from the Boundaries of Diffracting Apertures. 123 



the extent to which the knife-edge has been advanced in the 

 focal plane beyond the centre of the field, and f 2 defines an 

 upper limit for the aperture in the focal plane. If fi = 

 and f 2 is very large, this expression has the value 



at the boundaries <j)/0=dzl, and becomes logarithmically 

 infinite with f 2 - If : fi and f 2 are both finite, the intensity 

 at the boundaries is given by 



which is also very large compared with the intensity of the 

 other parts of the field. 



Fig. 23 (PI. IV.) represents the luminosity observed at 

 the edges of a rectangular diffracting aperture in Foucault's 

 test. In taking this photograph, f t was small and f 2 large. 

 The luminosity accordingly appears highly condensed at the 

 edges. Fig. 20 reproduces a photograph obtained when 

 fi» ft did not differ very considerably. Diffraction fringes 

 are clearly seen on either side of the boundary in this case. 

 Fig. 17 reproduces a photograph of the aperture obtained 

 with two parallel slits in the focal plane on the same side. 

 It will be noticed that the central fringe which coincides 

 with each boundary is tohite. Figs. 21 and 24 represent 

 photographs obtained when the central band and a few 

 fringes on either side of the diffraction-pattern at the focal 

 plane were cut off by a wire parallel to the edges of the 

 aperture. It will be observed that the positions of the 

 boundaries in these two photographs appear as fine black 

 lines with luminous bands on either side. The same 

 feature, but with the dark lines at the boundaries much 

 broader, is shown in figs. 18 & 25, which were secured 

 by placing two parallel slits symmetrically in the focal 

 plane — that is, one on either side of the centre of the 

 field. 



We proceed to consider the explanation of the black lines 

 marking the positions of the boundaries in the four photo- 

 graphs mentioned in the preceding paragraph. In the 

 focal plane we have two apertures extending from fj to f 2 

 and from — £ x to — f 2 respectively. On account of the 

 symmetry, the Ci-functions disappear from the expression 



