DIFFRACTION. 65 



may be discerned in the spectra. The distances of these lines, in 

 the diffracted spectrum, are always proportional, whatever be the 

 diffracting substance ; while the ratios of their intervals, or the 

 breadths of the coloured spaces, in the spectra formed by refrac- 

 tion, vary with the nature of the prism. This fact appears to be 

 decisive against the Newtonian theory of inflexion, in which in- 

 flexion and refraction are referred to the same cause. 



The analytical investigation of the problem of diffraction 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 general 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, as Fraunhofer observed, were produced by 

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

 to the same principles, the light reflected from the surfaces be- 

 tween 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 ob- 

 served by Boyle and Grimaldi ; Young showed that they were 

 consequences of the principle of interference, and determined the 

 law of their recurrence depending on the incidence ;f 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 phe- 

 nomena indicate the superficial structure more unerringly, perhaps, 

 than the most powerful microscopes. Among the most important 

 and beautiful instances of this application of optical science may 



* Math. Tracts, p. 321, See. 



t " On the Theory of Light and Colours. "Phil. Tran$. 1801. 



