REFLEXION AND REFRACTION. 35 



to interpose a column of water between the mirrors, to observe 

 the deviation, and to calculate the velocity. 



Let e denote the length of the water tube, and a (as be- 

 fore) the interval of the two mirrors. Then, Y being the ve- 

 locity of the light in the compound path, determined by the 

 preceding method, it is obvious that 



a _ a - e e 

 V ~ ~~~ + 7' 



r and v' being the velocities in air, and in water, respectively. 

 But experiments with the revolving mirror give the values 

 of V and v ; therefore v', the velocity of light in water, is 

 known. By these means Foucault and Fizeau established 

 the fact, that the velocity of light is less in water than 

 in air, in the inverse proportion of the refractive indices. 

 The result is, therefore, decisive in favour of the wave- 

 theory. 



(43) The refractive index being equal to the ratio of 

 the velocities of light in the two media, whichsoever 

 theory we adopt, it follows that any change in the velocity 

 of the incident ray must cause a variation in the amount 

 of refraction, unless the velocity of the refracted ray be al- 

 tered proportionally. Now the relative velocity of the light 

 of a star is altered by the Earth's motion ; and the amount 

 of the change is obviously the resolved part of the Earth's 

 velocity in the direction of the star. It was, therefore, a 

 matter of much interest to determine how, and in what de- 

 gree, this change affected the refraction. The experiment 

 was undertaken by Arago, at the request of Laplace. An 

 achromatic prism was attached in front of the object-glass of 

 the telescope of a repeating circle, so as to cover only a por- 

 tion of the lens. The star being then observed, directly through 

 the uncovered part of the lens, and afterwards in the direc- 



D2 



