Radiation Pressure. 399 



simple experiment to illustrate sound-pressure. The sound- 

 waves from strong induction-sparks are focnssed by a concave 

 mirror on a set of vanes like those o£ a radiometer, and when 

 the focus is on the vanes as they face the waves the mill spins 

 round. 



Theory and experiment, then, justify the conclusion that 

 when a source is pouring out waves, it is pouring out with 

 them forward momentum as well as energy, the momentum 

 being manifested in the reaction, the back pressure against 

 the source, and in the forward pressure when the waves reach 

 an opposing surface. The wave train may be regarded as a 

 stream of momentum travelling through space. This view is 

 most clearly brought home, perhaps, by considering a parallel 

 train of waves which issues normally from a source for one 

 second, travels for any length of time through space, and 

 then falls normally on an absorbing surface for one second. 

 During this last second, momentum is given up to the ab- 

 sorbing surface. During the first second, the same amount 

 was given out by the source. If it is conserved in the mean- 

 while, we must regard it as travelling with the train. 



Since the pressure is the momentum given out or received 

 per second, and the pressure is equal to the energy-density 

 in the train, the momentum- density is equal to the energy- 

 density -r- wave-velocity. 



This idea of momentum in a wave train enables us to see 

 at once what is the nature of the action of a beam of light on 

 a surface where it is reflected, absorbed, or refracted, without 

 any further appeal to the theory of the wave-motion of which 

 we suppose the light to consist *. 



It is convenient to consider the energy per linear centi- 

 metre in the beam, and the total pressure force, equal to this 

 linear energy-density, so as to avoid any necessity for taking 

 into account the cross section of the beam. 



Thus, in total reflexion, let a beam AB (fig. 3) be reflected 

 along BC. and let AB = BC represent the momentum in each 

 in length V equal to the velocity of light. 



Produce AB to D, making BD=AB. 



Then DC represents the change in the momentum per 

 second due to the reflexion — the force on the beam, if such 

 language is permissible ; and CD is the reaction, the total 

 light-force on the surface. 



If there is total absorption, let AB (fig. I) represent the 



* A discussion, on the electromagnetic theory, of the forces exerted by 

 lijrht is given by Goldhammer, Ann. der Phys. 1901, 4. p. 483. 



