278 Dr. E. Lommel on the Theory of the 



If the individual apertures be as small as has been assumed 

 above, even their equality is not necessary. In the case of larger 

 unequal apertures, the diffracted light arising from one source of 

 light will appear white, because the maxima of the various colours 

 almost coincide, and thus give white from their mixture ; but 

 with such small apertures, only reddish tints can mix with red- 

 dish, and the action will be of the same quality as in the case 

 of a single aperture. Hence, if a distant white luminous point be 

 viewed through a screen which is perforated by very small arbitra- 

 rily arranged apertures, it appears white, but surrounded by reddish 

 diffracted light ; it is therefore immaterial whether the apertures 

 be equal or unequal, provided their dimensions do not exceed a cer- 

 tain limit. 



3. We will now return to the consideration of the action of 

 an individual aperture, and compare it with the action of a small 

 dark screen of the same form which stands in the path of the 

 direct rays, or of the incident wave-plane. 



We disregard in this the diffractive action of the aperture of 

 the object-glass, or of the pupil, as compared with that which a 

 small aperture or a small screen produces ; this amounts to re- 

 garding this object-glass, and the incident wave, as unlimited on 

 all sides. 



Let A (fig. 1) be any w tf a a i c b d w 

 given point at the edge 

 of a small aperture, and 

 A S a diffracted ray pro- 

 ceeding from it, and let a 

 plane through AS cut the 

 aperture along the straight line AB, To determine the result- 

 ant of all the diffracted rays parallel with A S proceeding from 

 the band A B, we set off on A B equal pieces A a, a b, be, 

 whose length is such that the difference of phase A / of the mar- 

 ginal rays A S and a s is exactly a wave-length for every pencil 

 of rays corresponding to one such division. The action of the 

 complete pencils A «, ab, b c then entirely disappears, because, 

 in each, to any given ray another pencil may be assigned which 

 is displaced towards it by half a wave-length ; and there only 

 remains the action of the imperfect pencil c B (the breadth of 

 which in the figure is assumed to be less than J c d) . If now, 

 without any other alteration, in place of the small aperture a 

 small screen coinciding with it be substituted, and if the same 

 construction be made as before, A B represents the section of 

 the small screen, while the straight lines AW and B W, sup- 

 posed to be infinitely long, represent the section of the unlimited 

 luminous wave. If now the straight line W W be divided right 

 and left, commencing at A as above, into equal parts A a, ab, be, 



