SPHERICAL ABERRATIONS. 29 
ASTIGMATISM. 
In the case of an oblique bundle of rays impinging on the lens, as in Fig. 
21, from a point not on the optical axis, the lens does not present a sym- 
metrical front to the incident rays; as indicated in the figure, the lens 
appears foreshortened in the plane of incidence (containing optical axis PP' 
and point A ; usually called tangential or meridional plane). The effect 
of the lens is to produce an emergent wave of less radius of curvature for 
the tangential plane than for the plane normal to it (sagittal plane) (Figs. 21, 
22*). The image formed in the tangential plane will then fall short of the 
image formed in the sagittal plane. The distance between the image points 
in the tangential and sagittal planes is the astigmatic difference and the aber- 
ration is called astigmatism. The total effect of astigmatism on an incident 
spherical wave is to produce an emergent wave of spherical front whose 
radius of curvature in the tangential plane is less or greater than that in 
FIG. 22. 
the sagittal plane; the practical consequence of this is that astigmatism 
produces from a plane object an image which consists of two coaxial warped 
and irregular surfaces. In correcting for astigmatism, the effort is made 
to make these two surfaces coincide for the useful field of the objective. 
Astigmatism is not, in general, very noticeable in microscopic objectives, 
because the inclination of the chief rays is comparatively small. It usually 
*Fig. 22 was suggested to the writer by a drawing by Dr. H. Kellner. illustrating astigmatism. 
