160 J. FHEINBEBG ON THE COLLECTED PAPERS OF 



know of Abbe's investigations in the same direction and of their 

 results, although they had been published for almost a year. 

 Abbe had started his investigations on the correct assumptions 

 by taking into account the actual conditions which prevail in 

 the employment of the microscope, and drew his conclusions only 

 for the formation of images of non-self-luminous objects. 



Both investigators had so far arrived at the same result that 

 they were able to express the limit of resolving power by the 

 same formula. Abbe's theory at once gave the explanation of 

 the dependence of the resolving power on the aperture. Every 

 non-self-luminous object diffracts the light transmitted through 

 it, or reflected from it, to a greater or less extent. It depends 

 on the amount of light which is grasped by the objective 

 whether any image of the object will be formed, and, provided 

 this is the case, to what extent it will resemble the object. 

 But as a measure of the resolving power we cannot take 

 angular value, i.e. the angle of aperture, but the sine of half the 

 angle of aperture, i.e. the value later called " Numerical Aper- 

 ture " by Abbe. It must be noticed that the simple value of the 

 sine is only for dry systems, and that with immersion systems 

 the numerical aperture is arrived at by multiplying the sine by 

 the refractive index of the immersion fluid. 



The description of the trials carried out for the experimental 

 confirmation of the theory is of the greatest interest. 



Gratings scratched in glass, or in silver deposited on glass, and 

 similar well-known structures, were the objects used for the 

 experiments, which were no less than astounding in their results. 

 Every microscopist should make himself conversant with these 

 experiments, which can be made in the simplest manner, with 

 practically any microscope, by the use of Abbe's diffraction 

 apparatus, How little these experiments are known was shown 

 on the occasion of their demonstration at the Naturalists' 

 Congress at Halle, in 1891, where they created a sensation as 

 something quite new, although they ought to have been the 

 common property of the physical and biological sciences for 

 almost two decades at that time. 



Abbe summed up the result of these experiments as follows : 



"That different structures always produce the same image as 

 soon as the difference of their diffraction effects is removed, and 

 like structures always give different images if the diffraction 



