flowing down an Inclined Plane Bed. 277 



that there is a certain residual stability, so long as the dis- 

 turbances do not exceed a given amount.". . . 



ee And it was a matter of surprise to me to see the sudden 

 force with which the eddies sprang into existence, showing a 

 highly unstable condition to have existed at the time the 

 steady motion broke down.' - ' 



" This at once suggested the idea that the condition might 

 be one of instability for disturbance of a certain magnitude, 

 and stable for smaller disturbances/'' 



49. The motion investigated experimentally by Reynolds, 

 and referred to in the preceding statements, was that of 

 water in a long straight uniform tube of circular section. It 

 is to be hoped that candidates for the Adams Prize of 1888 

 may investigate this case mathematically, and give a complete 

 solution for infinitesimal deviations from rectilineal motion. 

 It is probable that for it, and generally for a uniform straight 

 tube of any cross section, including the extreme, and extremely 

 simplified, case of rectilinear motion of a viscous fluid between 

 two -parallel jixed planes, which I have worked out above, the 

 same general conclusion as that stated at the end of § 26 and 

 in §§43-48 will be found true. 



50. In the case of no gravity (g sin 1 = 0), and the viscous fluid 

 kept in "shearing" or "laminar" motion by relative motion 

 of the two parallel planes, there is, when viscosity is annulled, 

 no disturbing instability in the steady uniform shearing mo- 

 tion, with its uniform molecular rotation throughout, which 

 viscosity would produce; and therefore our reason for sus- 

 pecting any limitation of the excursions within which there 

 is stability, and for expecting possible permanence of any kind 

 of turbulent or tumultuous motion between two perfectly 

 smooth planes (or between two polished planes with any 

 practical velocities) does not exist in this case. But a 

 great variety of general observation (and particularly Ran- 

 kine and Froude^ s doctrine of the " skin-resistance " of 

 ships, and Froude's experimental determination of the re- 

 sistance experienced by a very smooth, thin, vertical board, 

 19 inches broad and 50 feet long, moved at different uni- 

 form speeds* through water in a broad deep tank 278 feet 



* ' Eeport to the Lords Commissioners of the Admiralty on Experiments 

 for the Determination of the Frictional Resistance of "Water on a Surface 

 under various conditions, performed at Chelston Cross (Torquay), under 

 the Authority of their Lordships.' By W. Froude. (London : Taylor and 

 Francis. 1874.) 



Froude found that, at a constant velocity of 600 feet per minute, the 

 resistance of the water against one of his smoothest surfaces, at positions 

 two feet abaft of the cutwater and 50 feet abaft of the cutwater, respec- 

 tively, was -295 of a pound per square foot, and -244 of a pound per square 



