332 Prof. L. Yessot King on 



experimental results briefly described above, it is hardly 

 necessary to consider in further detail the various theoretical 

 treatments referred to. While the condition of incom- 

 pressibility assumed in these discussions might possibly be 

 justified in the case of liquids (and some evidence seems to 

 point to compressibility as a determining factor affecting 

 stability in this case as well) 26 , it is hardly to be supposed 

 that this factor could be entirely ignored in the case of 

 gases. 



In the light of the preceding remarks it appears that still 

 another factor may plaj' a part in determining the instability 

 of flow in tubes and channels, that is, the deterrninateness 

 of the various transverse modes of sound-vibrations which 

 may be set up. In a two-dimensional channel (or channel 

 of elongated cross-section) the nodes and loops are extremely 

 determinate in position, and we should expect laminar flow 

 to persist to very high velocities. In the case of a tube of 

 circular cross-section, however, some of the normal trans- 

 verse modes (e. g. those having diameters as nodes) are 

 indeterminate in position, and in an actual case would be 

 determined by accidental inequalities on the interior of the 

 tube or by slight departures from circular form. It would 

 thus appear that in such cases (which include practically all 

 experimental data) Reynolds's Criterion of " sinuous " motion 

 would be decided, not by instability of steady flow in the 

 usual sense, but by the appearance of the first transverse 

 mode having a diametral node. Relatively to the fluid, 

 these indeterminate modes would tend to twist around, 

 resulting in a state of affairs which, if continued long enough 

 would, in spite of the stabilizing effect of viscosity, result in 

 a complete destruction of conditions of steady flow. Many 

 phenomena relating to the " critical velocity " are thus 

 capable of explanation; for instance, the "flashing" first 

 observed by Reynolds 27 , making use of the colour-band 

 method, i. e. a state of " sinuous " motion over a short length 

 of tube followed by a region of stream-line flow. The effect 

 of the material of the tubes on the critical velocity observed 

 by several experimenters is probably due, for the most part, 

 to the degree of mechanical finish of the interior surface 

 obtainable with the particular substance employed 28 . In the 



2(5 See footnote (36). 



-~ Reynolds, footnote (15), fig. 16. 



28 According; to the ideas developed in the preceding paragraph, it 

 would seem that the acoustic properties of the walls of the tube or 

 channel may not be without influence on the velocity-gradients in the 

 immediate neighbourhood of the boundary. 



