706 Sir J. Larmor on the Reflexion of Electromagnetic 



energy-density multiplied by a factor which involves the first 

 power of v/c. But to get to this he introduces (p. 514) the 

 auxiliary magnetic force due to the motion of an electric 

 held, as formulated by Heaviside in 1885 for reasons of 

 symmetry, a force which does not exist according to the 

 modern electron-theory. The Amperean circuital relation 

 invoked at the top of p. 515 applies to a circuit fixed in 

 aether, not to one moving with the matter ; so it would 

 appear that, for the case of direct incidence, the current- 

 sheet C should be (E — E')/47rc instead of the expression in (9) . 

 The pressure is equal to the intensity of the current-sheet 

 multiplied by the mean magnetic force acting on it, which is 

 i(E-E')/c '; thus it is equal to the value of (E-E') 2 /8ttc 2 

 at the surface, where E, E' are in phase, which averages to 

 the sum of the separate energy-densities of the superposed 

 incident and reflected radiations, the argument being A>alid 

 up to the first order in v/c. 



The argument for the case of oblique incidence is more 

 intricate. At the interface, however, H is tangential and E 

 is normal. The traction on the interface might be presumed 

 to be represented by the force of the magnetic field on the 

 current-sheet H/47T and the force of the electric field on the 

 electric density E/47rc 2 . This makes it along the normal 

 and equal to H 2 /87r-f-E 2 /87rc 2 , where H and E are now the 

 aggregates due to the superposed incident and reflected 

 waves. Averaging leads to the previous result, namely, 

 pressure equal to the total density of radiant energy in 

 front of the reflector, correct up to the first power of v/c 

 inclusive. 



The uncertainty in this way of estimating may be obviated 

 by the more general and precise procedure based on the 

 Maxwell stress-theory. Consider the system consisting of an 

 incident beam of restricted breadth, the reflected beam, and the 

 receding reflector. Draw a boundary, fixed in aether, repre- 

 sented by the dotted curve of the diagram. Then the Maxwell 

 stress exerted from outside over this boundary, together with 

 the force represented by the time-rate of increase of the actual 

 momentum throughout the volume, is equal to the mechanical 

 force exerted by the electric field on the bodies inside the 

 boundary. In time St this momentum is increased by that 

 contained in the layer of breadth v$t which is added to the 

 radiation-space during that time. Now the Maxwell stress 

 at I is a thrust along the beam equal to its energy-density 

 (say e) ; at R it is a like thrust. The actual momentum in 

 each beam is along its direction of propagation and equal to 



