by Apertures with Curvilinear Boundaries. 293 



4. Plane Apertures or Screens with undulating or 

 corrugated boundaries. 



The cases of apertures with undulating boundaries are of 

 particular interest. The projection of the boundary of the 

 aperture on the plane of observation being also undulating, 

 its evolute has one asymptote for each point of inflexion of 

 the boundary, and a cusp for each point at which the 

 curvature of the boundary passes through a maximum or a 

 minimum value. Broadly speaking, the general form of 

 the large-angle diffraction pattern is determined by the 

 form of the evolute. This is illustrated by fig. b in the 

 Plate, which refers to a case in which the aperture was 

 bounded by three arcs, each of which contained a point of 

 inflexion. The three asymptotic lines limiting the form 

 of the pattern can clearly be made out. 



Figs, g and j in the Plate show the distribution of 

 luminosity within the shadow of a disk having 12 undula- 

 tions in its margin (this was an one-anna nickel coin J. The 

 concentration of luminosity along the evolute (with 12 cusps) 

 of the geometrical boundary of the shadow is clearly seen. 

 Parallel to the evolute run a series of alternately dark and 

 bright fringes of decreasing luminosity, and radial brushes 

 of light also emerge from the cusps of the evolute. 



Fig. i shows the distributions of luminosity inside the 

 shadow of a square screen with rounded corners. 



When the undulations are so very numerous and close 

 together as to form corrugations of very small radius of 

 curvature, interesting new phenomena arise. Fig. k shows 

 the observed distribution of illumination within the shadow 

 of a circular disk having a milled edge. The total number 

 of corrugations on the circumference was 162, and the dia- 

 meter of the disk was 2*94 cm. In addition to a central spot 

 analogous to that observed in the well-known Fresnel-Arago 

 circular disk experiment, we have a circular ring rather 

 brighter than the central spot at a considerable angular 

 distance from it, and one or two other fainter rings farther 

 outside. With white light, these rings were found to be 

 sharply defined circular spectra somewhat similar to those 

 produced by a circular grating, and the central spot was also 

 coloured in certain cases. These rings are due to the corru- 

 gations on the edge of the disk and are situated at much 

 greater distances from the central spot and from each other 

 than the Lommel rings round the central spot of the shadow 

 of a circular disk. The relative intensities of the central 

 spot and rings were found to depend upon the exact form of 



