SECT. XXIII. OBJECTIONS BEHOVED. 199 



SECTION XXIII. 



Objections to the Undulatory Theory, from a difference in the Action of 

 Sound and Light under the same circumstances, removed The Disper- 

 sion of Light according to the Undulatory Theory Arago's final proof 

 that the Undulatory Theory is the Law of Nature. 



THE numerous phenomena of periodical colours arising from the 

 interference of light, which do not admit of satisfactory explana- 

 tion on any other principle than the undulatory theory, are the 

 strongest arguments in favour of that hypothesis ; and even 

 cases which at one time seemed unfavourable to that doctrine 

 have proved upon investigation to proceed from it alone. Such 

 is the erroneous objection which has been made, in consequence 

 of a difference in the mode of action of light and sound, under 

 the same circumstances, in one particular ID stance. When a 

 ray of light from a luminous point, and a diverging sound, are 

 both transmitted through a very small hole into a dark room, 

 the light goes straight forward and illuminates a small spot on 

 the opposite wall, leaving the rest in darkness ; whereas the 

 sound on entering diverges in all directions, and is heard in 

 every part of the room. These phenomena, however, instead of 

 being at variance with the undulatory theory, are direct conse- 

 quences of it, arising from the very great difference between the 

 magnitude of the undulations of sound and those of light. The 

 undulations of light are incomparably less than the minute 

 aperture, while those of sound are much greater. Therefore 

 when light, diverging from a luminous point, enters the hole, 

 the rays round its edges are oblique, and consequently of dif- 

 ferent lengths, while those in the centre are direct, and nearly 

 or altogether of the same lengths. So that the small undula- 

 tions between the centre and the edges are in different phases, 

 that is, in different states of undulation. Therefore the greater 

 number of them interfere, and by destroying one another pro- 

 duce darkness all around the edges of the aperture ; whereas the 

 central rays, having the same phases, combine, and produce a 

 spot of bright light on a wall or screen directly opposite the hole. 



