21^ Astronomicat and Nautical Collections 



exactly similar for the two series of vibrations wliicli are pro- 

 pagated in the parallel directions, D/ and Gk, the intensities 

 of these will always be the same, as well as the directions of 

 the elementary motions ; and since these undulations differ in 

 their progress by half an undulation, their motions will neu- 

 tralise each other : and it will be impossible that any lumi- 

 nous oscillation should become sensible in the second medium, 

 except in that direction which makes such an angle of refrac- 

 tion, that its sine shall be to the sine of the angle of incidence 

 as d' is to d. 



In the case of the divergence thus neutralised, it is not 

 only the oscillatory motions that^re destroyed, but also the 

 condensations and dilatations which accompany them: in short, 

 every thing being symmetrical and equal among the quanti- 

 ties with opposite signs that belong to the primitive motions, 

 the same must be true of the elementary undulations which 

 are derived from them: and this equality is sufficient to cause 

 the mutual destruction of all the quantities with contrary 

 signs that are concerned, whether velocities direct and retro- 

 grade, or condensations and dilatations, when any one of the 

 positive quantities is neutralised by a corresponding negative 

 quantity; or when there is a difference of half an undulation 

 in the lengths of the paths described. 



It may here be remarked again, as In the case of reflection, 

 that when the surface AB is not infinite, some elementary 

 rays are always emitted by its extremities^ which are not 

 totally destroyed, unless the intervals, hke GD, answering 

 to the difference of a semiundulation, that are contained in 

 DL, happen to be in even number within the extent of the 

 surface. But when this breadth Is at all considerable, 

 the diffracted light, that spreads from the edges, is much 

 fainter than that which has been regularly refracted. For 

 further details of this theory of refraction, the reader is re- 

 ferred to the Notes on the Memoir in the Collection of the 

 Savans Etr angers. 



When the velocity of the propagation of light remains the 

 same in all directions, for the same medium, the relation of 

 d to d, and consequently that of the sines of the angles of 

 incidence and refraction, remains constant, and the light fol-. 

 lows the well known law of ordinary refraction. But there 



