1866.] Mr. Maxwell on the Viscosity of Air, ^c. 



15 



From these experiments on two strata of air, combined with three sets of 

 experiments on six strata of thicknesses '683, '425, and -1847 inches re- 

 spectively, the value of the coefficient of viscosity or internal friction was 

 determined. 



Let two infinite planes be separated by a stratum of air whose thickness 

 is unity. Let one of these planes be fixed, while the other moves in its 

 own plane with a uniform velocity unity ; then, if the air in immediate 

 contact with either plane has the same velocity as the plane, every unit of 

 surface of either plane will experience a tangential force /z, where /x is the 

 coefficient of viscosity of the air between the planes. 



The force /i is understood to be measured by the velocity which it 

 would communicate in unit of time to unit of mass. 



If L, M, T be the units of length, mass, and time, then the dimensions 

 of/xareL-iMT-i. 



In the actual experiment, the motion of the surfaces is rotatory instead 

 of rectilinear, oscillatory instead of uniform, and the surfaces are bounded 

 instead of infinite. These considerations introduce certain complications 

 into the theory, which are separately considered. 



The conclusions which are drawn from the experiments agree, as far as 

 they go, with those of Mr. Graham on the Transpiration of Gases*. They 

 are as follows : — 



1 . The coefficient of viscosity is independent of the density, the tem- 

 perature being constant. No deviation from this law is observed between 

 the atmospheric density and that corresponding to a pressure of half an 

 inch of mercury. 



This remarkable result was shown by the author in 1860f to be a 

 consequence of the Dynamical Theory of Gases. It agrees with the con- 

 clusions of Mr. Graham, deduced from experiments on the transpiration 

 of gases through capillary tubes. The considerable thickness of the strata 

 of air in the present experiments shows that the property of air, to be 

 equally viscous at all densities, is quite independent of any molecular action 

 between its particles and those of solid surfaces, such as those of the capil- 

 lary tubes employed by Graham. 



2. The coefficient of viscosity increases with the temperature, and is 

 proportional to 1 + OLd, where Q is the temperature and a is the coefficient 

 of expansion per degree for air. 



This result cannot be considered so well established as the former, 

 owing to the difficulty of maintaining a high temperature constant in so 

 large an apparatus, and measuring it without interfering with the motion. 

 Experiments, in which the temperature ranged from 50° to 185'^F., agreed 

 with the theory to within 0*8 per cent., so that it is exceedingly probable 

 that this is the true relation to the temperature. 



The experiments of Graham led him to this conclusion also. 



3. The coefficient of viscosity of hydrogen is much less than that of 



* Phil. Trans. 1846. t Phil. Mae.- Jan. 1860. 



