Transpiration and Radiometer Motion. 485 



The last point to be attended to in applying our equations 

 to the experimental results is that when one side of the mica 

 vane is irradiated the glass bulb is also warmed in such a 

 manner that it is hottest where nearest the candle, and there- 

 fore there is thermal transpiration along the inner surface 

 of the bulb tending to raise the pressure near the hottest 

 point with diminution towards the coldest point ; now we 

 can afford to neglect the effect of this near the vane until 

 the pressure gets so small that the mean free path of a 

 molecule becomes, say, nearly equal to the radius of the 

 bulb, for then the walls of the bulb, on account of their 

 much greater area than that of the effective edge of the 

 vane, must dominate the distribution of temperature and 

 pressure in the gas even quite close to the vane, and there- 

 fore at the highest exhaustions the relation between pressure 

 and deflecting force must tend to a limit determined rather 

 by the bulb than by the vane. With these explanations (27) 

 is now applicable to the experiments of Crookes. 



With his apparatus Crookes was able to study concurrently 

 the viscosity of a gas and the forces at play in the radiometer 

 at pressures from one atmo down to the lowest measurable 

 by the M'Leod gauge. The form of his vibrating system 

 renders the mathematical problem of obtaining an expression 

 for the viscosity of the gas from the constants of the apparatus 

 and the observed decrement per vibration of the logarithm 

 of the amplitude of the vibrations of the mica plate intract- 

 able ; but it is obvious, from the theory of the vibrating disk 

 method of measuring viscosity, that the motion of the mica 

 plate when oscillating must be retarded by the viscosity of 

 the gas in such a way that the difference of the logarithms of 

 successive amplitudes is proportional to the viscosity of the 

 gas, so that although absolute values of viscosity are un- 

 obtainable with the apparatus, approximate relative ones can 

 be got with it. At a number of different densities of the gas 

 Crookes measured the logarithmic decrement and also the re- 

 pulsive effect of a candle-flame radiating towards the blackened 

 half of the mica plate from a horizontal distance of half a metre, 

 the latter being measured by a reading of the permanent 

 deflexion of the plate from its position of rest in darkness. 



Now from Maxwell's well known discovery that the 

 viscosity of a gas is independent of its pressure it follows that 

 the logarithmic decrement is independent of the pressure so 

 long as slipping of the gas on the solid surfaces is negligible ; 

 but, as already indicated, Kundt and Warburg showed 

 experimentally, with some support from theoretical reasoning, 

 that slipping ceases to be negligible when the mean free path 



Phil. Mag. S. 5. Vol. 42. No. 259. Dec. 1896. 2 M 



