244 Mr. R. Potter on the Application of 



produits par ces rayons se detriment presque complctement 

 des qu'ils s'inclinent sensiblement sur la normale, en sorte que 

 ceux qui influent d'une maniere appreciable sur la quantite de 

 lumiere que i^oit chaque point P peuvent etre regardes 

 comme d'egale intensite." 



In the application of the above principle, we take the origins 

 of the elementary waves on any proposed surface as that of a 

 reflecting or refracting substance, or an aperture, without its 

 being necessary that this surface should coincide with any 

 one wave surface as it arrives. 



There are only a few cases in which the integration for the 

 whole vibration of a particle can be effected directly ; in the 

 following, however, the integration involves no difficulty, and 

 they suffice for proving the discordance of the results of the 

 principle with acknowledged facts. They show that the 

 labour which has been expended in investigating more com- 

 plicated cases, might with ordinary caution have been saved. 



The integration is readily performed when a series of plane 

 waves fall on a plane reflector, or an aperture parallel to 

 their surfaces, the reflector or aperture being of one of the 

 circular forms enumerated below, and the particle whose vi- 

 bration is required, being in the normal to such surfaces 

 through the centre of the circular arcs. These forms com- 

 prise a circular aperture of any radius, an annulus contained 

 between two circles, a circular sector, and the quadrilateral 

 figure bounded by two radii, and two circular arcs : this latter 

 form approximates to a rectilinear parallelogram, when the 

 angle between the bounding radii is small, and the radii of the 

 circular arcs are large. 



The integration for apertures or reflectors of the same 

 forms, is readily performed also when light diverges from a 

 luminous point in the normal line through the centre of the 

 arcs ; and the particle whose vibration is required is equally 

 distant from the surface in the same line, and on the opposite 

 or same side with the luminous point, according as an aper- 

 ture or a reflector is considered. 



Let us commence with a series 

 of plane waves falling directly on 

 a quadrilateral aperture KLMN, 

 bounded by the two concentric 

 circular arcs K N, L M, and the 

 radii C M, C L containing the 

 angle M C L = 0. 



Let B be the position of the 

 particle whose vibration is re- 

 quired situated anywhere in 



