161 



described in that paper, and the attempt there made to refute the 

 theory of interferences, he remarks, that the theory of interferences 

 explains perfectly both the internal and external fringes of a shadow ; 

 that the breadth of the fringes has no dependence on the length of 

 route of the rays, but it has on the angle at which they intersect ; 

 and that interference also perfectly explains the fringes, even when 

 the action is wholly on one side of the ray or edges. 



Passing from these points of confessedly less importance, the 

 author proceeds to consider the most material and fundamental ex- 

 periment, in which, when fringes are formed by the edge of an opake 

 body, if a second edge be placed at a greater distance along the ray, 

 from the origin, on the same side as the first edge, it produces no 

 change in the fringes ; but on the opposite side it does, the fringes 

 being shifted in position towards the first side ; or, in other words, 

 that the second edge, in the one case, has no power of producing 

 further diffraction, in the other it has ; and which has been viewed 

 as supporting the theory of a peculiar action exerted by the edge 

 upon the ray passing near it, by which it is disposed or indisposed 

 for further ^^e^^wre- according to the conditions just expressed. 



With reference to the edges on opposite sides, he observes, that 

 when they are at the same distance from the origin, and form there 

 a narrow aperture, they give (as is well known) fringes on each side 

 extending into the shadow, with a white centre. As one edge is 

 removed successively further from the origin along the ray and nearer 

 to the screen, the fringes on that side dilate, become faint, and at 

 length disappear ; so that beyond a certain distance there remain 

 only the fringes on the other side, or on that of the edge nearest 

 the origin ; which diverge further into the shadow on that side as 

 the breadth of the effective aperture is diminished. In this way, 

 then, the second edge, if beyond the limits of distance just men - 

 tioned, will cause an appearance of fringes on the side towards the 

 first edge, diverging into the shadow. 



When the two edges are at the same distance from the origin, 

 forming a narrow aperture, the nature of the fringes is perfectly ex- 

 plained and reduced to quantitative results by Fresnel's theory. 

 When the second edge is placed at a greater distance along the raj^ 

 this would be equivalent to a wide aperture placed obliquely to the 

 direction of the ray, so as to be effectively as narrow as before. On 

 the undulatory theory, this particular case has not been actually re- 

 duced to calculation, and it appears that it would certainly involve 

 most complicated and difficult analysis to do so. It has however 

 been treated in a general way by Fresnel himself (Memoire sur la 

 Diffraction, Mem. de I'lnstit., tom. v. note, p. 452), who points out 

 the general conditions for determining the condition of a fringe, and 

 shows that the fringes will in this case undergo a modification, and 

 will not be symmeti^ical, but more expanded on one side than on the 

 other ; which exactly agrees with observation. 



After some remarks having the same bearing on other facts and 

 propositions in the paper referred to, the author concludes by ob- 

 serving, — I have thus, I trust, with perfect impartiality, gone through 



