THE OPTICAL EQUIPMENT 47 



results would in general be obtained by using a reliable form of 

 chromatic condenser with such adjustments rather than an 

 achromatic without them. 



The simplest sub-stage illuminator is the mirror, which is 

 fitted to all microscopes, and which is on one side plane and on 

 the other concave. By its aid, assuming that a large source of 

 light is being used, parallel rays are projected on to the object 

 when the flat mirror is used, and convergent when the concave 

 side is in use. While no further arrangement may be necessary 

 for the examination of simple objects under very low powers, 

 the mirror alone is quite inefficient for illuminating an object 

 of any complexity or where other than the lowest powers are 

 in use. The simplest form of sub-stage condenser is that known 

 as the Abbe illuminating apparatus, introduced so long ago 

 as 1872. This is very easy to use, owing to its having rather 

 considerable aberrations, and to its not being sensitive to 

 moderate variation in its position in relation to the object 

 either so far as focussing or centration is concerned; it is, 

 therefore, a convenient piece of apparatus for visual work, and 

 may for medium powers be used satisfactorily for photo- 

 micrography. With direct light it has comparatively few 

 limitations ; but wfc^aised as an oblique illuminator that is, 

 with its central rays stopped out it at once breaks down, 

 and fails to fulfil its purpose in the way that better corrected 

 condensers will do. 



It is as important in a condenser as in an objective that the 

 numerical aperture should be large. The numerical aperture 

 of the Abbe apparatus does not exceed 1-0; and what is known 

 as its aplanatic cone does not exceed 0-45. It will be advisable 

 here to explain briefly the difference between the total numerical 

 aperture and the size of the aplanatic cone in sub-stage con- 

 densers, as it is rather on the latter that the efficiency of the 

 apparatus depends. 



Eeference to Fig. 13 a will show that, with a simple un- 

 corrected lens, the marginal rays do not come to a focus at the 

 same point as the central rays : the lens, in fact, is not well 

 corrected for spherical aberration. The diagram is of course 

 exaggerated, as there is a portion of even a simple lens that 

 will very nearly bring the incident rays exactly to one focal 

 point ; but it is obvious that this central portion is comparatively 



