4 8 



VISION WITH THE COMPOUND MICROSCOPE 



expressed by the sine of half the angle of aperture () L multiplied 

 by the refractive index of the medium (??.) in front of the objective, 

 or n sin , (n being I'O for air, T33 for water, and 1/5 for oil or 

 balsam). 





FIG. 32. Illustration of the law of consequence for aplanatic systems. 



Let and O* (fig. 32) be the conjugate aplanatic foci of a wide- 

 angled system ; u, U the angles of inclination of any two rays admitted 



1 In the original translation of the papers of Professor Abbe from German into 

 English the German mathematical symbols have been retained. In the summary of 



A 



N.A. of objective-ni sin 0-1-5.X -573 = -86. 



oi/ ju^ 



ylass ju =1-5 \ 



air *= 1-0 x'60 



u 



N.A. of condenser =n* sin * = l-0x -86=-8G. 



ii sin w = l*5 x'573 = '86 = N.A. of objective. 



35V oil n = l- 



/ ff/ass // =1-5 



Angularaperture of 

 objective = 35 + 

 35 = 70 in glass, 

 which is equiva- 

 lent to the angular 

 aperture of the 

 condenser = 60 + 

 6U=120 in air. 



/a' sill (/>'= 1-Ox -86 = -86 = N. A. of condenser. 



B 



FIG. Al. Identity of n sin n (Cermiui math, form) with p. sin </> (English). Also N.A. and 



a Titular aperture. 



Abbe's theories and demonstrations presented in the following pages the Editor has 

 scarcely felt justified in altering this, especially as the German form of symbol ob- 



