THE MICROSCOPE. 131 



angle of aperture is utilized to its widest extent, and, as a 

 result, the resolving 1 power is increased. 



The resolving power of an objective, therefore, depends 

 upon the angle of aperture and on the index of refraction 

 of the medium, which is between the cover-glass and the 

 front lens. Abbe' has reduced these factors to a mathe- 

 matical expression, which is known as the numerical aper- 

 ture. The numerical aperture of an objective corresponds 

 to the sine of half the angle of aperture, multiplied by the 

 index of refraction of the medium that lies between the 

 front lens and the objective. It is usually expressed as, 



N.A. = n sine, u. 



n represents the index of refraction, and u represents 

 half the angle of aperture. 



It is well to repeat, that, the value of an objective de- 

 pends not upon its magnification, but upon its resolving 

 power, and that this is directly proportional to its numerical 

 aperture. Of the lenses having the same magnifying 

 power, the one that has the highest numerical aperture is 

 the most valuable and the most expensive. 



For ordinary work, it is not desirable to have an oil im- 

 mersion objective of more than about 1.30 N.A. since above 

 this, on account of their peculiar construction, they are very 

 liable to suffer injury. Zeiss has succeeded in making ob- 

 jectives possessing a N.A. of 1.50, where the theoretical 

 limit is 1.52. By means of fluorite lenses, and a special im- 

 mersion fluid, mono-brom naphthalen, Zeiss has been able 

 to produce a lens having a N.A. of 1.63, which represents 

 the highest achievement in the construction of objectives. 



The penetrating power, or depth of focus, is expressed by 

 ^-^ In other words, it is reduced by increasing the aperture, 

 as well as the magnification. Just as the resolving power 

 is necessary, in order to bring out the structure, or lines in 

 a given plane, so a penetrating power is desirable, in order 

 to perceive depth in an object. For ordinary work, there- 

 fore, it is preferable to employ a low objective, with a mod- 



