Some Abbe Letters. 231 



Now, with Fleurosigma, those more distant spectra are not 

 \dsible by any objective, from the great angular dispersion of the 

 diffracted rays off the incident ray — owing to the smallness of the 

 structure. (Those more distant pencils could be visible only in a 

 medium of considerably higher refractive index than air, or water has.) 



The microscopic image, depending on the distance and relative 

 position of the diffraction pencils, which are effective in the micro- 

 scope, must be the same for all the different structures, named 

 above, as far as the first row of spectra is admitted only ; what 

 you see in that case, either on Pleurosigma or on the gratings, is 

 the typical image belonging to the inner part of a diffraction- 

 phenomenon of this kind (fig. 2). Therefore nothing can be 

 inferred from the microscopic image of P. angulatum, relating to 

 the detail of the structure. There may be two sets of lines, or 

 three sets, or isolated apertures in the scale, etc. — in every case 

 the known images will result. 



That rhomboidal apertures, as on the grating [with two sets of 

 lines inclined at 60°], look as hexagonal fields, is not surprising, if 

 you consider my theoretical explanation : that the microscopic 

 images result from the interference of the different diffraction- 

 pencilswhich enter the microscope (the direct pencil there included). 

 From this point of view, the real forms of the structure have no 

 direct relation to the image — only an indirect relation, by deter- 

 mining the diffraction-phenomenon partially. 



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 object, produces a copy of the real 

 structure, alike to a dioptrical image. This is the keystone of my 

 theory. From this is to be inferred : the smaller a structure is 

 (the more dispersed therefore the diffraction-pencils) the less 

 similar the microscopic image will be, for any aperture of the 

 objective applied ; and those objects as the fine diatoms, give, with 

 any lens, only typical images (not copies of the real forms), 

 because any lens will admit only a few pencils of the diffraction- 

 phenomenon. 



I am sorry not to have in my possession one single copy, 

 neither German nor English, of my paper, iu which I have stated 

 more precisely, though very briefly, the consequences of this theory 

 touching the interpretation of microscopical images. Perhaps it 

 will be possible to you to lend [borrow ?] the first volume of the 

 Bristol Naturalists' Society's " Proceedings," Part 2, in which you 

 will find Mr, Fripp's translation in extenso ; but you should 

 observe the table of " Errata " which Mr. Fripp has given some 

 time afterwards, because many sentences in the translation are 

 quite unintelligible by errata. The abstract which appeared in 

 the M. jNI. Journal is useless. 



