On Improvements of the Microscope. By Prof. E. Ahhe. 27 



derived from known experiments. From these two data — the absolute 

 size of the smallest reproducible detail in the object and the requisite 

 visual angle of the same detail in the image — may be deduced the 

 minimum value of the magnifying power which a Microscope with the 

 given aperture onusi have if this aperture is to be fully utilized. On 

 the other hand, it must be remembered that an increase of the visual 

 angle beyond a certain small multiple of the value necessary for clear 

 vision leads to an empty magnifying power which has no advantage for 

 any purpose, and this multiple gives the maximum value which the total 

 magnifying power of the Microscope does 7iot need to exceed with the 

 given aperture. In this way are obtained the limits of the useful 

 magnifying power of an objective of given aperture. 



The focal length which must be given to the objective in order that 

 hy means of the eye-piece the magnifying poiver of the Microscope may 

 he conveniently varied within these limits, will depend entirely upon 

 what proportion of the total magnifying power of the Microscope is to 

 be obtained by the eye-piece. 



On optical grounds there would here be no limitation if an absolutely 

 perfect collection of the rays could be secured in the image formed by 

 the objective. The division of the whole magnifying power between 

 objective and eye-piece, would in this case be entirely immaterial as 

 regards the optical effect. A limitation is however necessitated by the 

 unavoidably imperfect collection of the rays, a result partly of uncorrected 

 residual aberration in the objective, and partly of defects in its mechanical 

 construction which cannot be completely overcome by any art. From 

 both these causes the image produced by the objective exhibits not sharp 

 points but circles of dispersion of greater or less diameter, which, with 

 increased magnifying power in the eye-piece are presented to the eye 

 under an increased visual angle, so that the sharpness and distinctness 

 of the image is more and more affected. Having regard to these cir- 

 cumstances, the question then arises : how far can the requisite useful 

 magnifying power be produced by the action of the eye-piece without 

 making the circles of dispersion visible in the image ? 



The circles of dispersion which result from insufficient collection of the 

 rays are in their absolute magnitude, when reduced to the measure of the 

 object, directly proportional to the focal length of the objective, provided 

 objectives of the same type and the same technical perfection are compared. 

 From this it follows that the visual angle which they subtend at the eye 

 with a definite total magnifying power of the Microscope, the objectives 

 being otherwise similar, must be inversely proportional to the ratio of 

 the focal length of the whole Microscope with this magnifying power to 

 that of the objective, or directly proportional to the ratio of the total mag- 

 nifying power N to the magnifying power n of the objective used by itself 



N 

 without eye-piece. This ratio — which represents the increase of the 



magnifying power due to the eye-piece, consequently determines in the 

 case of objectives of equal perfection the point at which the circles of 

 confusion are visible, that is to say, for each degree of perfection there 

 exists a definite value of this ratio beyond which defects in the union of 

 the rays in the image pass the limits of distinct vision. 



