Tlieories of Microscopical Vision. By A. E. Conrady. 545 



whatever, whilst screen No. 2 is so cut and adjusted that when 

 superposed it exactly covers the apertures in No. 1. Therefore, if 

 we apply screen No. 1 by itself we shall have the set of apertures 

 cut in it ; if we apply screen No. 2 by itself we shall have a new 

 set of apertures corresponding precisely to the dark portions of 

 screen No. 1 ; screen No. 2 therefore represents a grating reciprocal 

 to that formed on screen No. 1. 



The apertures in screen No. 1 will produce a set of diffraction- 

 spectra peculiar to their shape and configuration ; the apertures in 

 screen No. 2 will also produce a set of diffraction-spectra. If now 

 we let both sets of apertures act at the same time, we are justified 

 by the Huyghenian principle in stating that the diffraction-effects 

 of both sets are now superposed. But the uncovering of both sets 

 of apertures means the removal of both our screens with the con- 

 sequent exposure of a simple large aperture producing no sensible 

 diffraction-effect ; in other words, we are driven to the conclusion 

 that the diffraction-spectra produced by the apertures in screen 

 No. 2 exactly blot out or neutralise those produced by the recipro- 

 cal screen No. 1. According to the undulatory theory, this can 

 only be explained on the assumption that the light diffracted by 

 screen No. 2 is precisely equal in intensity, but also exactly 

 opposed in phase to the light diffracted by the reciprocal screen or 

 grating, which we designated as No. 1. 



This, then, is Babinet's theorem ; it states that reciprocal 

 gratings produce diffraction-spectra in the same directions and of 

 the same intensities, but opposed to each other — cceteris paribus — 

 in phase. 



It will be seen that this convenient theorem enables us to 

 determine the complete diffraction-pattern produced by any bright 

 line device by first ascertaining that of a perforation pattern having 

 perforations exactly corresponding to the opaque dots of the bright 

 line device, and then attributing to the latter diffraction-spectra of 

 the same distribution and intensity, but of the opposite phase 

 when referred to some definite point of reference such as the centre 

 of the dots. Babinet's theorem does not, however, give us any 

 direct information about the intensity of the direct light; this, 

 therefore, remains to be determined in each individual case. 



Having learned how the diffraction produced by.the complicated 

 structures now under consideration may be completely determined, 

 we are in a position to discuss the image resulting from the co- 

 operation of a greater or lesser number of the diffraction-spectra in 

 the field of a Microscope directed and focused upon such structures. 



We will first take a pattern consisting of relatively small 

 perforations arranged in perfect squares such as we have repre- 

 sented (as a negative) in fig. 125. Owing to the smallness of the 

 dots, they may be considered as intermittent portions of relatively 

 narrow slits, and, in accordance with the reasoning given in my 



