Page:FizeauFresnel1859.pdf/15

 By making the numerical cancelation, it is found:

$\Delta$ = 0.00010634 millimeters

This is the difference in speeds between the two rays that interfere, established by the motion of the water. Dividing this result by the length of a wave, $$\lambda$$, the fringe displacement is obtained

$\frac{\Delta}{\lambda}=0,2022;$

The experimental result was 0.23.

These two values are almost identical. I also want to demonstrate that the difference between the observed and the calculated values can very likely be described by an error in the evaluation of the water speed, with a source easy to assign, and whose value can be assumed by analogy to be very small.

The speed of water in each tube has been calculated by dividing the volume of water flowing in one second by the tube section. In this way, the median speed of the water has been obtained, which would be the actual one if the motion of the liquid threads were the same through the cross section of the tube, along the center as well as along the walls. But, reasoning shows that this is not the case, and that the resistance experienced by the liquid along the walls has an immediate effect upon the neighboring layers closer to the center. This means that the speed is different for liquid threads flowing at different distances from the wall. The speed value obtained by calculation is intermediate to these different speeds. The speed near the center is much greater than the median speed, which in turn is greater than the speed near the walls.

Also, the slits, placed in front of each tube to admit the light rays that will eventually cause the interference, are located in the middle of the circular end of the tubes, so that the rays traverse the central zones where the speed of the water should be greater than the median speed. (Each slit