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 It is known that the ordinary phenomenon of refraction is due to the fact that the speed of propagation of light in the interior of bodies is less than in a vacuum. Fresnel admits that this change in speed takes place because the ether possesses a greater density in the interior of bodies than in vacuum. In the case of two media with the same elasticity but different densities, the squared powers of the speeds of propagation are in inverse proportion to the densities. Thus we have

$\frac{D'}{D}=\frac{v^{2}}{v'^{2}}$|undefined

in which D and D' are the densities of the ether in vacuum and in the body, and v and v' are the corresponding propagation speeds, respectively. Consequently,

$D'=D\frac{v^{2}}{v'^{2}}$ and $D'-D=D\frac{v^{2}-v'^{2}}{v'^{2}}$.|undefined

This last expression gives the excess density of the interior ether.

If the body is set in motion, only a part of the interior ether is set in motion with the body; this is the portion that has a greater density than that of the surrounding ether. The density of this mobile portion is expressed by D' - D. The other portion of the ether, which remains immobile while the motion takes place, has a density D.

What is the speed of propagation of the waves in this type of medium — a portion in motion and a portion motionless — supposing, for simplicity's sake, that the body moves in the direction of propagation of the waves?

Fresnel considers that the speed assumed by the center of gravity of the system is added to the speed of propagation of the waves.

If u is the speed of the body, $$u\left(\tfrac{D'-D}{D'}\right)$$ will be the speed of the center of gravity of the system, and from preceding considerations, this expression is equal to