252 M.H. Fizeau on the Effect of the Motion of a Body 
the preceding formula becomes 
A=41~ m? ; 
v 
and the numerical calculation being performed, we find 
A=0:0002418 millim. 
Such is the difference of path which, under the present hypo- 
thesis, ought to exist between the two rays. 
Strictly speaking, this number has reference to a vacuum, and 
ought to be divided by the index of refraction for air; but this 
index differs so little from unity, that, for the sake of simplicity, 
the correction, which would not alter the last figure by a unit, 
may be neglected. 
The above quantity being divided by the length of an undula- 
tion, will give the displacement of the bands in terms of the 
breadth of one of them. In fact, for a difference of path amount- 
ing to 1, 2,... m undulations, the system of bands suffer a dis- 
placement equal to the breadth of 1, 2, ... m bands. 
For the ray E the length of an undulation is X=0-000526, 
and the rays about it appear to preserve the greatest intensity 
after the light has traversed a rather considerable thickness of 
water. Selecting this ray, then, we find for the displacement 
the value 
5 =0°4597. 
Had, therefore, the zther participated fully in the motion of 
the water, in accordance with the hypothesis under consideration, 
a displacement of 0°46 of a band would have been observed in 
the foregoing experiments. But the mean of our observations 
gave only 0°23; and on examining the greatest particular values, 
it will be found that none approached the number 0:46. 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 ex- 
periment. 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 phenomena of refraction are due 
to the fact that light is propagated with less velocity in the in- 
terior of a body than in a vacuum. Fresnel supposes that this 
change of velocity occurs because the density of the ther within 
a body is greater than that ina vacuum. Now for two media 
