4 Gibson, IManncr of JSIotion of Water in a Curved Path, 



out of its side. An approximation to a free vortex is 

 formed by discharge through the central orifice, the 

 velocity increasing as the radius diminishes, and attaining 

 its maximum value within a short distance of the periphery- 

 of the central drum. Aniline dye was introduced at 

 different points in the vessel, and by its behaviour shows : 

 (i) That the motion is unstable around the peripher}' of 

 the outer vessel. (2) That the eddies formed at this 

 periphery die out as the centre is approached, and that 

 the motion, except in the neighbourhood of the inner and 

 outer boundaries, is essentially stable. (3) That the motion 

 is unstable around the periphery of the inner drum, but 

 that this instability is confined to the immediate neigh- 

 bourhood of the peripher}', the eddy formation being 

 confined to a c}-lindncal annulus, whose radial thickness 

 did not in general exceed one-quarter of an inch. 



The conclusions which would appear to be justified as 

 a result of these experiments, and of those previously 

 mentioned, are (i) that whenever flow takes place past a 

 curved solid surface, whether this is exposed to water on 

 its concave or its convex side, the motion, except for the 

 slowest velocities, is unstable ; and (2) that in the fluid 

 itself curvature with the velocit}' greatest on the viside of 

 the path tends to stability, while curvature with the 

 velocity greatest at the outside of the path tends to 

 instability. The fact that in the original experiment the 

 eddy formation noted at the periphery of the containing 

 vessel when the latter was stopped, did not extend 

 throughout the whole mass of fluid, is doubtless due to 

 the extremely low velocities obtaining near the centre of 

 the fluid. However inherently unstable the type of motion 

 may be, a certain critical velocity is necessary in order 

 that this may be manifested, and under the conditions 

 of the experiment, the actual velocity was extremely small. 



