68 



Lord Eayleigh. 



"On the Viscosity of Argon as affected by Temperature." By 

 Lord Eayleigh, F.RS. Eeceived January 12, — Eead Jan- 

 uary 18, 1900. 



According to the kinetic theory, as developed by Maxwell, the 

 viscosity of a gas is independent of its density, whatever may be the 

 character of the encounters taking place between the molecules. In 

 the typical case of a gas subject to a uniform shearing motion, we may 

 suppose that of the three component velocities v and w vanish, while 

 is a linear function of y, independent of x and z. If fi be the viscosity, 

 the force transmitted tangentially across unit of area perpendicular to 

 y is measured by ixdu/dy. This represents the relative momentum, 

 parallel to x, which in unit of time crosses the area in one direction, 

 the area being supposed to move with the velocity of the fluid at the 

 place in question. We may suppose, for the sake of simplicity, and 

 without real loss of generality, that to is zero at the plane. The 

 momentum, which may now be reckoned absolutely, does not vanish, 

 as in the case of a gas at rest throughout, because the molecules come 

 from a greater or less distance, where (e.g.) the value of u is positive. 

 The distance from which (upon the average) the molecules may be 

 supposed to have come depends upon circumstances. If, for example, 

 the molecules, retaining their number and velocity, interfere less with 

 each other's motion, the distance in question will be increased. The 

 same effect will be produced, without a change of quality, by a simple 

 reduction in the number of molecules, i.e., in the density of the gas, 

 and it is not difficult to recognise that the distance from which the 

 molecules may be supposed to have come is inversely as the density. On 

 this account the passage of tangential momentum per molecule is in- 

 versely as the density, and since the number of molecules crossing is 

 directly as the density, the two effects compensate, and upon the 

 whole the tangential force and therefore the viscosity remain un- 

 altered by a change of density. 



On the other hand, the manner in which this viscosity varies with 

 temperature depends upon the nature of the encounters. If the 

 molecules behave like Boscovich points, which exercise no force upon 

 one another until the distance falls to a certain value, and which then 

 repel one another infinitely (erroneously called the theory of elastic 

 spheres), then, as Maxwell proved, the viscosity would be proportional 

 to the square root of the absolute temperature. Or again, if the 

 law of repulsion were as the inverse fifth power of the distance, 

 viscosity would be as the absolute temperature. 



In the more general case where the repulsive force varies as r"'\ the 

 dependence of ft upon temperature may also be given. If v be the 

 velocity of mean square, proportional to the square root of the tem- 



