332 FOUUTH REPORT — 1834. 



M. Poisson applied Fresnel's integral to the case of diffraction 

 by an opaque circular disc, and arrived at the singular result, 

 that the intensity of the light in the centre of the shadow is 

 precisely the same as if the disc were removed. This remark- 

 able anticipation of theory has been verified by the observation 

 of M. Arago*. Fresnel has himself solved the problem in the 

 analogous case of a circular aperture^ and arrived at the result, 

 that the intensity of the light of anj^ simple colour, at the cen- 

 tral spot, will be the same as that reflected by a plate of air, 

 whose thickness bears a certain simple relation to the radius of 

 the aperture, and its distances from the luminous origin and from 

 the eye. With homogeneous light, therefore, the iUumination 

 of the central spot vanishes periodically, as tlie distance of the 

 eye fi'om the aperture is varied ; and in white light it assumes in 

 succession the most vivid and beautiful hues, coinciding with 

 those of the reflected rings of thin plates. These interesting 

 phenomena were observed about the same time by Sir John 

 Herschel, and their laws deduced, independently, from observa- 

 tiont. 



With the exception of the observations now referred to, no 

 attempt has been made to verify the theory, by comparing the 

 intensify/ of the light in the fringes with that deduced from the 

 formulae ; and indeed it is obvious that a comparison of this 

 nature is ill calculated to afford any conclusive evidence on the 

 question. Fresnel thought, however, that the expression for the 

 intensity might be indirectly verified, by superposing two sets 

 of fringes (such as the interior and exterior fringes of a narrow 

 opaque bodj^,) by means of double refraction, and then examin- 

 ing the ])Osition of the new maxima and minima. This ingeni- 

 ous suggestion does not appear to have been acted on. 



The intensity of the light in the partial waves sent from each 

 point of the primary wave, considered as a distinct centre of 

 disturbance, will necessarily be different in different directions, 

 depending on the angle which these directions form with the 

 front of the original wave ; and to solve the problem of diflrac- 

 tion in its most general form, it would be necessary to know the 

 law of this variation. Fi'esnel has shown, however, that the 

 rays whose directions are inclined at sensible angles to the nor- 

 mal to the front of the primary wave, destroy one another by 

 interference; so that the actual effect is produced by rays inde- 

 finitely near that normal, and which therefore may be regarded 

 as of equal intensity. The truth of tliis assumption, however, is 



• Manoirc sur la Diffraction, p. 4G0. f Essay on Light, Art. 729. 



