4 8 



VISION WITH THE COMPOUND MICEOSCOPE 



expressed by the sine of half the angle of aperture (u) l multiplied 

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

 or n sin u (n being !() for air, 1'33 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 



N.A. of objective -/x sin <_l-5x -573 = - 



oil ju^ 1-5 \35 

 glass ju =1-5 \ 



ar n*= 



N.A. of condenser =M* sin *- 1-0 x -86 = -86. 



M sin M = l-5x'573='86=N.A.of objective. 



35/ Oil 71 = 1-5 Angular aperture of 



objective = 35 + 



35 = 70 in 



, glass ?i = f-5 



which is equiva- 

 lent to the angular 

 of the 

 = 60 + 

 60 =120 in air. 



'= 1-0 x -86 = -86 = N.A. of condenser. 



Fre. Al. Identity of n sin u (German math, form) with p. sin $ (English). Also N.A. and 

 angular 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- 



