PROCEEDINGS OF THE SOCIETY. 479 



must needs be very small. And in the case of a grating or complex 

 object, we can readily see how it throws up strong beams or pencils of 

 light in certain directions, weaker ones in other directions, and no light 

 at all in some directions. Is it not evident therefore that the diaphragm 

 above the objective is only one factor in the formation of the antipoint ; 

 the nature of the light as it reaches the objective from the object being 

 a factor of at least equal importance ? It is the latter point on which 

 the Abbe theory lays emphasis. 



It has been argued that in practical microscopy we do not deal with 

 plane waves of light but with cones ; this argument, however, does not 

 affect the theory, since Dr. G. J. Stoney, in his memoir mentioned above, 

 has shown how the action of a cone of light may be traced by con- 

 sidering it as made up of plane waves of varying obliquities ; and, as 

 regards the light emitted from the object, he tells us : " However com- 

 plex the contents of the objective field, and whether it or parts of it be 

 self-luminous or illuminated in any way, however special, the light 

 which emanates from it may be resolved into undulations, each of which 

 consists of uniform plane waves." 



The second matter which Mr. Gordon seems at times not to have 

 taken into account is that the Abbe theory postulates that the regular 

 interference effects can be produced or calculated only from the com- 

 bined action of spectra which proceed from a single point of the light 

 source, or from secondary points derived from this which are known to 

 be in the same phase. 



If now we take into consideration these two points, we shall find 

 that the proofs which Mr. Gordon brings against the Abbe diffraction 

 theory break down, and that none of his experiments are out of con- 

 sonance with it. 



But before dealing with some of his remarks and of his expert 

 ments, I take leave to state what I understand to be the fundamentals 

 of the Abbe diffraction theory. They are : 



(1) The recognition that every object illuminated by plane waves 

 emits diffracted as well as direct light, the latter being as essential to 

 the formation of a correct image as the former. 



(2) That the more nearly the whole of this light is grasped by the 

 objective, the more nearly will the image conform to the object. 



(3) That when an appreciable portion of the direct or diffracted light 

 is not grasped by the objective, the image may be obscured by false 

 effects, such as doubling of lines, intercostal markings, &c. 



(4) That when light proceeds from an object in maxima and minima, 

 at least two maxima (either a dioptric and a diffraction beam, or two 

 diffraction beams) must be grasped by the objective for the formation 

 of any effect which could be called an image. 



(5) The recognition that the resolving power of the Microscope is 

 dependent on this last clause ; because, seeing that the further the 

 maxima are apart, the closer together are the lines or points resolved, 

 it follows that the limit of resolving power must be reached when 

 matters are so arranged that a dioptric beam and the first diffraction 

 maximum are just and only just grasped by the opposite sides of the 

 marginal zone of an objective. 



It is these fundamental assertions of the Abbe theory, some of 

 which have been challenged and brought in question by Mr. Gordon, 



