# Page:1860 Fizeau en.djvu/11

water in the centre of the tubes, therefore, must be greater than that of the water near the sides, and consequently also greater than the mean of both velocities.

Now the slits placed before each tube to admit the rays whose interference was observed, were situated in the middle of the circular ends of the tubes; so that the rays necessarily traversed the central zones, where the velocity of the water exceeded the mean velocity[1].

The law followed by these variations of velocity in the motion of water through tubes not having been determined, it was not possible to introduce the necessary corrections. Nevertheless analogy indicates that the error resulting therefrom cannot be considerable. In fact, this law has been determined in the case of water moving through open canals, where the same cause produces a similar effect; the velocity in the middle of the canal and near the surface of the water is there also greater than the mean velocity. It has been found that, for values of the mean velocity included between 1 and 5 metres per second, the maximum velocity is obtained by multiplying this mean velocity by a certain coefficient which varies from 1.23 to 1.11. Analogy therefore permits us to assume that in our case the correction to be introduced would be of the same order of magnitude.

Now on multiplying $u$ by 1.1, 1.15, and 1.2, and calculating the corresponding values of the displacement of the bands, we find in place of 0.20 the values 0.22, 0.23, 0.24 respectively; whence it will be seen that in all probability the correction would tend to cause still greater agreement between the observed and the calculated results. We may presume, then, that the small difference which exists between the two values depends upon a small error in estimating the real velocity of the water; which error cannot be rectified in a satisfactory manner, in consequence of the absence of sufficiently accurate data.

Thus the displacement of the bands caused by the motion of water, as well as the magnitude of this displacement, may be explained in a satisfactory manner by means of the theory of Fresnel.

It was before observed that the motion of air causes no perceptible displacement of the bands produced by the interference of two rays which have traversed the moving air in opposite directions. This fact was established by means of an apparatus which I will briefly describe.

A pair of bellows, loaded with weights and worked by a lever, impelled air forcibly through two parallel copper tubes whose extremities were closed by glass plates. The diameter of each

1. Each slit was a rectangle 3 millims. by 1.5, and its surface was equal to one-fifth that of the tube.