238 Transactions of the Society. 



At all events, the main point which I think we want to bear 

 in mind is that, owing to false deductions which were prevalent 

 after Abbe brought out his diffraction theory, the theory itself was 

 largely misunderstood, and led to an inordinate amount of opposi- 

 tion and controversy. 



What does the theory, looked at in a broad way, amount to ? 

 Abbe has shown that the microscope system is equivalent to a 

 telescope with an ordinary simple magnifying lens to parallelize 

 the rays of the object placed in front of it. Abbe then treats the 

 problems of microscope image formatian in two steps ; he investi- 

 gates firstlv the nature of the light distribution in the back focal 

 plane of the objective where the spectra produced by reason of tlie 

 diffractive action of the object on the light source are formed, and 

 secondly, he deduces the image of the object formed in the image 

 plane trom this. The diffraction phenomena "which he is able to 

 obtain by means of suitable objects, such as gratings in the back 

 focal plane of the objective, are so simple and striking, and the 

 results wliich follow from this particular mode of analysing image 

 formation are so easily demonstrable and lend themselves to so 

 manv experiments, the interpretation of which would have been 

 difficult by other means, that they led immediately, as is known, 

 to far-reaching results. He can, for example, immediately deduce 

 from this the important fact stated in the letter read this 

 evening : — 



" The microscopic image which any structure will show 

 is the more similar to the structure the more all the diffracted 

 light is admitted to the microscope. The interference of all 

 the diffraction pencils which come from, the ohject produces a 

 copy of the real structure alike to a dioptrical image. This 

 is the keystone of my theory." 



He goes on to infer from this that the smaller a structure is, 

 the more dispersed therefore the diffracted pencils, the less similar 

 the microscopic image will be, because the objective will admit 

 fewer of these pencils. 



There is nothing in this theory which necessarily clashes with 

 any other well-grounded theory of the action of image formation by 

 optical instruments. I refer to the methods of Airey and Eayleigh, 

 for example. Long ago I tried to show that a common basis under- 

 lies all the theories of microscopic vision, and Professor Conrady, 

 who has gone into the matter of the Abbe theory deeply, has 

 sufficiently shown in his able papers how it suffices to cover all 

 the results which we obtain by observation, no matter whether we 

 use wide-angled cones of illumination, or narrow-angled cones, or 

 indeed any method of illumination which we please. 



It is interesting to note on the subject of wide cones of light 

 that Abbe himself says in one of these letters : — 



