1916] ON THE DYNAMICS OF REVOLVING FLUIDS 453 directions, this disposition involves discontinuities, and the stability exists only under the condition that symmetry with respect to the axis is rigorously maintained. If this limitation be dispensed with, the motion is cfertainly unstable, and thus the stability of motion in cylindrical layers really requires that the circulation be one-signed. On the general question of the two-dimensional motion of liquids between nxed coaxial cylindrical walls reference may be made to a former paper*. The motion in cylindrical strata is stable provided that the " rotation either continually increase or continually decrease in passing outwards from the axis." The demonstration is on the same lines as there set out for plane strata. * Proc. Land. Math. Soc. Vol. xi. p. 57 (1880); Scientific Papers, Vol. i. p. 487. See last paragraph.