upon the Velocity with which it is traversed by Light. 251 
rapidly. Had it been possible to maintain the velocity of the 
current of water constant for a greater length of time, the mea- 
surements would have been more precise; but this did not 
appear to be possible without considerably altering the appa- 
ratus, and such alterations would have retarded the prosecution 
of my research until the season was no longer favourable for 
experiments requiring solar light. 
I proceed to compare the observed displacement with those 
which would result from the first and third hypotheses before 
alluded to. As to the second hypothesis, it may he at once 
rejected ; for the very existence of displacements produced by the 
motion of water is incompatible with the supposition of an ether 
perfectly free and independent of the motion of bodies. 
In order to calculate the displacement of the bands under the 
supposition that the zther is united to the molecules of bodies 
in such a manner as to partake of their movements, let 
v be the velocity of light in a vacuum, 
v' the velocity of light in water when at rest, 
wu the velocity of the water supposed to be moving in a direc- 
tion parallel to that of the light. It follows that 
v +u is the velocity of light when the ray and the water move 
in the same direction, and 
v'—u when they move in opposite directions. 
If A be the required retardation and E the length of the 
column of water traversed by each ray, we have, according to the 
principles proved in the theory of the interference of light, 
DvD Vv 
A=8(5", ri you) 
v2 
v2 —y?" 
Since wu is only the thirty-three millionth part of v, this expres- 
sion may, without appreciable error, be reduced to 
or 
A=2E~. 
v 
A=2E-. = 
If m= “5 be the index of refraction of water, we have the ap- 
proximate formula 
A=2E = nt. 
Since each ray traverses the tubes twice, the length E is double 
the real length of the tubes, Calling the latter L=1:4875 metre, 
