; and on examining the greatest particular values, it will be found that none approached the number
. I may even remark that the latter number ought to be still greater, in consequence of a small error committed in the determination of the velocity of the water; an error whose tendency is known, although, as will soon be seen, it was impossible to correct it perfectly.
I conclude, then, that this hypothesis does not agree with experiment. We shall next see that, on the contrary, the third, or Fresnel's hypothesis, leads to a value of the displacement which differs very little from the result of observation.
We know that the ordinary phænomena of refraction are due to the fact that light is propagated with less velocity in the interior of a body than in a vacuum. Fresnel supposes that this change of velocity occurs because the density of the æther within a body is greater than that in a vacuum. Now for two media whose elasticity is the same, and which differ only in their densities, the squares of the velocities of propagation are inversely proportional to these densities; that is,
and
' being the densities of the æther in a vacuum and in the body, and