300 Diffraction by Apertures with Curvilinear Boundaries. 



portion of the boundary passes through it). If the point be 

 situated on the convex side, it will be seen (vide fig. 4, where 



B is the boundary, E its evolute, and P the point) that it 

 would be possible to draw two normals through P, and since 

 there would be a difference of path between the two waves 

 arriving at P, they could interfere and produce a maximum 

 or minimum of illumination. This explains the fluctuation 

 of intensity seen alongside the evolute. As P recedes farther 

 and farther from the evolute, the two contiguous points which 

 send the waves to P become more and more distant from 

 one another, and the illumination due to either becomes 

 insignificantly small. 



(c) When the undulations on the edge are numerous and 

 close together, the evolute becomes a highly complicated 

 curve, and the phenomena assume a different character 

 owing to the superposition of the effects of different parts of 

 the boundary. Each of the corrugations on the boundary 

 practically acts as a source of radiation (the intensity of the 

 radiation in any direction depending on the exact form of 

 the indentation), and the phenomena observed within the 

 region of shadow are due to the interference of these effects. 

 Within the particular disk used, the first ring was brighter 

 than the central spot (PI. IV. fig. &), but this is not always 

 the case. The distance between the corrugations beino- 

 •057 cm., the distance of the plane of observation from the 

 disk 350 cm., and the wave-length of the light employed 

 being 42xl0 -6 cm., the radii of the successive rings are 

 easily found on the above hypothesis to be '26 cm., *52 cm., 

 etc. The value obtained by measurements on the photo- 

 graphic plate are '21 cm., '51 cm. A fuller treatment of the 

 radiation from a corrugated edge would be very interesting 

 in virtue of the analogy with the problem of the influence 



