upon the Velocity with which it is traversed by Light. 258 
whose elasticity is the same, and which differ only in their den- 
sities, the squares of the velocities of propagation are inversely 
proportional to these densities ; that is, 
Dp! v 
Do 
D and D’ being the densities of the ether in a vacuum and in 
the body, and », v' the corresponding velocities. From the above 
we easily deduce the relations 
grag? 
ha al D!—D=D—_— 
ye ea 
the latter of which gives the excess of density of the interior 
ether. 
It is assumed that when the body is put in motion, only a part 
of the interior ether is carried along with it, and that this part 
is that which causes the excess in the density of the interior 
over that of the surrounding ether; so that the density of this 
moveable part is D!—D. The other part which remains at rest 
during the body’s motion has the density D. 
The question now arises, With what velocity will the waves be 
propagated in a medium thus constituted of an immoveable and 
a moveable part, when for the sake of simplicity we suppose the 
body to be moving in the direction of the propagation of the 
waves ? 
Fresnel considers that the velocity with which the waves are 
propagated then becomes increased by the velocity of the centre 
of gravity of the stationary and moving portions of «ther. Now 
u being the velocity of the body, 
D'—D 
D! 
will be the velocity of the centre of gravity of the system in 
question, and according to the last formula this expression is 
equal to 
vy —_ yl2 
2 
uu. 
Vv 
Such, then, is the quantity by which the velocity of light will be 
augmented ; and since v 1s the velocity when the body is at rest, 
nel? inal? 
v 
su and v!— 
v v 
ol + 
su 
will be the respective velocities when the body moves with and 
against the light. 
By means of these expressions the corresponding displacement 
of the bands in our experiment may be calculated in exactly the 
