28 TEXT-BOOK OF BACTERIOLOGY. 



The sharpness of the ima^e is dependent on the exact spherical 

 and chromatic correction of the object-glass. 



Recently a great advantage has been gained since Abbe in 

 Jena, in conjunction -with C. Zeiss, has succeeded, by means of new 

 glass pastes, in constructing lenses distinguished by a number of 

 superior qualities. 



The object-glasses previously in use had always the essential 

 fault of not evenly uniting the different-colored rays — i.e., the chro- 

 matic correction was not equal in all parts of the lens. This fault 

 prevented the formation of an evenly correct and clear image to a 

 sensible degree; the lenses could not be employed up to the full 

 limit which one had a right to expect, because the so-called over- 

 enlargement by eye-pieces was already limited by the difQculties of 

 correction increasing with every increased magnifying power. All 

 this is swept away by the new system. 



The chromatic variation is almost entirely avoided, and there is 

 no longer any hindrance to increasing the magnifying power by 

 means of eye-pieces. In fact, the advantages of these " apochro- 

 matic" object-glasses are extraordinary. They yield an image of 

 remarkable sharpness and clearness. 



Now as to the last point : The distinguishing power of a system 

 depends on many factors, among which the most important is the 

 size of the angle of aperture of the lens in question. 



Imagine a diameter drawn through the front plane of the lens 

 so that it connects the two most distant points in the circumfer- 

 ence of the lens, and imagine, further, that the object is a single 

 point; then connect the ends of the lens circumference with this 

 object, and we have in' the angle formed at the object-point the 

 angle of aperture of the system. In other words, this angle is 

 formed by the axial point of the object-plane and the two marginal 

 rays — the last two rays which, proceeding from the object, could 

 pass through the lens. It is self-evident that the size of the angle 

 of aperture has a decisive influence on the amount of light passing" 

 through an objective. Abbe of Jena, to whom our knowledge of 

 these abstruse relations is almost exclusively due, has, by a series 

 of extremely ingenious and peculiar experiments, ascertained that 

 the penetrative power of a system also stands in direct relation to 

 the size of its angle of aperture. 



He even succeeded in giving to this relation a definite formula, 

 in expressing it by a definite number, and in proving that "the 

 penetrating power of an object-glass equals the sine of half its angle 

 of aperture." 



It is true that this is not the only factor to be considered. As 



