544 



' Transactions of the Society. 



this, therefore, remains to be investigated in each individual case, 

 and will have to be attacked by applying the Huyghenian principle 

 in the same manner in which I applied it to simple gratings in 

 my first paper. 



Before proceeding to this we must, however, study another 

 class of gratings, viz., those consisting of bright line-patterns, or of 

 opaque dots. At first sight this looks a more formidable problem 

 than that of the perforation-patterns, but it can be dealt with at 

 once by the application of Babinet's theorem concerning " reciprocal 

 gratings." Two gratings are said to be reciprocal when the 



Fig. 125. Fig. 125a. 



Fig. 126. 



Fig. 126a. 



opaque portions of one are precisely similar to the transparent 

 portions of the other, and when it is therefore just possible to so 

 superpose one upon the other as to produce uniform opacity. In 

 other words, a grating and its reciprocal stand in the exact relation 

 to each other of a photographic negative and the corresponding 

 positive transparency. 



The simple process of reasoning first applied by Babinet then 

 leads to the discovery of a very simple and valuable relation 

 between the diffraction-spectra from reciprocal gratings. 



Supposing we have an aperture fitted with two screens in such 

 a 'manner that either one or both together may be applied or 

 removed, screen No. 1 having perforations of any shape and design 



