Study of Huy gem's Secondary Waves. 215 



value, both of which results are contradicted by experiment. 

 The expression (g) shows that the illumination at points in 

 the pattern on the side of the central band, nearer to the 



rrr 



limiting plane = — , is less than at the corresponding points 



on the farther side : and that since cos 2 6 is zero if =—, 



the curve of illumination falls continuously to zero at the 

 limiting plane. Both these results are verified by experiment. 

 Photographs (1) and (2) (see Plate III.) of the diffraction- 

 bands formed by reflexion at the face of a prism, and photo- 

 graph (3) by transmission through an aperture, all exhibit 

 these effects. 



The investigation of the intensity at different points on a 

 secondary wave> given above, is for the case of the incidence 

 of light on a perfectly reflecting screen. It can be shown 

 that by a suitable modification of the integral (a) it can be 

 made to cover the case of the reflexion and refraction of light- 

 waves at a dielectric medium, and that the obliquity-factor in 

 these cases, as given by theory and as applicable to experi- 

 ment, is cos 0. As a matter of fact the photographs (1) and 

 (2) in the Plate are of the diffraction-bands formed by 

 reflexion at a glass prism. 



Similar obliquity-effects should be obtained with other 

 forms of aperture, for example with a reflexion or trans- 

 mission grating, with ivide ridings, if it is held obliquely and 

 if points in the field of view receive no light from the grooves 

 of the grating, the only effective parts being plane portions 

 of the grating, these being parallel to, or coincident with, 

 its general surface. These and other considerations will form 

 the subject of a future paper. 



Summary and Conclusion. 

 Each element of a reflecting surface, may, when waves are 

 incident upon it, according to Huygens, be supposed to send 

 out into each of the two media meeting at the surface, hemi- 

 spherical secondary wavelets. The amplitude of the distur- 

 bance at points on these secondary waves may be investigated 

 mathematically, as in this paper, and shown to be a maximum 

 at the pole of the hemisphere and zero at points on its equator. 

 A similar result for the case of an aperture in a screen can 

 be deduced therefrom. Observation of diffraction-phenomena 

 at oblique incidences confirms this result. The law of varia- 

 tion of the amplitude of the principal component of the light- 

 vector is the cosine of the obliquity. This may be subjected 

 to experimental investigation, and it is hoped that if the 



