LIMITS OF OPTICAL CAPACITY OF THE MICROSCOPE. 439 



be situate a little more to the front or to the back. The image of 

 this aperture formed by the ocular lenses will be very slightly 

 larger when it is situate at the back lens than when it lies in the 

 front lens, but the difference is without any practical significance. 



In equation (8) d' is the breadth of fringe in the last image, a the 

 divergence angle in the medium where the aperture lies, \ the 

 wave length at the same place, iVthe amplification of the last image, 

 as distinguished from'^that formed by the rays passing the aperture. 



If, on the other hand, we put iVj for the amplification of the last 

 image referring to the object Aj, and Wj for the wave length, and 

 refraction index for the medium in which the object lies, we may 

 according to equation (7) make as a is, by assumption, small 



if, sin. «. = ^ . a. 



ai is the divergence angle in the first medium. 



Putting the value of -tj in equation (8) it becomes 



i'=ix!L 1 



JVi 7ii sin ay 



or, as X n=\i Wi=Xo ^o> which last refers to air medium, we have 



j^ Xi ^^ Xq ^ 



iVj 2 sin ttx 2 sin a^ 



This s is the true^ magnitude of those lengths in the object, which 

 in the magnified] image of the fringes appear equal, and will, 

 therefore, be effaced. Therefore, e may be considered the measure of 

 the smallest distinguishable distances in the object, e will be smallest 

 when Oo is largest, — that is to say, when amounting to a right angle. 

 In that case 



^=\K . (9) 



