ON THE THEORY OF THE MICROSCOPE. 221 



be made out more clearly and with greater ease, but it will in no 

 wise raise the optical power of that particular objective. 



Assuming equal relative perfection of construction, the angular 

 magnitude of the dispersion circles of the objective virtual image 

 of lens-systems possessing widely different focal lengths, must 

 be the same ; therefore the absolute magnitude of the smallest 

 particles which can be separately delineated must constitute the 

 same fraction of the focal length. From this it follows, on the 

 one hand, that the necessary angular amplification for such 

 objectives is equal, and its amount represents accordingly the 

 measure of relative perfection; on the other hand, that the 

 necessary linear amplification, and therewith the absolute optical 

 power, must — assuming always equal relative perfection of con- 

 struction — increase in the same proportion as that in which 

 the focal length diminishes. 



In the practical application of the definitions here propounded, 

 it must not be forgotten that the dispersive circles of the objective 

 virtual image, caused by defective technical execution and 

 residual aberration, never attain, when the higher power 

 objectives are used, so serious an import as they would in the 

 case of dispersion produced in large pencils, filling the whole 

 aperture. As a matter of fact, as soon as the angular aperture 

 becomes considerable, a small portion of it only is occupied at one 

 and the same time by image-forming pencils, and the aberrations 

 are, therefore, proportional to the amount of surface occupied. 

 And since, as we learn from the study of '* aperture-images," the 

 area actively occupied with image-forming pencils is constantly 

 changing place and size, according to the mode of illumination 

 and the struct are of the preparation under view, it follows that 

 any determination of the '^ necessary magnifying power " which 

 shall be valid in all cases is impossible. "^ Nevertheless, the 



* Neither does the method recommended by Harting of determining the 

 limits of resolving power through observation of minute images, such as 

 are obtained by means of small air bubbles, &c., ensure the determination 



Q 



