DIFFRACTION. 61 



partial waves, cannot be regarded as sensibly equal in directions 

 inclined to it at very small angles.* Fresnel's reply to this part of 

 M. Poisson's theory has been already referred to. The principle 

 of Huygens itself, which forms the basis of Fresnel's theory, 

 though not denied by M. Poisson, is yet objected to as introducing 

 a needless complication into the question ; and indeed it does not 

 seem easy to understand, at first view, why each point of the pri- 

 mary wave in this mode of composition should not give rise to a 

 retrograde as well as to a direct wave.f 



An objection of a different nature has been raised against 

 Fresnel's theory, derived from its supposed discordance with phe- 

 nomena. It is a consequence of that theory, when applied to the 

 case of diffraction by a narrow aperture bounded by parallel 

 straight edges, that if a point be taken in the axis of the pencil, 

 whose distances measured from the centre and edge of the aperture 

 differ by half a wave, that point will be the limit within which all 

 the interior fringes are confined ; and beyond that point the centre 

 of the image will be always white. This result is confirmed by the 

 previous experiments of M. Biot ; by the observations of Fresnel 

 himself ; and by those of Professors Airy and Powell, by whom 

 they have been since repeated. M. Biot found that the central 

 band was dark and white alternately, to a certain distance from 

 the aperture ; after which it was always white. He remarks that 

 when this limit is attained, we may diminish the breadth of the 

 aperture, and even bring its sides into actual contact, without any 

 change in the central band, except its enlargement and consequent 

 diminution of intensity. J 



Newton's celebrated experiment with the two knife-edges has 

 been adduced in opposition to these results. Newton found that 

 when the distance of these edges was the 400th part of an inch, 

 the light which passed between the knives parted in the middle, 



* It may be necessary to state that it was part of M. Poisson's theory, that tho 

 vibrations are normal to the wave. 



t See Annales de Chimie, torn. xxii. p. 270 ; and Airy's Mathematical Tracts, 

 p. 267. 



} Traits de Physiqut, torn. iy. pp. 749, 760. The description of the phenomenon 

 given by Mayer is very similar : " Prout ilia distantia acierum semper magis magisque 

 imminuitur, fasciae adeo evanescunt, ita ut denique non nisi fascia media remaneat ; 

 sed ad dextram atque sinistram adeo in latitudinem extensa, ut non nisi lumen langui- 

 dum, a medio spectri initialis utrinquc instar caudse cometce sese dilatans, represents." 

 G'dttingen Memoirs, vol. iv. p. 61. 



