﻿528 Mr. W. Ellis Williams on the 



in air, and, in fact, the lowest pressures experimentally 

 observed on aeroplane wings and similar bodies are never 

 more than a few cms. of water below atmospheric pressure. 

 In the second place, the difference is by no means confined to- 

 cases in which sharp edges are present, but is quite as great 

 when the moving bodies are spherical or cylindrical so that 

 cavitation cannot take place even in heavy liquids, and, in 

 fact, the difference may be shown to exist in cases where the 

 absence of cavitation may be experimentally demonstrated. 



The reason for the discrepancy appears to lie rather in the 

 nature of the boundary conditions and the impossibility of 

 satisfying them in the irrotational solutions. All the experi- 

 mental evidence available goes to show that for fluids such as- 

 water and air the particles of fluid in the immediate neigh- 

 bourhood of a solid boundary have no motion relative to that 

 boundary, while the irrotational solutions cannot be made to* 

 satisfy this condition owing to the fact that, viscosity being 

 neglected, tangential motion gives rise to no stress, so that 

 in general the solutions indicate a large amount of slipping- 

 at the boundary. 



In the case of solids of " stream-line " or fish-like shape 

 the motion appears to be similar to that given by the 

 irrotational solution except in a layer of fluid in the neigh- 

 bourhood of the surface of the moving body *. In this 

 layer, which is relatively thin, the velocity changes rapidly 

 from the value given by the boundary condition to that 

 given by the irrotational solution. Within this layer the 



value of ^— 2 is therefore large compared with u and the 



term containing the viscosity is no longer negligible. The 

 high value of the space differential of the velocity gives rise 

 to a considerable tangential force on the surface of the body, 

 which is generally known as " skin friction." 



In most cases, however, the transition layer is not confined 

 to the surface of the moving body, but departs from it near 

 midsection and gives rise to a "wake" of eddying motion,, 

 which persists in the fluid for a considerable distance behind 

 the moving body, completely altering the character of the 

 motion. 



In certain cases the motion may be approximately repre- 

 sented by the assumption of surfaces of discontinuity in the 

 fluid, and the solutions obtained in this way by Kirchhoff and 

 Rayleigh, though far from giving an exact representation of 

 the observed motion, are yet a great advance on the older 

 theory. The methods developed do not, however, throw any 

 * Vide Prandtl, Handbuch d. Naturwiss. iv. 



