401 



seldom) the variation in |)ressnre was greatei', the corresponding 

 mpasurement was not used. 



If 2/ is tlie length of the whole water-coiiinin tlial is in motion, 

 the double shift to be expected is 



{ 1 I du\ 



V fx' H dlj 



:. Wniax (4) 



c . K 

 expressed in parts of tiie distance between two fringes, vr'max is the 

 axial velocil_y, while («, ), and c are respectively the index of 

 refraction of the water, the wavelength of the light used, and c the 

 velocity of light in vacuo. 



For / has been taken 302,0 cm ; that is the distance between corres- 

 ponding poijils of contact of the dotted lines with the axis in the head- 

 pieces at the ends of the tube (see fig. 3). If the current in the 

 tubes was governed by the laws of Poisiaii.i.K, for viscous fluids, the 

 maxifiium velocity would be ecpial to twice the mean velocity and 

 the distribution of the velocities over the li-uusverse section wotild 

 be represented by a parabola. In our experiments however the 

 velocity of the water was more uniform ; we are in the region of 

 the turbulent motion. From the axis of the tube towards the side 

 the velocity decreases much more slowly than in the case of a 

 parabolic distribution and liiially only decreases very rapidly. In the 

 neighbourhood of the a.Nis of the tube there is thus a considerable 

 region, where the velocity may be regarded as being constant, at 

 least more constant than in llie case of a distribution of the velocities 

 according to Poiski'ii.i.k. From numerous and very careful researches 

 of American engineers ') the ratio of the mean velocity to that 

 along the axis of the tube has been deduced. The result was always 

 found in the neighbourhood of (J, 84, so that the mean velocity ii\ 

 becomes »>„ = 0,84 '/'„kix- 



The mean velocity for a definite pressure was determined by 

 measuring the (|uantity of the fluid that streamed out in a certain 

 time or rather the time (about half an hour) necessary to let stream 

 out 10 ni'. By the latter method the determination was independent 

 of the excentricity of the scale division, which gives the volume 

 of the water that has passed through the watermeter. For the 

 pressures used between 1.95 and 2.40 kg/cm' it was proved, that 



1) Williams, Hubbel and Frenkell, Tians. Am. Sot", of Civ. Eng. Vol. 47. 190:2. 

 Lawrence and Braunworth ibid. Vol. 57. 1906. 



CI', also R. BiEL. Heft 44 dor Mitleikingcn fiber Forschungsaibeitcn lieraus- 

 gegeben v. Ver. deutscl.. Ing. 11107. 



