The Helmholtz Theory of the Microscope. By J. W. Gordon. 385 



one of these half-sets will cancel the second, and the three half- 

 sets taken together will have no more effective radiating surface 

 than one of them would if it stood alone. Now, any one of them 

 occupies only one-third of the aperture, so that the light which gets 

 through and survives can only be compared with the light given off 



•■la i«;e»»<i).| 



Fig. 77. 



from one-third part of the aperture if occupied by an uniphasal 

 front or plane wave-front. This may be expressed by saying that 

 the aperture value of the polyphase front cf> 3 is only one-third 

 full aperture value. But to say so would be to exaggerate, for it 

 will be observed that the effective area is not uniphasal. On the 

 contrary, it contains one complete half-set of phases, which are of 

 course to some extent discordant, although not entirely destructive 

 of one another's impulses like the paired points of the two cancelled 

 thirds. The numerical evaluation of the deduction from focal 

 brightness which ought to be made on this account, will not con- 

 cern us in the present paper. The conclusion necessary for 

 present purposes is sufficiently indicated in the diagram where 

 two-thirds of the convergent beam are shown in full black and the 

 remaining third in subdued white. It is evident that the light- 

 carrying power of this series of polyphase fronts is greatly dimin- 

 ished. 



A word will suffice to dispose of <£ 4 . This surface carries four 

 half-sets of undulation phases, and from what has been already 

 said it is plain that they will mutually cancel one another. It 

 therefore focusses in full shadow as shown, a fact winch we may 

 express by saying that its aperture value = 0. 



In the foregoing diagrams a method of representing the effects 

 of diffraction has been worked out, .which will make the following 

 diagram (fig. 78) intelligible without verbal description. Assuming 

 the wave-length indicated in the diagram to represent goooo m -> 

 the aperture shown would have a diameter of 3 o^oo m -> anc ^ the 

 various polyphase fronts ty x , </> 2 , &c. would lie at the angles shown. 

 It will be noticed that even with an aperture so small as this the 

 aperture value of the diffracted beams, even of the successive 

 maximum beams, becomes inconsiderably small before the diffrac- 

 tion angle has reached any great magnitude. Thus the maximum 



