Radiation Pressure. 395 



equal amplitudes. Suppose now that the reflector is moving 

 forwards towards the source. By Doppler's principle, the 

 waves of the reflected train are shorteued, and so contain 

 more energy than those of the incident train. This extra 

 energy can onlv be accounted for by supposing that there is 

 a pressure against the reflector, that work has to be done in 

 pushing it forward. When the velocity of the reflector is 



small, the pressure is easily found to be equal to E ( 1 + -yf ) 



E . . 



where - } is the energy-density just outside the reflector in 



the incident train, U is the wave-velocity, and u the velocity 

 of the reflector. If u = 0, the pressure is E ; but it is altered 



by the fraction -yr when the reflector is moving, and the 



alteration changes sign with u. A similar train of reasoning 

 gives us a pressure on the source, increased when the source 

 is moving forward, decreased when it is receding. 



It is essential, I think, to Larmor's proof that we should be 

 able to move the reflecting surface forward without disturbing 

 the medium except by reflecting the waves. In the case of 

 light-waves it is easy to imagine such a reflector. We have 

 to think of it as being, as it were, a semipermeable membrane, 

 freely permeable to aether, but straining back and preventing 

 the passage of the waves. In the case of sound-waves, or of 

 transverse waves in an elastic solid, it is not so easy to picture 

 a possible reflector. But for sound-waves I venture to suggest 

 a reflector which shall freeze the air just in front of it, and 

 so remove it, the frozen surface advancing with constant 

 velocity it. Or perhaps we may imagine an absorbing surface 

 which shall remove the air quietly by solution or chemical 

 combination. In the case of an elastic solid, we may perhaps 

 think of the solid as melted by the advancing reflector, the 

 products of melting being passed through pores in the surface 

 and coming out to solidify at the back. 



Though Larmor's proof is quite convincing, it is, I think, 

 more satisfying if we can realize the way in which the pressure 

 is produced in the different types of wave-motion. 



Jn the case of electromagnetic waves, Maxwell's original 

 mode of treatment is the simplest, though it is not, I believe, 

 entirely satisfactory. According to his theory, tubes of 

 electric and of magnetic force alike, produce a tension length- 

 ways and an equal pressure sideways, equal respectively to 

 the electric and magnetic energy-densities in the tubes. We 

 1 a train of waves as a system of electric and magnetic 

 tubes transverse to the direction of propagation, each kind 



2D2 



