90 THEORY OF THE MICROSCOPE. 



fraction of the calculated brightness with low and medium 

 magnifications, and consequently make no essential difference in 

 the accuracy of the mathematical expression. 1 



X. 



THE OPTICAL POWER OF THE MICROSCOPE. 



THE delineating power of the Microscope does not, as is known, 

 bear a strict proportion to its magnifying power. While some 

 Microscopes exhibit the form and details of a given object with an 

 amplification of, say, 100 linear, others require 150 200 to render 

 the same details apparent. On these differences is based the idea 

 which is generally termed the optical power of the Microscope ; it 

 embraces all the properties which influence the distinctness and 

 brilliancy of the microscopic image. Of the nature of these 

 properties, however, conceptions are prevalent which are in many 

 ways vague, and which require to be carefully sifted, and in part 

 formulated on an entirely new basis. We will therefore separate 

 the different considerations which must be estimated. 



1 According to the explanation above given (p. 40), the magnitude of the 

 aperture-image above the eye-piece is with given optical constants dependent 

 only upon the magnitude of the effective objective-aperture ; its diameter, d, is 

 given by the formula 



( l ?JE_? X focal length, 



in which 8 denotes the angle at which half the diameter of the source of light 

 is seen from the focus of the Microscope. If; consequently, in ordinary vision 

 the aperture of the pupil is also equal to c?, the image-forming cones of rays 

 have the same aperture as those reaching the eye from the Microscope. We 

 may therefore say that the field of view in microscopic vision appears as bright 

 as it would to the naked eye if a diaphragm were held before it, having a clear 

 opening just admitting the image of the source of light which appears above 

 the eye-piece. With this proposition the theorem propounded by Abbe (" Archiv 

 fur mikr. Anatomic," Bd. ix. p. 438) agrees in all essential points. 



