Study of Huygenss Secondary Waves. 205 



The illumination at any point in the pattern is, as deduced 

 by the ordinary method, proportional to 



/ 2 2 



sin 2 — (sin i — sin &) / -^-5- (sin i — sin #) 2 , 



a being the aperture, \ the wave-length, and /, 6 being the 

 angles o£ incidence and diffraction respectively. Plotting 

 this expression against 0, it is seen to be the ordinary sym- 

 metrical curve sin 2 ^'/# 2 with its abscissae distorted but its 

 ordinates the same : (1) the maxima of illumination in corre- 

 sponding bands on either side of the central one (i = 0) are 

 equal : (2) the illuminations at corresponding points on 

 either side of the diffraction-pattern 



(sin z— sin Q x = sin 6 2 — sin i), 



are equal: (3) as the largest value of 9 admissible is -, it 



follows that the curve of illumination at this point drops 

 suddenly to zero ; in other words, there is a discontinuity in 

 the illumination-curve at this point. All three results are 

 contradicted by observation. As has been stated above, the 



bands on the side nearer to the limiting plane = ~ were 



found to be fainter than those on the other side and the 

 illumination at points in the diffraction-pattern decreased to 

 zero as the limiting plane was approached. 



The diffraction- fringes were observed through a nicol; 

 there was no relative change in the illumination at different 

 points in the pattern as the nicol was rotated, and at very 

 oblique incidences no change at all. 



An explanation of the effect was sought for on the 

 following lines : each element of the reflecting surface may 







be supposed to send out hemispherical secondary wavelets 

 (fig. 1) and the illumination in the diffraction-pattern may be 



