Waves hy a moving perfect Reflector- 703 



the definite analogical system formed by a stretched cord 

 transmitting transverse waves) leads in fact to the result that 

 the pressure on the reflector is equal to the energy density in 

 front of it multiplied by a reducing factor [c" — v 2 )\ (c 2 + v 2 ). 

 Mr. Edser challenges this result on p. 513. But it appears 

 from his discussion that he is considering a reflector moving 

 up into the radiation instead of one receding from it ; in that 

 case the reflexion piles up the radiation as it advances, and 

 to an infinite degree when it advances with the velocity of 

 radiation, — which of course no one would deny. 



I have been for long aware that the general problem of 

 reflexion from a moving reflector, with which Mr. Edser's 

 paper is mainly concerned, involves considerations as to the 

 relation of aether to moving matter, which it would be inter- 

 esting to disentangle. But as the modification introduced in 

 the law of radiation pressure, which is the main object of the 

 theory, seemed to be of the order (v/c) 2 , nothing substantial 

 appeared to be obtainable without much complication : for it 

 would thus rank with the other second-order phenomena, 

 which either require the introduction into the analysis of 

 the FitzGerald-Lorentz deformation of material media pro- 

 duced by their motion through nether or, alternatively, involve 

 the complexities of the relativity-theories. 



It will assist and test ideas, however, to pursue to some 

 degree the problem of oblique reflexion. It will suffice for 

 present illustration to restrict it, following Mr. Edser, to a 

 reflector moving with only translational velocity, and that at 

 right angles to its own plane. 



The law of reflexion of the rays, and the law of the change 

 in their wave-length, are a purely kinematic affair, independent 

 of dynamics of propagation. Thus if, following Mr. Edser' s 

 equations (13) and (14), the properties of the incident 

 wave-train, travelling now towards x positive, are defined as 

 functions of m(x cos # + // sin — ct). and those of the reflected 

 as functions of m'(#cos 6'+// sin 0' + ct), the quantities in- 

 volved in these arguments must satisfy the condition that the 

 waves pass along the reflecting surface oc=vt in step. Now 

 when vt is put for a?, these arguments become m(y cos — c)t 

 + my sin 6 and m'(v cos 0' -f c)t + m'y sin 0' ; and these must 

 therefore be equal. Hence 



c + v cos 0' _ sin 0' __ m 



c — vcos0 sin m r ' ' ' \ J 



To determine the relation between the amplitudes of the 

 waves, the structural interfacial conditions must enter. If 

 v/c is small, we can apply general electric principles. For 



