86 



THE AMEEICAN MONTHLY 



[May, 



that a light-cone of t8o° will give 

 only half the light that a modern 

 wide-angled objective can take in. 



The alleged limit of i8o° being ex- 

 ceeded by makers of objectives, the 

 swinging mirror proved inadequate 

 to send the light through the outer 

 angle of the objective ; so condensing 

 lenses, prisms, reflex illuminators, and 

 very wide-angle dimmersion-conden- 

 sers, both achromatic and non-achro- 

 matic have been constructed for this 

 purpose. Of all this apparatus, the 

 Abbe condenser has apparently been 

 the most efficient, and has been gen- 

 erally adopted, either directly or as 

 slightly modified by others (to no 

 particular advantage), as the most 

 suitable illuminator for the widest 

 angled objectives. Hence, it is ad- 

 visable to inquire whether this form 

 of condenser is capable of doing all 

 that is demanded of it now, or that 

 will be demanded in the near future ; 

 and to this inquiry I have given much 

 s]3ecial study. 



The Abbe condenser, in any of its 

 modifications, is a non-achromatic 

 system of lenses, resembling an ob- 

 jective, so constructed as to com- 

 bine as small a weight and size as 

 possible with a certain very wide 

 angle of aperture, and sufficient 

 working-distance to work through 

 the thickest object-slides. It has 

 this advantage over most other 

 forms of oblique illuminators, that, 

 by means of a movable diaphragm, 

 pencils of light can be made to pass 

 through the objective successively 

 from the center to the extremity of 

 its angle without changing the axial 

 position of the mirror. 



As the full advantage of a very 

 wide-angled objective cannot be had 

 unless light can be made to pass 

 through any part of its aperture at 

 will, this form of condenser would 

 be the best, if it were possible, prac- 

 tically, to increase its angle to cor- 

 respond with that of the objective ; 

 but it can be shown, and I will 

 indicate the method, that it cannot 

 be so increased, and that it cannot 



approach within 20° or more of 1.52 

 n. a., as is now, or soon will be, 

 desirable. 



If the point where the optical axis 

 of the objective cuts the plane of the 

 object be considered the vertex of an 

 angle which has the extended optical 

 axis of the objective for one side, 

 then the other side of the angle ex- 

 tended downward will cut the under- 

 side of the slide on which the object 

 is mounted, at a certain distance from 

 the axis, and this distance is propor- 

 tional to the thickness of the slide. 

 Besides, if the said angle is equal to 

 half the angle of aperture of the ob- 

 jective, then this distance is the radius 

 of a circle which the available front 

 of the condenser, or other apparatus, 

 must cover, so that light may enter 

 the objective at the most extreme 

 angle of obliquity. If this distance, 

 which we will call D, be three- 

 sixteenths of an inch, then the avail- 

 able surface of the condenser must 

 be a circle of at least three-eighths of 

 an inch in diameter. 



Now, assuming the thickness of the 

 usual object-slide to be one-twelfth 

 of an inch — though this is hardly 

 enough — if the angle of aperture of 

 the objective is given, we may find 

 the distance D; for, with the thick- 

 ness of the slide, one-twelfth of an 

 inch, as the cosine, the distance D 

 will be the sine of half the angle of 

 aperture of the objective. If the 

 angle of aperture of the objective be 

 120°, or 1. 31 n. a. in crown-glass of 

 1.52 refractive index, then the dis- 

 tance Z> would be 0.144-inch, which, 

 however, will not introduce any spe- 

 cial difficulty in the construction of 

 an Abbe condenser, as the connect- 

 ing, or front surface, of the condenser 

 need not be larger in diameter than 

 0.288, or a little over one-fourth of 

 an inch. But when we come up to 

 140° crown-glass angle, or 1.42 n. a., 

 the distance D increases at once to 

 0.228-inch, and the connecting sur- 

 face of the condenser must be at 

 least 0.456, or near half-an-inch in 

 diameter. With so large a front sur- 



