600 



current, we may expect that — uv lias nol a constant value between 

 the boundary layers, but that it is slightly "rounded oif". This 

 might be ascribed to slight irregular displacements of the vortices 

 caused by the irregularly distributed velocities which they impart 

 to each other. This "Browiiian" movement might give a distribution 

 of the smaller vortices resembling the one determined by the law 

 of Boi,tzmann-Maxwei,l for a gas under the influence of gravity, 

 which possibility has been pointed out by von Kakman in the lecture 

 mentioned above. 



The true distribution of vorticity in the turbulent motion will 

 take some mean position between the two extremes of paragraph 5 

 (uniform distribution over the whole breadth with C proportional to 



II 



lO" 



a-Ta± 



Fig. 4. Logarithmic-scale diagram of the dependence of C on R. 



■ 1 

 Curve L : laminar region, C= — (form. 3). 



R 



Curve C: results of Couette's experiments (the value of 



R has been calculated using ju. = 0,01096, comp. 



GOUETTE, 1. c. p. 460). 

 Curve K: = 0,008 R-'U (form, ib), deduced from the 



investigations by voN KaRM^N on the behaviour 



of U{y). 

 Curve I: formula (39), deduced from the supposition that 



all vortices have the same dimensions, and are 



uniformly distributed over the section. 

 Curve 77: formula (47), deduced from the supposition that 



the vortices have different dimensions, and are 



lying against the walls. 



