from the Boundaries of Diffracting Apertures. 127 



comes successively over different parts of the diffraction- 

 pattern formed at the focus, and the luminosity at the 

 boundaries observed through it undergoes a series of 

 changes. For instance, with a triangular aperture, it 

 is known that the diffraction-pattern at the focus consists 

 of a six-rayed " star/' the " rays " being perpendicular to 

 the three sides of the triangle respectively. When the hole 

 comes over any one of the rays the corresponding boundary 

 appears luminous, but in other cases it becomes practically 

 invisible. Similarly, with a quadrilateral aperture, the 

 diffraction-pattern is a " star " with eight rays perpendi- 

 cular to its four sides, and each of these appears luminous 

 when the excentrically-placed hole in the focal plane comes 

 over the corresponding ray of the pattern. 



Whether any particular part of the boundary appears 

 luminous or not seems in general to depend on the normal 

 to the boundary at that point being parallel to the radius 

 vector from the centre of the focal plane to the aperture 

 in the screen through which it is viewed. This is stated 

 here as an experimental fact, the detailed mathematical 

 explanation of which is deferred till a future occasion. An 

 interesting illustration of its generality is furnished by the 

 observation that minute irregularities on the boundary often 

 appear luminous when the adjoining parts which are straight 

 are invisible from any given point in the focal plane. A 

 discussion of the cases in which the boundary is a com- 

 plicated figure such as a grating or a series of parallel 

 apertures is also reserved for a future occasion. 



5. On the Flow of Energy in a Diffraction Field. 



The phenomena described in the preceding sections 

 suggest two important problems for study. In the ordinary 

 Fresnel-Kirchhoff treatment of diffraction problems, the 

 disturbance at any point of the field is expressed as an 

 integral taken over a surface bounded by the diffracting 

 aperture. It is a subject for investigation whether, in 

 any circumstances, the surface integral can be resolved 

 either wholly or partially to a line integral taken over 

 the boundary, and w r hether the disturbance in the region 

 of shadow could be expressed practically in terms of the 

 line-integral alone. Another interesting problem which 

 also suggests itself for investigation is the determination 

 of the forms of the lines of flow of energy in the optical 

 field due to rectangular or circular boundaries in convergent 



