Turbulent Flow in Pipes and Channels. 327 



of about 0*5 of one per cent, exist in determinations of the 

 coefficient of viscosity by the various methods employed, and 

 that these cannot be attributed to errors of experiment. 



As has already been pointed out, measurements of the 

 viscosity of gases carried out by these methods depend on 

 the shear between a solid surface and a gas, the laws 

 for which may not be identical in all circumstances with 

 those relating to tractions between successive layers of gas. 

 Moreover, all these methods entail very low relative velocities 

 and rates of shear, while any slight departures from the 

 theoretically specified motion have generally been attributed 

 to the breakdown of viscous stream-line flow to " turbulent 

 flow'"' without further examination. Any direct measure- 

 ments of velocity-gradients do not appear to have been 

 carried out, although this is now possible owing to the 

 development of the linear hot-wire anemometer described in 

 a previous paper by the writer. Any factor other than the 

 viscosity resulting from the free-path transfer of momentum 

 might easily have escaped observation in the type of experi- 

 ments referred to, as the inertia of the moving surfaces 

 employed would tend to smooth out any extraneous irregu- 

 larities in viscous tractions which might exist. The writer 

 hopes, at some future date, to undertake the analysis of 

 velocity-gradients in these cases by means of the hot-wire 

 anemometer; it may well happen, as in the case of flow 

 between parallel planes, that factors other than the viscosity 

 due to free-path phenomena may play a part in determining 

 the velocity-gradients and tractions referred to. 



Part II. 



On the Stability of Laminar Flow in 

 Pipes and Channels. 



Section 5. Historical and Ci ideal Survey of the 

 Theoretical Development. 



The origin of the theoretical work on the subject of the 

 present chapter dates back to Helmholtz's remark that 

 surfaces of discontinuity in perfect fluids are unstable 1 ' 3 . 

 The subject was treated mathematically at an early date by 

 Rayleigh, especially in connexion with the stability of jets 

 and the explanation of phenomena relating to sensitive 



13 Helmholtz, Phil. Mag. Nov. 1868 ; Gesammelte Ahhandlungen, i 

 p. 146 (1882-3). 



