A convenient method of examining the variation of the fringes, 

 whether of reflexion or of flexion, at various distances, is to incline 

 the screen upon which they are received, so that it crosses the rays 

 forming the fringes, which are exhibited upon it, at various distances 

 from the edges. The line which each fringe describes being the 

 projection of the line which the rays follow that form the fringe, we 

 can in this manner observe if the course of these rays after flexion is 

 rectilinear or curvilinear, the projection being, generally speaking, a 

 line of the same kind with the original line ; and at least never rec- 

 tilinear if that original line is curvilinear. 



If y=/ (^) be the line which the rays follow after flexion ; (p the 



sin (jj 



angle of the screen's inclination ; ; = m ; and the abscissae of 



^ cos (p 



the line of projection ; then its equation is y—f{ V \-\-w:^ . :c^). If 

 the curve of the rays be supposed to be the equilateral conic hyper- 

 bola, the radius of curvature in the curve of projection, it is stated, 

 must be less than that in the original line ; and so the curvature 

 is more easily discerned by the eye. As under no circumstances of 

 inclination of the screen, and at no part whatever of the course of the 

 fringes could the author perceive the least diflerence of form from all 

 the other parts, he infers, either that the rays follow a rectilinear 

 course, or that their deviation from it must be very small. 



Though the phenomenon seem to indicate a crossing of the rays 

 both in flexion and reflexion, at or near the distance at which the 

 dark or deep purple line is formed, yet the author has never been 

 able to observe that an obstacle placed between that point and the 

 speculum (or the bending edges), made the fringes on the opposite 

 side of the disc at the screen to disappear, but only the fringes on 

 the same side with itself. 



Referring to Fresnel's memoir, the author states that the principle 

 laid down in it, that the dilatation of the fringes depends solely upon 

 the breadth of the aperture," will not afl^ord an explanation of the 

 phenomena described in his former paper respecting fringes formed 

 by edges acting in succession, for he there showed that their breadth 

 and their distances from the direct rays are in the inverse proportion 

 of the distance of the edges ; and if the edges are so placed that the 

 rays pass parallel to each other, and not diverging, and the edges are 

 moved to difl'erent distances in the same line, e. g. horizontally, then 

 their distance from each other vertically being the same, the aperture 

 is the same at all distances of the edges from each other horizontally, 

 and yet the breadth of the fringes is inversely as the horizontal di- 

 stance. Further, where the edges are not placed in succession, but 

 directly opposite to each other, the breadths of the fringes do not 

 appear to follow the exact inverse proportion of the distances of the 

 edges (that is the size of the aperture), the observed breadths corre- 

 sponding more nearly with the curve y=—+ — , ^ being the distance 



of the edges, and y the breadth of the fringes. 



The author considers that the internal fringes, or those of the 



