REPORT ON PHYSICAL OPTICS. 337 



prism. This fact appears to be decisive against the Newtonian 

 theory of inflexion, hi which inflexion and refraction are referred 

 to the same cause. 



The analytical investigation of the problem of difi'raction in 

 the cases last alluded to, — those, namely, in which a lens is 

 combined with the aperture, and the intensity of the light is 

 sought at any point of a parallel plane passing through the focus, 

 — is far more manageable than in most other cases. The gene- 

 ral expression of the displacement is at once integrated with 

 respect to one of the variables, and the complete integral can, 

 in many cases, be exactly found. Professor Airy has given the 

 solution of this problem in his valuable tract on the Undulatory 

 Theory*, and in applying it to the phenomenon last mentioned 

 has deduced all the appearances observed by Fraunhofer. The 

 remarkable appearance of the six-rayed star, observed by Sir 

 John Herschel, when a triangular diaphragm was placed before 

 the object-glass of a telescope, has been likewise deduced as 

 another case of the same problem. 



The same effects, Fraunhofer observed, were produced by re- 

 flexion from grooved surfaces ; and their theory is to be referred 

 to the same principles, the light reflected from the surfaces 

 between the grooves interfering in a manner precisely analogous 

 to that admitted through the apertures of the gratings. The 

 colours exhibited by such surfaces under ordinary circumstances 

 were observed by Boyle and Grimaldi ; Young showed that they 

 were consequences of the principle of interference, and deter- 

 mined the law of their recurrence depending on the incidencef ; 

 and Sir David Brewster seems to have been the first to observe 

 that the spectra formed in these cases of multiplied diffraction 

 approached the solar spectrum in purity, far more nearly than 

 the ordinary diffracted bands, or the coloured rings of Newton. 

 These phenomena indicate the superficial structure more uner- 

 ringly, perhaps, than the most powerful microscopes. Among 

 the most important and beautiful instances of this application 

 of optical science may be ranked the analysis of the colours of 

 mother-of-pearl J, and the investigation of the structure of the 

 crystalline lenses of the eyes of fishes and other animals, by 

 Sir David Brewster §. The same author has also described a new 

 series of periodical colours, which are exhibited by some of the 

 plates of grooved steel constructed by Mr. Barton, and which suc- 



* Math. Tracts, p. 321, &c. . - 



t " On the Theory of Light and Colours," Phil. Trans. 1801. 

 : Phil. Trans. 1814. § Ibid. 1833. 



1834. Z 



