•"^OS FOURTH REPORT — 1834. 



phase. Consequently, as the direction of the refracted ray de- 

 pends on its velocity, the transmitted beam will consist of rays 

 refracted in widely different angles, and will be scattered and 

 irregular. 



In some of his writings Newton attributes the reflexion and 

 refraction of light to a difference in the density of the ether 

 within and without bodies ; or rather he refers the attractive 

 and repulsive forces to this, as to a more general principle. The 

 ether is supposed to be rarer within dense bodies than without, 

 and the rays of light, in crossing the bounding surface, are 

 pushed from the side of the denser ether ; so that their motion 

 is accelerated if they pass from the rarer to the denser body, 

 and retarded in the opposite case. Reflexion at the surface of 

 the rarer medium is explained on the same suppositions ; but, 

 to account for the ordinary reflexion by a denser medium, 

 Newton Avas obliged to introduce new and gratuitous hypotheses 

 respecting the constitution of the ether at the confines of two 

 media in which its density is different*. 



The velocity of propagation, in the wave-theory of light, de- 

 pends solely on the elasticity of the vibrating medium as com- 

 pared with its density. If, then, • a plane wave be incident ob- 

 liquely on the bounding surface of two media, it is obvious that 

 its several portions will reach that surface at different moments 

 of time ; and each of these portions will become the centime of two 

 spherical waves, one of which will be propagated in the first me- 

 dium with the original velocity, while the other will be propa- 

 gated in the new medium, and with the velocity which belongs 

 to it. But, by the principle of the coexistence of small motions, 

 the agitation of any particle of either medium is the sum of the 

 agitations sent there at the same instant from these several cen- 

 tres of distui'bance ; and the surfaces on which they are accumu- 

 lated at any instant will be the reflected and refracted waves. 

 These surfaces are those which touch all the small spherical 

 waves at any instant. It is easy to see that they are both plane ; 

 and that the reflected wave is inclined to the surface at the same 

 angle as the incident wave, while the sine of the angle of incli- 

 nation of the refracted wave is to that of the incident in the con- 

 stant ratio of the velocities of propagation in the two media. 



Such is the demonstration of the laws of reflexion and re- 

 fraction given by Huygens f . The composition of the grand, or 

 primary wave, by the union of the several secondary or partial 

 waves, in this demonstration, has been denominated the princi- 

 ple of Hnt/getis ; and it is obviously a case of the more general 



* Birch's Hintori/ of the lioyal Sociefi/, vol. iii. p. 247. Optics, Query 19. 



I Tni'itl; lie la Litmiire. 



