By making water move in the two tubes at the same time and in contrary directions in each, it will be seen that the effects should be added. This double current having been produced, the direction maybe again reversed simultaneously in the two tubes, and the effect would again be double.
All the movements of the water were produced in a very simple manner, each tube being connected by two conduits situated near their extremities, with two reservoirs of glass, in which a pressure is alternately exercised by means of compressed air. By means of this pressure the water passes from one reservoir to the other by traversing the tube, the two extremities of which are closed by the mirrors. The interior diameter of the tubes was 5mm·3, their length 1m·487. They were of glass.
The pressure under which the flowing of the water took place might have exceeded two atmospheres. The velocity was calculated by dividing the volume of water running in one second by the area of the section of the tube. I ought to mention, in order to prevent an objection which might be made, that great care was taken to obviate the effects of the accidental motions which the pressure or the shock of the water might produce. Therefore the two tubes, and the reservoirs in which the motion of the water was made, were sustained by supports independent of the other parts of the apparatus, and especially of the two lunettes; it was therefore only the two tubes which could suffer any accidental movement; but both theory and practice have proved that the motion or flexions of the tubes alone were without influence upon the position of the fringes. The following are the results obtained.
When the water is set in motion the fringes are displaced, and according as the water moves in the one direction or the other, the displacement takes place towards the right or the left.
The fringes are displaced towards the right when the water is running from the observer in the tube situated to his right, and towards the observer in the tube situated to his left.
The fringes are displaced towards the left when the direction of the current in each tube takes place in a direction opposed to that which has just been described.
With a velocity of the water equal to 2m. a second, the displacement is already very sensible; with a velocity of 4 to 7 metres it is perfectly measurable.
After having demonstrated the existence of the phænomenon, I endeavoured to determine its numerical value with all the exactitude which it was possible to attain.
By calling that the simple displacement which was produced when the water at rest in the commencement was set in motion, and that the double displacement which was produced when the motion was changed to a contrary one, it was found that the average deduced from nineteen observations sufficiently concurring, was 0.23 for the simple displacement, which gives 0.46 for the double displacement, the width of a fringe being taken as unity. The velocity of the water was 7.069 metres a second.