RELATIVE POWER OF DISCRIMINATION. 141 



accordance with the numbers given, it is of special interest to 

 compare what has been already attained with that which 

 ought theoretically to be attainable, provided the Microscope were 

 mathematically perfect in every respect. It is geometrically 

 evident, that with such an instrument the image of a wire network 

 should be seen just as distinctly with an amplification of m times, 

 as if viewed by the naked eye in an m-fold proportion. The 

 brightness of the image is not, however, necessarily the same, as it 

 is dependent on the angle of aperture of the objective, and, so far 

 as this circumstance exercises an influence upon the discrimina- 

 tion of the meshes, it is conceivable that even in the most perfect 

 instruments the optical power should not increase in exact ratio 

 with the magnifying power. We will, however, for the sake of 

 simplification, assume provisionally that the brightness in the 

 Microscope either = 1, or that the choice of the source of light is so 

 made, that the resulting images possess equal brightness. If, then, 

 D is the diameter of the meshes at the limit of distinct vision with the 

 naked eye, d the diameter of the same on a given amplification m ; 



then (disregarding all influences of a physiological nature) d = - 



or, what comes to the same, - = 1, if the instrument is perfect ; 



111 ct 



on the other hand - < 1, if it is not perfect. In the latter case 

 m d 



the larger or smaller value of the fraction is of course related to 

 the optical power ; it does not give its absolute magnitude, but only 

 its relation to the performance of a perfect instrument. We may 



therefore also say that _ is the mathematical expression of the 



m d 



relative power of discrimination. 



The quantity D may easily be determined, in default of 

 sufficiently large air-bubbles, by placing a suitable objective (for 

 instance Hartnack's No. 7) upon the object-stage with its 

 anterior surface turned upwards, and observing the image which it 

 forms of the wire-gauze through the empty microscope-tube, or 

 if necessary, with the naked eye after the removal of the tube. 

 In this case the eye must be at the distance from the object at 

 which it most easily accommodates itself, and we determine the 

 magnitude of the image by the micrometer, when it is just 

 clearly recognizable. 



I 



