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 ml \ 



v , ( 



and mf receives a velocity 



(2.) 



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 vfbrations partly to another mass (mf) 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 si perpendicular incidence the two masses are simply proportional 



TO 1 

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



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

 the reflected ray will be ( - - 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 asther in the two adjacent media, we 

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



1 See Mr. Airy s Tract of the Undulatory Theory. Art. 128, 

 et seq. 



11* 



