1240 
Physics. — “An optical method for determining the ratio between 
the mean and maximal velocities in the turbulent motion of 
fluids in a cylindrical tube. Contribution to the experiment of 
Fizeau’. By Prof. P. Zeman. 
(Communicated in the meeting of January 29, 1915), 
1. In my experiments on tbe Fresnet-coefficient for different 
colours *) the mean velocity of the water-current was found by deter- 
mining the total volume that had passed through the tubes. Thence 
the maximal velocity near the axis of the tubes was derived by 
division of this mean velocity by 0,84. This numerical coefficient 
has been calculated from numerous and careful observations of 
American engineers. It seems however not quite satisfactory, that 
this coefficient has not been measured under the same circumstances 
that occur in the experiment of Fizwav. This is the reason I have 
made some measurements myself. The particularity of the method used 
was that no measuring apparatus had to be brought into the tube 
in which we are going to investigate the motion. 
If PoispuiLe’s law were valid for the tubes used in Fizeau’s ex- 
periment, the maximal velocity v,, might directly be derived from 
the mean velocity v,, v, being equal to 2v,. In Fizeau’s experiment 
however only velocities occur far above the limit of the critical 
velocity given by the eriterion of OsBORNE Rerynoups. If PorsbuiLLe’s 
law did hold, the distribution of the velocities in the tube would 
be represented by a parabola, so that near the axis the velocity 
would change rather rapidly. Im the case of the great velocities 
occurring in our experiments the distribution of the velocities is 
much more uniform and the interference fringes are much sharper 
than else might have been expected. As the velocity is not every- 
where the same, a curving of the wavefronts must occur, from 
which a broadening of the interference fringes will result. At the 
inspection of the interference fringes we are struck by the fact, 
that the turbulence of the motion leaves the interference fringes so 
sharp. This is also shown by the sharpness of the photos added to 
my communication of May 25 1915. 
2. In Fizwau’s experiment the water is led into the tubes through 
which the interfering beams pass, by symmetrical connecting-pieces. 
In the experiments to be described in this communication the water 
supply has been arranged in the same way. To the wall of the 
1) These proceedings 445, 17, 1914; 398, 18. 1915. 
