510 Convection Coefficient in a Dispersive Medium. 



Mr. Cunningham in ' The Principle of Relativity,' p. 63. A 

 fin 's a different expression, the quantity in brackets being 



1 5 ^ instead of that given above. This is obtained 



fjb 2 fid\ ° 



by comparing the period in the moving medium to an 



observer at rest in S' with what it would appear to an 



observer at rest in S, that is to an observer placed so that 



the medium would flow past him with velocity v. But it 



seems to me that the comparison should be between the 



period of the light in S before it falls on the medium to an 



observer in S with the period which it has in the moving 



medium to an observer at rest relative to that medium. 



There are three different periods to which we may refer. 



There is the period, r, of the source of light to an observer at 



rest in S. This is the period to this observer before the 



light falls on the moving medium and after it has left it. 



Then there is the period of the light in the moving medium 



to an observer moving with it, and there is the period of the 



light in the mo vino- medium to an observer at rest in S. By 



applying the formulas of transformation of special relativity 



these periods are found to be, respectively, 



. /— 



V c — v 



j c + v 



and t 



C ■+- fjLV 



Mr. Cunningham uses the ratio of the first of these latter 



to the second, that is — - " or 1+ — , if we neglect the 

 square of v. \/ c —v 



On p. 44 of Mr. Cunningham's ' Relativity and the Electron 

 Theory/ a reference is made to experiments of Zeeman to 

 determine the value of a:, the quantity in brackets, and a 

 table is given showing an excellent agreement for certain 

 wave-lengths between Zeeman's results and those calculated 

 from Mr. Cunningham's formula. 



The most careful experiments on the dispersion of light in 

 wator seem to have been made by E. Flatow (1903), but I 

 find that his results in the region of the visible spectrum 

 agree closely with those calculated from the formula of 

 Martens (1901). This formula is 



where a = l"76148, c=-0134M 5 6 = '0065438,/3 = -11512,and 

 X •= wave-length x 10 4 . 



