Some Abbe Letters. 233 



to the object ( = length of tube of the microscope) the maxima 

 and minima of light, resulting by interference in the plane C, 



have a distance 8^ = - . Now if the two rays considered are 



\ f 

 consecutive rays from a grating with the distance S, A = ^-, 



o 

 therefore 8^ = 8 ^ — that is the same distance, in whicli the lines 



of the grating would appear in a purely dioptrical image, under 

 the same circumstances. A, being eliminated from the expression 

 of 8\ the intervals in the interference-image must be equal for the 

 different colours ; this image must be achromatic, if the objective 

 is achromatic (constant for different colours). 



If the two rays considered were not consecutive (as in the 

 experiment with the three-holes- stop), A would have double or 

 triple the value taken above ; 8^ would be ^, or ^ .... of the 

 distance, which corresponds to the real distance 8 in a similar 

 image. 



This reasoning shows, that the interference of the diffracted 

 rays can give a similar image of the structure, but not must. 



The want of mathematical exactness in the deduction above 

 (in 4) arising from the supposition, / infinitely great in relation to 

 / and A, is perfectly removed by considering the dioptrical effect 

 of the microscope in a different manner, which I have stated in 

 No. VI. of my paper (page 213 in Mr. Fripp's translation). 



The theses in (1) and (2) involve the determination of the 

 limit of visibility, as deduced from the fact, that two pencils must 

 enter the objective in order to get an image. If vj (Fig. 6) be the 

 semi-aperture of any objective, and 8 the minimum-distance of 

 visible lines in an object, there is for purely central illumination : 



sin to = 



and for the extreme oblique illumination, when the incident ray 

 touches the margin of the lens on the one side (Fig. 7), the next 

 diffracted ray on the other side : 



2 sin vj = - ; 8 = h -. 



6 sm w 



as stated on p. 244 of Mr. Fripp's translation. I hope these 

 remarks will be sufficient to you for getting a clear notion of the 

 mathematical principles of the theory. 



I shall be very glad, if you should like to show the experiments 

 to the Microscopical Society — especially if you should think it 

 convenient to produce them not as paradox phenomena but rather 



