Page:1860 Fizeau en.djvu/13

was not accidentally compensated by a difference of density, which, though small, might be sufficient totally to mask such displacement.

Notwithstanding these precautions, however, no displacement of the bands occurred in consequence of the motion of the air; and according to an estimate I have made, a displacement equal to one-tenth of the breadth of a band would have been detected had it occurred.

The calculations with respect to this experiment are as follows. Under the hypothesis that the air, when moving, carries with it all the æther, we have

${\displaystyle \Delta =2L{\frac {u}{v}}m^{2}=0.002413}$

${\displaystyle m^{2}}$ being equal to 1.000567 at the temperature 10° C.

This experiment having been made in air, the maximum illumination was due to the yellow rays; and this maximum determined the breadth of the bands. Hence the value of ${\displaystyle \lambda }$ corresponding to the ray D being taken, we have

${\displaystyle {\frac {\Delta }{\lambda }}=0.4103.}$

Now so great a displacement could certainly not have escaped observation, especially since it might have been doubled by reversing the current.

The following would be the results of the calculation according to the hypothesis of Fresnel: —

${\displaystyle \Delta =2L{\frac {u}{v}}\left(m^{2}-1\right)=0.0000001367}$

${\displaystyle {\frac {\Delta }{\lambda }}=0.0002325.}$

Now a displacement equal to ${\displaystyle {\tfrac {1}{5000}}}$th of the breadth of a band could not be observed; it might, in fact, be a hundred times greater and still escape observation. Thus the apparent immobility of the bands in the experiment made with moving air may be explained by the theory of Fresnel, according to which the displacement in question, although not absolutely zero, is so small as to escape observation.

After having established this negative fact, and seeking, by means of the several hypotheses respecting æther, to explain it as well as the phenomenon of aberration and the experiment of Arago, it appeared to me to be necessary to admit, with Fresnel, that the motion of bodies changes the velocity with which light traverses them, but that this change of velocity varies according to the energy with which the traversed medium refracts light; so