Royal Society. 231 



of light and is inclined so that the reflected rays shall make a small 

 angle with the surfaces. Near the speculum the axis of reflected 

 rays coincides with that of the direct rays, but at a greater distance 

 the two discs are separate. The speculum being placed horizontally 

 across the pencil, coloured fringes appear both on the upper and lower 

 side of the reflected disc. These two sets of fringes are alike in their 

 colours and in the order of their colours, but the upper fringes are 

 narrower than the lower, and they diminish in breadth with their 

 distance from the disc, while the lower ones increase in breadth with 

 their distance. If only one edge of the speculum is in the pencil 

 there are only fringes on one side of the disc. 



It appears that the breadth of the fringes is in some inverse pro- 

 portion to the breadth of the speculum. When the speculum is a 

 triangle with a very acute angle, the broadest fringes, and those most 

 removed from the disc, answer to the points of the speculum where 

 it is narrowest, and they increase regularly towards the point which 

 answers to the acute angle or apex of the speculum. Their form is 

 hyperbolic. 



When the edges of the speculum are parallel, the disc near to it 

 is filled with groups of fringes which vary in number, in breadth and 

 in colour, at all the distances from the speculum. At one distance 

 they form only a dark line running through the disc, and this is deep 

 purple when examined closely. At a greater distance the fringes 

 have other colours, and become broader again ; and at a still greater 

 distance they emerge into the shadow on bath sides of the disc. 



The phenomena of reflexion, it is stated, closely resemble those of 

 flexion, as to the fringes, their colours, their magnitude, their varia- 

 tion at diff"erent distances from the bending edges, and at diflerent 

 distances of those edges from each other. 



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 vai-ious 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 curviHnear. 



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



sin <b 

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



° cos 



the line of projection ; then its equation is y=.f['/\ -\-ni- . a?'). 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 tlie original line ; and so the curvature 

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

 inclination of tiie screen, aud at no part whatever of the course of the 

 fringes could the author perceive tlie least diflcrence of form from all 

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

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



