26 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
is called spherical zones. If the angular aperture (angle under which the 
rays meet) is large, the effect of zonal aberration becomes serious. Objec- 
tives of high aperture should be corrected for axial, marginal, and at least one 
other zone, as indicated in Fig. 17, e, in which only rays 2 and 4 are still 
aberrant. If this residual spherical aberration is slight and not disturbing 
to the eye the correction for spherical aberration is, for practical purposes, 
satisfactory. For low apertures sufficient correction can be obtained by the 
use of two lenses, one positive and one negative. The higher the aperture 
the more lenses are necessary. 
In the practical calculations for conection of spherical aberration, advan- 
tage is taken of the fact that the eye is an imperfect optical instrument such 
that an area which subtends less than one to two minutes of arc appears as 
FIG. 17. 
a point to the eye. In the image, therefore, a point which subtends less 
than one minute of arc appears to the eye sharply defined. To carry the 
corrections below this limit would be labor wasted, as the eye would fail to 
appreciate the improvement. 
SPHERICAL ABERRATION FOR OBJECT POINTS NEAR THE AXIS (SINB 
CONDITION). 
When spherical aberration is corrected for a point on the axis an object 
point near the axis is not then necessarily sharply imaged. The rays enter- 
ing the lens along the chief axis AM (Fig. 18) are brought to focus at the 
point A', while the marginal rays AN converge to the point A". In the 
