So7ne Abhe Letters. 229 



point, the effect must be the same — from the principle of my 

 theory. For every single ray in the broad incident pencil is dis- 

 persed, by diffraction, into separated rays distant one from another 

 in a definite angle. The image is formed, in every case, by the 

 interference of those rays, belonging together, i.e. derived from one 

 incident ray; as on those rays only the vibration is in equal phase. 

 Now if, by the diaphragm, some ray is stopped off, or admitted, in 

 one group, the same ray is stopped off, or admitted in every group 

 — provided the apertures are exactly adjusted. You will do 

 best to make the experiments at first in this manner, using a 

 full and strong illumination. All the effects are got by simply 

 turning the diaphragm. 



Hoping you will find pleasure in these experiments, 



I remain, 



Yours sincerely, 



(Signed) E. Abbe. 



Third Letter. 



Jena, 

 15th December, 1876. 



Dear Sir, 



You are too obliging a correspondent, and I am rather 

 ashamed of your praise. For I myself take pleasure in writing 

 about my microscopical interests, to a gentleman whom I know to 

 have a perfect understanding of those things by his mathematical 

 training — since microscopists in general, have no, or little, under- 

 standino-. 



I add a few remarks which, I hope, will remove a difficulty 

 you have found in my explanation, perhaps. 



In some passages of my letter I distinguish : the pencil of direct 

 rays and the diffraction-pencils. But this distinction does not 

 mean any principal difference in the function, or action, of these 

 rays. From a general point of view, the pencil of direct rays, 

 transmitted by a lined, or marked object to the microscope, is one 

 among the diffraction pencils : it is different from the others only 

 by its greater intensity of light ; but in its action, in the formation 

 of the images of structured objects, it is quite on the same range 

 with the others. (The outlines of any object, it is true, are 

 delineated by the direct rays alone, in l:)right field ; by diffracted 

 rays only in dark field.) 



Therefore in the production of the image of Fleurosigma, with 

 oblique light, you have at least three active pencils, not two ; the 

 direct pencil a being the third (fig. 1). The three sets of lines 

 arise from the three combinations : a, h ; a, c ; and b c — every pair 

 producing one set, rectangular to the connecting line of correspond- 



