534 Transactions of the Society. 



out that a reciprocal grating consists of two complementary struc- 

 tures, and assuming that the grating lies on the stage, so that one 

 of the comparatively narrow slits in its upper half is on the optic 

 axis, then the zero, first and second maxima, are, as we have seen 

 above, alike in phase. Call them 4- + + . Now if one of the 

 comparatively wide slits in the lower half of the grating were on 

 the optic axis, then, as we have seen above, the second maximum 

 would differ in phase from the zero and first by half a phase 

 period, so the three maxima would be represented by + + — . 

 But we cannot have one of the slits in both upper and lower half 

 of the reciprocal grating in the optic axis at the same time, for if 

 a slit of the upper half lies on the axis, then a bar of the lower 

 half must be there. That comes to the same thing as if the lower 

 half of the grating had been shifted by half a grating interval, and 

 this change in position, as was shown under (1), necessitates half a 

 phase period difference in the first spectrum, whilst the second 

 remains unchanged. Consequently, we actually have the phases 

 of the lower half of the grating + — — , i.e. the zero spectrum 

 remains in the same phase as that of the upper half of the grating, 

 whilst the other spectra are opposed in phase. 



All except the zero maximum cancel out, just as from Babinet's 

 principle we should be led to expect. 



It will be seen that Dr. Strehl has thus in a particularly simple 

 way harmonised specific results with the general theory of diffrac- 

 tion by complementary structures. 



