On the stability of the motion of a viscous liquid

has established an energy criterion for the stability of the motion of a viscous liquid, and has applied it to the case of a liquid moving between two parallel planes.For a liquid of density p and viscosity p, moving between two planes 26 apart with mean velocity U he found that the motion is unstable when 2MT>517. P-Using the principle that the critical velocity is inversely proportional to the hydraulic mean depth he inferred that for a cylindrical pipe of radius a the critical velocity is given by ^>1034, Pand he compared this with his experimental value 1900.In the following paper I discuss directly the case of the cylindrical pipe and find that the motion is unstable when -i->470.P-I also find, by using a different solution of the equation of continuity and the boundary conditions, that the motion between two parallel planes is unstable when ^>167, P" instead of 517 as found by Reynolds.§ 2. Bectilinear flow through a pipe.When the motion through a pipe is symmetrical the equations of motion, expressed in cylindrical coordinates r, 0, z, are J