92 THEORY OF THE MICROSCOPE. 



follows that if the incident pencils only partially fill the aperture 

 of the objective, the unoccupied portion is entirely ineffective. 



Let us now investigate whether, and in what sense, the idea of 

 penetrating power, as above explained, can be applied to the Micro- 

 scope, and whether the properties usually indicated by that 

 expression really correspond to that idea. In the case of telescopes, 

 the pencils of rays which emanate from the points in the (generally 

 self-luminous) object fill the entire aperture of the objective ; an 

 enlargement of the aperture acts consequently like the enlargement 

 of the pupil of the eye. This obtains when the light coming from 

 the object is very faint ; on the other hand, when the light is too 

 strong, errors will be perceived, since all optical appliances with 

 large apertures are accompanied by stronger aberrations. Now, as 

 an increase of light is possible to any extent in microscopic observa- 

 tion (for direct sunlight can be employed if desired), the case of 

 the larger aperture of the objective does not come into considera- 

 tion from this point of view. The diaphragms of the illuminating 

 apparatus are so small, that the rays converging towards the points 

 of the stage generally form cones of light of 20 30 aperture. 

 After undergoing a deviation in the object, these rays group them- 

 selves again into pencils, which appear to come from the separate 

 object-points, and depict their image in the Microscope. The 

 aperture of these pencils is somewhat larger or smaller than that of 

 the incident rays ; these differences are, however, so small that they 

 may be disregarded in our investigations. The pencils which reach 

 the objective only partially fill its aperture, if this be, say, 60- 

 80, and under the given conditions are not dependent upon the 

 magnitude of this aperture. The analogy between the telescope 

 and the Microscope drawn by Goring and others is therefore not 

 applicable. What has been termed penetrating power in the latter 

 (that is to say, the power of rendering perceptible fine structures, 

 lines, or points) is in reality quite distinct from the space-piercing 

 power of the telescope, as rightly pointed out by Harting. If it 

 were desired to retain the parallel, the differentiating power 

 of the Microscope should rather be compared with the property 

 of the telescope of resolving double stars. 



