REPORT ON PHYSICAL OPTICS. 331 



the fringes, but that the light which passed by tliose edges at 

 sensible distances was also deviated, and concurred in their for- 

 mation*. 



Fresnel was thus led to seek a broader foundation for his the- 

 ory, and the result of his investigations is given in the able 

 memoir which was crowned by the French Academy in 1819. 

 In this memoir the laws of diffraction are derived from the two 

 principles to which the laws of reflexion and refraction are them- 

 selves referred, — the principle of interference and the principle 

 of Huygens. To apply these principles to the present case, 

 Fresnel supposes the surface of the wave when it reaches the 

 obstacle to be subdivided into an indefinite number of equal 

 portions, and he applies the mathematical laws of interference, 

 unfolded in this memoir, to determine the resultant of all the 

 elementary waves sent by them at the same instant to any point. 

 This resultant is expressed by means of two integrals, which are 

 to be taken within limits determined by the particular nature of 

 the problem. Its square is the measure of the intensity of the 

 light ; and it is found that its value has several maxima and 

 minima which correspond to the intensities of the light in the 

 bright and dark bands. 



The problem of diffraction was thus completely solved, and 

 it only remained to apply the solution to the principal cases, and 

 to compare the results with those of observation. The cases of 

 diffraction selected by Fresnel are : 1st, The phenomena pro- 

 duced by a single straight edge ; 2nd, By an aperture terminated 

 by parallel straight edges ; and 3rd, By a narrow opaque body 

 of the same form. The agreement of observation and theory is 

 so complete, that the computed places of the several bands sel- 

 dom differ from those observed by more than the 100th part of 

 a millimetre, the case of diffraction by narrow apertures alone 

 excepted. The small differences between observation and theory, 

 in this case, Fresnel ascribes to a false judgment of the eye as 

 to the position of the centre of the dark bands, occasioned by 

 the different intensities of the bright bands on either side ; the 

 minimum always appearing nearer to the brighter light than it 

 really is. The computed places of the bands, in the first case 

 of diffi-action, were found to differ from those deduced from the 

 hypothesis of Young by a small numerical quantitj', the distance 

 of the first dark band being less in the former theory, in the 

 ratio of -936 to unity; but small as the difference is, tlie mea- 

 sures of Fresnel completely decide the questionf. 



• Mcmoire sur la Diffraction de la Lumiere, p. 368. f Jl^'il-, V- 4^0. 



