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of rays thus penetrated into each tube, and traversed its entire length, lm-487.
The two bundles, always parallel to each other, reached the object-glass of the second telescope, were then refracted, and by the effect of the refraction reunited at its focus. There they encountered the reflecting plane of a mirror perpendicular to the axis of the telescope, and underwent a reflexion back again towards the object-glass ; but by the effect of this reflexion the rays had changed their route in such a way that that which was to the right before, was to the left after the reflexion, and vice versa. After having again passed the object-glass, and been thus rendered parallel to each other, they penetrated a second time into the tubes; but as they were inverted, those which had passed through one tube in going passed through the other on returning. After their second transit through the tubes, the two bundles again passed the double chinks, re-entered the first telescope, and lastly intersected at its focus in passing across the transparent mirror. There they formed the fringes of interference, which were observed by a glass carrying a graduated scale at its focus.
It was necessary that the fringes should be very large in order to be able to measure the small fractions of the width of a fringe. I have found that that result is obtained, and a great intensity of light maintained, by placing before one of the chinks a thick mirror ■which is inclined in such a way as to see the two chinks by the effect of refraction, as if they were nearer to each other than they really are. It is in this way possible to give various dimensions to the fringes, and to choose that which is the most convenient for observation. The double transit of the light was for the purpose of augmenting the distance traversed in the medium in motion, and further to compensate entirely any accidental difference of temperature or pressure between the two tubes, from which might result a displacement of the fringes, which would be mingled with the displacement which the motion alone would have produced; and thus have rendered the observation of it uncertain.
It is, in fact, easy to see that in this arrangement all the points situated in the path of one ray are equally in the path of the other ; so that any alteration of the density in any point whatever of the transit acts in the same manner upon the two rays, and cannot consequently have any influence upon the position of the fringes. The compensation may be satisfactorily shown to be complete by placing a thick mirror before one of the two chinks, or as well by filling only one of the tubes with water, the other being full of air. Neither of these two experiments gives rise to the least alteration in the position of the fringes.
With regard to the motion, it is seen, on the contrary, that the two rays are subject to opposite influences.
If it is supposed that in the tube situated to the right the water runs towards the observer, that of the two rays which comes from the right will have traversed the tube in the direction of the motion, while the ray coming from the left will have passed in a direction contrary to that of the motion.
By making water move in the two tubes at the same time and iu contrary directions in each, it will be seen that the effects should be added. This double current having been produced, the direction may be 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 tube3 was 5mm-3, their length lm,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 phenomenon, 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.