Page:FizeauFresnel1859.pdf/18

recognized, even if it had been accompanied by an accidental displacement due mainly to some defect of symmetry in the diameters or in the orifice of the tubes. This would have resulted in unequal resistance to the passage of the gas, and, consequently, in a difference in density.

But it has been possible to give the apparatus such a high degree of symmetry that there were no apparent density differences in the two tubes during the flow of air. Thus, the double observation would not have been necessary. Nonetheless, this second observation has been done for added assurance, and to allay the fear that the displacement being looked for could have been accidentally compensated by a small difference in density, which would have masked it completely.

In spite of these precautions, no fringe displacement by air motion could be found.

I estimate that a displacement as small as 1/14 of a fringe, produced by the motion of the air, would have been noticed.

Here are the calculations related to this experiment.

Considering the hypothesis where the ether is completely affixed to the air in motion,

$\Delta =4L{\frac {u}{v}}m^{2}=0^{mm},002413,$

where $m^{2}$ is 1.000567 at a temperature of 10°C.

Since the experiment was conducted on air, the maximum lighting is obtained from yellow light rays, and this maximum is the one that determines the width of the fringes. Thus, it is convenient to use for $\lambda$, the value corresponding to ray D. Thus, we have

${\frac {\Delta }{\lambda }}=0,4103.$

page 402