32 REFLEXION AND REFRACTION. 



scribed in the least possible time, by a body moving from 

 any point on the incident to any point on the reflected or 

 refracted ray." If I therefore denote the length of the path 

 described by the incident light, between any assumed point 

 and the point of incidence, I' the corresponding length of the 

 path described by the refracted light, and v and v' the velo- 

 cities of propagation in the two media, the sum of the times, 



/ I' 



- + -, is a minimum ; or, multiplying by v, and denoting 



the ratio - by ^, 



/+ i 1 = minimum. 



The constant factor, /j, is the refractive index of the medium. 

 In the case of reflexion, ju = l, and Z+Z' is a minimum. 

 The course pursued by a reflected ray is therefore such, that 

 the sum of the paths described between any two points and 

 the reflecting surface is the least possible. 



(39) The intensity of the light, in the reflected and re- 

 fracted waves, will depend on the relative densities of the 

 ether in the two media. For we may compare the contiguous 

 strata of ether in these media to two elastic bodies of diffe- 

 rent masses, one of which moves the other by impact ; and it 

 is easy to deduce, on this principle, the intensities of the 

 reflected and refracted lights in the case of perpendicular 

 incidence. 



(40) On reviewing what has been said, we cannot but be 

 struck by the remarkable fact, that theories so widely opposed 

 as the theory of emission, and that of waves, should lead 

 mathematically to the same result. According to both, we 

 have seen, the ratio of the sines of incidence and refraction is 

 equal to the ratio of the velocities of light in the two media, 



