90 



THE AMERICAN MONTHLY 



[Mayl 



the diffraction-spectra alone enable 

 us to resolve minute structures, and 

 that this resolution takes place inde- 

 pendently of any dioptrical action of 

 the microscope. Precisely how the 

 interference-lines due to diffraction 

 become combined with the dioptric 

 image, so as to represent the mark- 

 ings of the object when the eye-piece 

 is applied, I will not attempt to 

 explain ; it will suffice to say that 

 this conception of the action of the 

 microscope, and every conclusion to 

 which it leads, is fully sustained by 

 mathematical analysis and is perfectly 

 in accord with the wave-theory of 

 light. However, I will mention a few 

 experiments which are easily made, 

 and which seem to fully demonstrate 

 the correctness of the theory. Ar- 

 range a series of diaphragms in, or 

 very near to, the upper focal-plane 

 of the objective, in such a manner 

 that any one or more of the spectra 

 can be shut off from the eye-piece at 

 pleasure. If all the spectra are thus 

 shut off, only those parts of the object 

 will be seen that are imaged by the 

 dioptric beam — not a trace of any 

 lined or dotted structure finer than 

 ^-jVo of 3,n inch (ii/^) can be seen, 

 although the outlines and grosser 

 parts are well defined. In the case 

 of a diatom-frustule, the markings 

 are invisible, while its shape is clearly 

 portrayed, but in the case of close 

 lines ruled on glass, there would be 

 no image whatever, because there is 

 nothing about such rulings to give 

 a dioptric image — no outline. For 

 this reason Nobert's test-plate is not 

 so good a test-object as diatom- 

 frustules. On the other hand, if the 

 spectra are all admitted, the minute 

 markings of the object are distinctly 

 seen, thus proving that the resolution 

 of these lines is entirely dependent 

 upon the spectral-images. Moreover, 

 as a still further demonstration that 

 the finer details are not resolved as 

 the ordinary theory assumes, we may 

 entirely shut off the dioptric beam, 

 without affecting the definition of the 

 minute structure, but then the out- 



lines will be totally lost. It will be^ 

 understood, therefore, that no minute 

 structural details can be seen with a 

 microscope, unless the diffraction rays 

 from the object enter the objective^ j 

 to form the spectral-images. '■■ 



The finer the markings of an object 

 are the greater is their diffractive 

 action, hence, the more the incident 

 rays are changed from their original 

 course, and, consequently the wider 

 the angular aperture of the objective 

 must be in order to receive them. 

 Therefore, the limit of the resolving 

 power of an objective is fixed by its 

 angular aperture entirely, for when 

 the structure becomes so very fine 

 that the diffracted rays pass outside 

 of the aperture, it is impossible for 

 the objective to resolve it. We are 

 thus led to a conclusion regarding 

 the capabilities of the microscope, 

 and we are able to determine the 

 limit of its resolving power. It is 

 evident, then, that the power of 

 resolution is a function quite distinct 

 from, and independent of, magnifying 

 power. 



It is well known that a certain 

 angular separation of points or lines 

 is necessary to enable a normal eye 

 to distinguish them. Therefore, if 

 an objective is capable of resolving 

 a series of lines, by virtue of its 

 angular aperture, those lines will 

 certainly be visible when the eye- 

 piece is sufficiently powerful to give 

 them the angular magnification that • 

 is necessary for distinct vision. 

 Hence, for a given angular aperture 

 of an objective, which limits its power 

 of resolution at a certain point, there 

 is a corresponding angular magnifica- 

 tion, to be attained by the eye-piece, 

 that is necessary to make the lines 

 visible. No further increase of mag- 

 nification, obtained in any way, can 

 make any more details visible, or in 

 any way add to the optical capability 

 of the instrument. The necessary 

 angular amplification can be easily 

 converted into terms of linear magni- 

 fication. We are thus led to the 

 conclusion that there is a limit to the 



