ASTIGMATISM 68 1 



In most calculations of the size of images, the positions of conjugate 

 foci, etc., in normal and abnormal eyes, a schematic eye reduced by 

 Bonders, after the example of Listing, is regarded as sufficiently exact 

 for all practical purposes. This simple scheme represents the eye as 

 reduced to a single refracting surface, the cornea, and a single liquid 

 assumed to have an index of refraction equal to that of pure water. The 

 distance between what are called the two nodal points and between the 

 two principal points of the dioptric system of the eye is so small, amount- 

 ing to hardly y^ of an inch (0.254 millimeter), that it can be neglected. 

 In this simple eye, there is assumed to be a radius of curvature of the 

 cornea of about of an inch (5 millimeters) and a single optical centre 

 situated \ of an inch (5 millimeters) back of the cornea, the " principal 

 point " being in the cornea, in the visual axis. The posterior focal dis- 

 tance, that is, the focus, at the bottom of the eye, for rays parallel in the 

 air, is about of an inch (20 millimeters). The anterior focal distance, 

 that is, for rays parallel in the vitreous humor, is about f of an inch (15 

 millirpeters). The measurements in this simple schematic eye can easily 

 be remembered and used in calculations. 



ASTIGMATISM 



In the normal human eye the visual line does not coincide exactly 

 with the mathematical axis ; but there is still another normal deviation 

 from mathematical exactness in the refraction of rays by the cornea and 

 the lens, which is of considerable importance. If two threads, crossing 

 each other at right angles in the same plane, are placed before the eyes, 

 one of these threads being vertical, and the other, horizontal, when the 

 optical apparatus is adjusted so that one line is seen with distinctness, 

 the other is not well defined. In other words, when the eye is accommo- 

 dated for the vertical thread, the horizontal thread is indistinct, and vice 

 versa. When the horizontal line is seen distinctly, in order to see the 

 vertical line without modifying the accommodation, it must be removed 

 to a greater distance. This depends chiefly on a difference in the ver- 

 tical and the horizontal curvatures of the cornea, so that the horizontal 

 meridian has a focus slightly different from the focus of the vertical 

 meridian. A condition opposite to that observed in the cornea usually 

 exists in the lens ; that is, the difference which exists between the 

 curvatures of the lens in the vertical and the horizontal meridians is 

 such that the deeper curvature in the lens is situated in the meridian 

 of the shallower curvature of the cornea. In this way, in normal eyes, 

 the aberration of the lens has a tendency to correct the aberration in 

 the cornea; but this correction is incomplete, and there still remains, 



