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at the axis of the tubes conveying the water must be known. This 
velocity at the axis was deduced from the mean velocity by means 
of a numerical coefficient gy, which represents the ratio between the 
mean velocity and the velocity at the axis in a cylindrical tube 
for turbulent motion. *) 
At first I adopted for p the valne 0,84 as determined by Ame- 
rican engineers. Afterwards I devised an optical method for meas- 
uring the mentioned coefficient. In a model of part of the apparatus 
for measuring FrersNer’s coefficient, the value ¢ — 0,843 was found. 
On that occasion (Communication JV) I suggested that it would be 
preferable, though rather difficult, to measure ¢, in the very appa- 
ratus used in my repetition of Frzeav’s experiment. Only lately have 
I succeeded in performing the necessary measurements with the 
original apparatus. The velocity at the axis, which is of primary 
importance, is now measured directly. The value of g is of minor 
importance, but may of course be calculated from the measured 
mean velocity. It should be noticed that for the measurement of 
the total volume a verification of the water meter is necessary, so 
that a fault in this verification affects also g. By the use of the 
method now under review one is quite independent of any veri- 
fication of watermeters. 
For the application of our optical method — rotating mirror ; air 
bubbles in the running water; intense, narrow beam of light at the 
axis -- it is necessary to have a small window in the wall of the 
brass tube. For this purpose an aperture of two centimeters length, 
one centimeter width made in the thin walled tube was closed with 
a cylindrical piece of glass of a mean curvature equal to that of 
the wall of the tube. Between the brass and the glass a thin layer 
of rubber was interposed to make the apparatus watertight ; in 
order to withstand the considerable pressure the window was 
pressed against the tube by means of adequately constructed springs. 
1) For easy references my communications relating to Fizrau’s experiment are 
referred to as Communications I, II, HI, and IV: 
I. The convection coefficient of FRESNEr for light of different colour (I). These 
Proceedings 17, 445, 1914. 
Il. The convection coefficient of FRESNEL for light of different colours (II). These 
Proceedings 18, 398, 1915. 
III. On a possible influence of the FRESNEL coefficient on solar phenomena. 
These Proceedings 18, 711, 1915. 
IV. An optical method for detérmining the ratio between the mean and axial 
velocities in the turbulent motion of fluids in a cylindrical tube. Contribution to 
the experiment of Fizrau. These Proceedings 18, 1240, 1916. 
