from Bradley to FresneL 133 



As in his previous investigations, he assumes that the 

 vibrations which constitute light are executed at right angles 

 to the plane of polarization. He adopts Young's principle, that 

 reflexion and refraction are due to differences in the inertia of 

 the aether in different material bodies, and supposes (as in 

 his memoir on Aberration) that the inertia is proportional to 

 the inverse square of the velocity of propagation of light in 

 the medium. The conditions which he proposes to satisfy at the 

 interface between two media are that the displacements of the 

 adjacent molecules, resolved parallel to this interface, shall be 

 equal in the two media ; and that the energy of the reflected 

 and refracted waves together shall be equal to that of the 

 incident wave. 



On these assumptions the intensity of the reflected and 

 refracted light may be obtained in the following way : 



Consider first the case in which the incident light is 

 polarized in the plane of incidence, so that the displacement is 

 at right angles to the plane of incidence ; let the amplitude 

 of the displacement at a given point of the interface be / 

 for the incident ray, g for the reflected ray, and h for the 

 refracted ray. 



The quantities of energy propagated per second across unit 

 cross-section of the incident, reflected, and refracted beams are 

 proportional respectively to 



where c b c 2 , denote the velocities of light, and p l} p z the densities 

 of aether, in the two media ; and the cross-sections of the beams 

 which meet the interface in unit area are 



cos i, cos i, cos r 



respectively. The principle of conservation of energy therefore 

 gives 



c,p! cos i ./ 2 = c,/o! cos i . g z + c 2 /o 2 cos r . h~. 



The equation of continuity of displacement at the interface is 



/ + 9 = h. 



