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LX. TJie Convection Coefficient in a Dispersive Medium. 

 By Prof. A. Andekson *. 



WHEN a transparent medium, such as the water in 

 Fizeau's experiment, is in motion with velocity v 

 away from a source of light, the velocity of light in it to 

 an observer moving with the medium is c///, where a ! is the 

 index of refraction of the medium for the light that passes 

 through it. We may regard the source of light as at rest 

 in a system S and the medium as at rest in a system S' 

 moving relative to S with velocity v. 



Let the period of the light of the source (which is at rest 

 in S) to an observer in S be r ; then, to an observer in S', 



v 

 the period is t + 8t, where Br= -r. This is an example of 



Doppler's principle. Hence if /u, is the index of refraction 

 of the medium for light of period t, 



, d/jb v 



V* ==/* + j~ - ~ T - 



r dr c 



If the medium is in motion towards the source with 

 velocity v, 



, da V 



ft =/*-— . -T. 



dr c 

 The velocity to an observer in S of the light in the medium 

 moving away from the source is, by the well-known formula 

 of special relativity, 



the square of v being neglected. 



If the medium is moving towards the source the velocity 

 of light in it to an observer in S is cJ\x — kv. 



Now if I is the total length of the water path in Fizeau's 

 experiment the difference of path measured is 

 / I 2lu?v 



—, ; = — • fC 



C//JU—KV C/fJU + V C M 



2lfi 2 v 





or 



p- fjr 



21 a' 2 v /, 1 



a' 2 v / 1 X dfju\ 



c a \ jju 1 \ir ' dX/' 



where X is the wave-length in air of the light leaving the 

 source. 



* Communicated by the Author. 



