Aberration in a Dispersive Medium, 131 



is at right angles to that of the earth's motion, and replace 

 the telescope, which would be used in practice, by a pair of! 

 perforated screens, on which the light falls perpendicularly. 

 We may further imagine the luminous disturbance to consist 

 of a single plane pulse. When this reaches the anterior 

 screen, so much of it as coincides with the momentary 

 position of the aperture is transmitted, and the remainder 

 is stopped. The part transmitted proceeds upon its course 

 through the sether independently of the motion of the 

 screens. In order, therefore, that the pulse may be 

 transmitted by the aperture in the posterior screen, it is 

 evident that the line joining the centres of the apertures 

 must not be perpendicular to the screens and to the wave- 

 front, as would be necessary in the case of rest. For, in 

 consequence of the motion of the posterior screen in its own 

 plane, the aperture will be carried forward during the time 

 of passage of the light. By the amount of this motion 

 the second aperture must be drawn backwards, in order 

 that it may be in the place required when the light reaches 

 it. If the velocity of light be V, and that of the earth be v, 

 the line of apertures giving the apparent direction of the 

 star must be directed forwards through an angle equal 

 to vjV." 



If the medium between the screens is dispersive, the 

 question arises in what sense the velocity of light is to 

 be taken. Evidently in the sense of the group-velocity ; 

 so that, in the previous notation, the aberration angle is v/XJ. 

 But to make the argument completely satisfactory, it is 

 necessary in this case to abandon the extreme supposition 

 of a single pulse, replacing it by a group of waves of 

 approximately given wave-length. 



While there can remain no doubt but that Ehrenfest 

 is justified in his criticism,, it does not quite appear from 

 the above how my original argument is met. There is 

 indeed a peculiarity imposed upon the regular wave-motion 

 constituting homogeneous light, but it would seem to be 

 one imposed for the purposes of the argument rather than 

 inherent in the nature of the case. The following analytical 

 solution, though it does not relate directly to the case of 

 a simply perforated screen, throws some light upon this 

 question. 



Let us suppose that homogeneous plane waves are incident 

 upon a "screen" at £ = 0, and that the effect of the screen 

 is to introduce a reduction of the amplitude of vibration in 

 a ratio which is slowly periodic both with respect to the 

 time and to a coordinate x measured in the plane of the 



K2 



