Page:Aether and Matter, 1900.djvu/48

12 belief that it would not do to actually take the aether to be an ordinary fluid, on the ground that this ideal motion of irrotational quality would then be unstable. In a subsequent note (Phil. Mag. 1848) he advanced as proof of this instability the fact that the mathematical solution for the steady motion of a sphere through a viscous fluid, which he had just obtained, is the same however slight may be the degree of viscidity of the fluid. Now an irrotational motion calls out no viscous reaction throughout the mass, and therefore satisfies the conditions of viscous as well as of perfect flow: but there is one circumstance which destroys its claim to be a solution in the former case, namely the presence of slip at the surfaces of the solids. If the surfaces of the solids were ideallv frictionless this would not matter: but if when the irrotational flow has there been fully established, the actual frictional character of the surface were restored, laminar rotational motion would spread out from each surface in the same manner as heat would spread out by diffusive conduction from a hot body, until a new state of steady motion would supervene. The solution of Stokes shows (as is also clear from general principles) that however small the viscosity, this new steady state is wholly different from the ideal irrotational steady state belonging to mathematical absence of viscosity and friction : and it might appear to follow that this state is, not precisely an unstable one, but rather one which could not exist at all in the fluid. The term unstable is however appropriate because, if the solids are impulsively started into their steady state of motion, the initial state of motion of the fluid will (assuming that there is no such thing as impulsive friction ) be the irrotational one, which will gradually be transformed by diffusion of vortex motion from the surfaces at a rate which is the slower the less the viscosity of the fluid. This conclusion follows as a special case of Lord Kelvin's general dynamical principle that when a material system is impulsively set into motion by imposing given velocities at the requisite number of