118 The Luminiferous Medium, 



The same result may easily be deduced from an experiment 

 performed by Hoek.* In this a beam of light was divided into 

 two portions, one of which was made to pass 

 through a tube of water AB and was then reflected 

 at a mirror C, the light being afterwards allowed to 

 return to A without passing through the water : 

 while the other portion of the bifurcated beam was 

 made to describe the same path in the reverse 

 order, i.e. passing through the water on its return 



,. journey from C instead of on the outward journey, 



On causing the two portions of the beam to inter- 

 fere, Hoek found that no difference of phase was produced 

 between them when the apparatus was oriented in the direction 

 of the terrestrial motion. 



Let w denote the velocity of the earth, supposed to be 

 directed from the tube towards the mirror. Let c/n denote the 

 velocity of light in the water at rest, and C/A* + <l> the velocity 

 of light in the water when moving. Let I denote the length of 

 the tube. The magnitude of the distance BC does not affect 

 the experiment, so we may suppose it zero. 



The time taken by the first portion of the beam to perform 

 its journey is evidently 



If i 



C/fi + ^ W C + W ' 



while the time for the second portion of the beam is 

 I I 



+ . 



C - W C/fJL - + W 



The equality of these expressions gives at once, when terms 

 of higher orders than the first in w/c are neglected, 



= Ou 2 - 1) w\^\ 

 which is FresneFs expression.! 



* Archives Neerl. iii, 180 (1868). 



t Fresnel's law may also be deduced from the principle that the amount of light 

 transmitted by a slab of transparent matter must be the same whether the slab is at 

 rest or in motion : otherwise the equilibrium of exchanges of radiation would be 

 tiated. Cf. Larmor, Phil. Trans, clxxxv (1893), p, 775. 



