26 G. I. TAYLOE ON EDDY MOTION IN THE ATMOSPHEEE. 



parallel planes at which there is no slipping is possible for an inviscid fluid when 

 there is perfect slipping, but is impossible as a steady state for an infinitesimally 

 viscous fluid which slips at the boundaries. 



The finite loss of momentum at the walls due to an infinitesimal viscosity may be 

 compared with the finite loss of energy due to an infinitesimal viscosity at a surface 

 of discontinuity in a gas.* 



If these views are correct we should expect that Lord RAYLEIGH'S result would 

 not apply when there are no bounding planes and space is filled with a fluid in which 

 d'TJ/dz 2 is everywhere positive ; for, in that case, there would be nothing to prevent 

 a positive amount of x-momentum from being communicated to every portion of the 

 fluid, provided the disturbance increases indefinitely for infinitely great values of z. 

 In obtaining his result Lord RAYLEIGH assumes that, if there are no bounding planes, 

 11! at infinity ;t it does not apply therefore to the case just considered. 



The conclusion arrived at is that the discrepancy between RAYLEIGH'S and 

 REYNOLDS' results is due to the fact that the perfect slipping at the boundaries 

 assumed in RAYLEIGH'S work prevents the escape of the momentum which is a 

 necessary accompaniment of a disturbance of a fluid for which d~U/dz 2 is everywhere 

 negative. The complete absence of slipping assumed in REYNOLDS' work enables 

 the necessary amount of momentum to escape, and so a type of disturbance may be 

 produced which is dynamically impossible under the condition of perfect slipping at 

 the boundaries. 



* See "Conditions Necessary for Discontinuous Motion in Gases," TAYLOR, 'Boy. Soc. Proc.,' 1910, 

 A, vol. 84, p. 371. 



t 'Phil. Mag.,' vol. 26, 191:?, p. 1002. 



