OPTICAL DEFECTS OF THE EYE 525 



As a rule, however, the actual astigmatism of the cornea is greater than 

 the total astigmatism as determined by the subjective method. This means 

 that it is compensated to some extent by some structures in the eye itself as, 

 e. g., the lens. 



According to measurements made by Nordenson on pupils between the 

 ages of seven and twenty, out of 452 eyes examined only 42 (nine per cent) 

 had no astigmatism of the cornea which could be detected. Sixty-nine pupils 

 had an astigmatism of more than 1 diopter, and four an astigmatism of more 

 than 1.5 D. However, a normal acuteness of vision is perfectly possible with an 

 astigmatism of 1.5 diopters. In 85.1 per cent of the astigmatic eyes examined 

 the vertical meridian was the most refractive; in 1.5 per cent the horizontal, 

 and in 13.4 per cent an oblique meridian. In the majority of cases therefore 

 the vertical meridian is the most sharply curved. 



The difference in static refraction between the most refractive and the least 

 refractive meridian of the eye, expressed in diopters, is known as the degree 

 of astigmatism. After this has been determined (by methods which we cannot 

 discuss here) it can be corrected by means of cylindri- 

 cal lenses i. e., glasses which represent segments of the 

 curved surface of a cylinder. 



In using such glasses for the correction of astigma- 

 tism the glass is so placed that its own asymmetry is the 

 reverse of that of the eye. Suppose an eye were myopic 

 in the vertical meridian and emmetropic in the horizontal. 

 Then the eye could be made emmetropic by placing before 

 it a suitable concave-cylindrical glass with a curvature in 

 the vertical meridian. The myopia in this meridian would FIG. 220. 



be corrected by the curvature. Kays falling in the hori- 

 zontal meridian would not be refracted at all, and would not need to be, for 

 the eye we suppose is already emmetropic in that meridian. Correction for 

 other sorts of astigmatism and for astigmatism combined with myopia and 

 hypermetropia can readily be devised by the reader. 



D. THE ANGLE BETWEEN THE LINE OF VISION AND THE VISUAL AXIS 



The laws of refraction thus far discussed proceed on the assumption that 

 the line of vision coincides with the optical axis of the eye. But this is not 

 the case. The line of vision in front of the eye lies inside of and somewhat 

 above the optical axis, the center of exact vision therefore lying outside of and 

 somewhat below the axis. In Fig. 210 (page 513) G f G> marks the line of 

 vision ; F,F f , the optical axis. 



The angle between the line of vision and the optical axis is designated as 

 the angle a. Its size in the horizontal meridian is 3.5-7.0, and in the vertical 

 approximately 3.5. 



The rays of light entering the eye in the line of vision therefore strike it 

 obliquely. Under these circumstances a homocentric beam remains no longer 

 homocentric, but becomes astigmatic (see page 523), the rays falling in the 

 horizontal meridian being most strongly refracted. This astigmatism how- 

 ever is more than compensated by the ordinary astigmatism of the opposite 

 kind in the cornea. 



Assuming the angle a to be 5, Gullstrand calculated the influence of the 

 oblique incidence of the line of vision for the schematic eye and found that the 



