Some Abbe Letters. 225 ' 



their positiou relating to tlie diffraction-phenomenon. In using, 

 with the crossed gratings, a broad beam of ■ light, which tills the 

 whole aperture of the objective and thereby, by superposition of 

 the spectra, makes them undiscernable, a diaphragm with a single 

 hole (slit) (fig. 8) of p p 1 mm. in breadth, gives, by simply turn- 

 ing it, the several sets of lines one after the other.* 



T'rom my point of view the scientific interest of all tliese 

 experiments is to prove experimentally, what is the summit of my 

 theory of microscopical vision : that all microscopical images of 

 fine structures are not direct dioptrical images, such as those of 

 .the outlines of an object, but are secondary images, produced by 

 the interference of those pencils of light into which, by diftraction 

 in the structure, the incident beam of light is resolved — the normal 

 image of the structure as well as the artificial ones. My theoretical 

 proof of this assertion is based on the fact, which is a direct con- 

 sequence of the undulatory theory, that all corresponding points 

 in the spectra which are formed by the objective (i.e. sucli points 

 of those spectra which are derived from the same point in the 

 illuminating face) make their oscillation with equal phase — there- 

 fore must produce interferences among the rays which from those 

 points pass to the plane of the dioptrical image. The experimental 

 proof, in my opinion, is given by the fact which the experiments 

 mentioned illustrate : that there is no constant relation between 

 the microscopical image and the structure itself, but only a con- 

 stant relation between the image and the number and position of 

 the diffraction pencils, wdiich form the image, different structures 

 producing identical images, if those dift'raction-pencils are made 

 equal, and one structure producing different images, if those 

 diffraction-pencils are made different. My theorems' about the 

 functions of the aperture, the resolving power of an objective and 

 the limits of visibility, are directly derived from the doctrine 

 mentioned above. 



You may repeat all the experiments with the rhombical grating 

 on Pleurosigna ang ulatum and show the most striking aspect of 

 longitudinal lines and new hexagonal markings on that diatom, 

 which my theory anticipates. For that experiment your Zeiss' 

 Immersion No. 1 in the short setting, you have got, is very con- 

 venient, if you apply the small tube of your binocular-apparatus 

 for fixing small diaphragms (in tin-foil) above the back lens. If 

 you bring to focus a good specimen of that diatom — flat and witli 

 distinct lines — using at first central light in a broad Ijeam, you 

 will see the diffraction spectrum in the following position within 

 the margin of the back lens (fig. 9) : a is the central incident 1 )eani 

 of light, b-f [g ?] the six diffracted beams which alone can be 

 observed with any objective. 



* Every positiou of the diaphragm showing that set of lines which — among 

 the various possible sets — is at right angle to the direction of the slic. 



