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. 



i m, mi \ 

 vl = ( . , ) f 1 -) 



and m> receives a velocity 



= 



\ (2.) 



) 



+' 



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

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

 cating its vibrations partly to another mass (ml ) 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 & perpendicular incidence the two masses are simply proportional 



m 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 



^ /* ~ j J. J 



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 cether in the two adjacent media, we 

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



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

 et seq. 



11 * 



