Mr. J. Bridge on the Diffraction of Light. 327 



sponding points lie at distances inversely as the I'adii of the 

 circles. Therefore corresponding points in different directions 

 in the case under consideration will lie at distances which are 

 inversely as the perpendiculars (from centre on tangent), and 

 therefore proportional to the normals, which have those direc- 

 tions ; but using the ordinary notation in conic sections, 



6^ "*■ «2 -«2- 



The curves are therefore concentric ellipses similar to the aper- 

 ture, turned through a right angle. 



The preceding paragraph applies to an aperture of the form 

 of the difference between two similar concentric ellipses, com- 

 parison being made by means of circular aunuli. 



To find the effect of an aperture of the form of the difference 

 between two similar concentric hyperbolas, we may proceed as 

 in the case of the ellipse, except that instead of a circle, or cir- 

 cular annulus, we must use a pair of equilateral hyperbolas 

 whose axis is in the given direction. The result will then be 

 that the figure obtained is a series of hyperbolic bands, having 

 asymptotes at right angles to those of the aperture, but occiipy- 

 ing the supplemental angle, in fact similar to the conjugate 

 hyperbola, turned through a right angle. 



The image produced by an aperture of the form of the differ- 

 ence between two equal parabolas, or several such bands, on the 

 same axis is a series of parallel coloured straight bands. As 

 before, let every chord perpendicular to a given line be moved 

 in the direction of its length, so that their middle points may all 

 lie in the given line; then let them all be altered so as to make 

 parabolas of given form. The resulting parabolic strips will 

 then be similar, and the distances of corresponding points in the 

 figure of diffraction in different directions will be inversely as the 

 distance between the vertices, that is, inversely as the perpen- 

 dicular distances in each dii'ection between parallel tangents in 

 the original parabolas ; but these are proportional to the nor- 

 mals ; and as the subnormal is constant, corresponding points 

 will lie in a straight line perpendicular to the axis of the pai'a- 

 bolas. The figure is therefore a series of parallel bands. 



(14) Taking the results for single apertures, those for any ar- 

 rangement of such apertures may be found by means of (8). 



Thus a pair of circular annuli give concentric rings crossed 

 by dark bands perpendicular to the line through the centres of 

 the apertures. 



Three circular annuli give concentric rings containing maxima 

 of brightness and points of darkness, each arranged in triangular 

 order. When the annuli are more numerous and regularly 



