of different 
gases would immediately result. The effect of the viscosity of a gas on its own motion 
is regulated by the value of a constant which I have elsewhere* called the index of 
friction of the gas, namely, the coefficient of viscosity divided by the density. Accord¬ 
ing to Maxwell’s law, the coefficient of viscosity is independent of the density, and 
therefore the index of friction varies inversely as the density. Hence as the exhaus¬ 
tion proceeds the motion of the gas tends to become what it would be if the viscosity 
were infinite, and the bounding surfaces had their actual motion. In the limit, the 
instantaneous motion of the gas depends only on that of the vibrating plate, to which 
it is proportional, except in so far as the finiteness of the angle of oscillation entails a 
* “On tbe Effect of the Internal Friction of Fluids on the Motion of Pendulums,” Cambridge Philo¬ 
sophical Transactions, vol. ix., p. [8]. 
MDCCCLXXXI. 3 L 
