REFLEXION OF POLARIZED LIGHT. 249 



In the system of emission these two angles have no 

 necessary dependence ; the contrary is the case if the 

 luminous rays are sets of waves, and the relation which, 

 in setting out from this hypothesis, one of our most dis- 

 tinguished colleagues has deduced from his scientific- 

 analysis is precisely that which experience has fur- 

 nished. Such an accordance between calculation and 

 observation ought at the present day to take its place 

 among the most forcible arguments which we can pro- 

 duce on which to support the system of vibrations. 



/ m mi \ 



vf = I ) (1.) 



\ m + ml J 



and ml receives a velocity 



It is also assumed that this analogy may be applied to a mass of 

 aether (m) in vibration outside the reflecting surface, and communi- 

 cating its vibrations partly to another mass (m') at rest within the 

 medium; these masses are dependent on and partly retaining it in 

 reflexion. Dependent on the densities, in two contiguous media, and 

 the inclination of the ray. 



At a. perpendicular incidence the two masses are simply proportional 



m 1 

 to the densities or of the refractive powers ; or = 5 hence in. 



this case the velocity of the incident ray being taken as unity, that of 

 the reflected ray will be f - J and according to the principle of 



vis viva the intensity will be proportional to the square of this quantity. 

 This is, however, only a particular case of the general formulas dis- 

 covered by Fresnel, and applying universally to intensities of reflected 

 light at all incidences. The demonstration of these formulas in- 

 volves some difficulties which Fresnel did not clear up, but which he, 

 with marvellous sagacity, got over by suppositions somewhat of an 

 empirical and hypothetical kind. 1 To express the masses of the cor- 

 responding vibrating portions of sether in the two adjacent media, we 

 take lengths I and ft of the incident and refracted rays inversely pro- 



1 See Mr. Airy's Tract of the Undulatory Theory. Art. 12*, 

 et seq. 



11* 



