704 SPECIAL SENSES. 



the example of Listing, is regarded as sufficiently exact for all practical pur- 

 poses. This simple scheme represents the eye as reduced to a single refract- 

 ing surface, the cornea, and a single liquid assumed to have an index of re- 

 fraction 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 sys- 

 tem of the eye is so small, amounting to hardly -^ of an inch (0-254 mm.), 

 that it can be neglected. In this simple eye, there is assumed to be a radius 

 of curvature of the cornea of about -J- of an inch (5 mm.) and a single optical 

 centre situated \ of an inch (5 mm.) back of the cornea, the " principal 

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

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

 the air, is about f of an inch (20 mm.). The anterior focal distance, that is, 

 for rays parallel in the vitreous humor, is about f of an inch (15 mm.). 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 crys- 

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

 each other at right angles in the same plane, be 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 perfect distinctness, the 

 other is not well denned. In other words, when the eye is accommodated 

 for the vertical thread, the horizontal thread is indistinct, and vice versa. If 

 the horizontal line be seen distinctly, in order to see the vertical line without 

 modifying the accommodation, it must be removed to a greater distance. 

 This depends chiefly upon a difference in the vertical 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 crystalline lens ; that is, the 

 difference which exists between the curvatures of the lens in the vertical and 

 the horizontal meridians is such that the deepest curvature in the lens is 

 situated in the meridian of the shallowest 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, in all degrees of accommodation, a certain difference in vision, as 

 regards vertical and horizontal lines. 



The condition just described is known under the name of normal, regular 

 astigmatism ; but the aberration is not sufficiently great to interfere with dis- 

 tinct vision. The degree of regular astigmatism presents normal variations 

 in different eyes. In some eyes there is no astigmatism ; but this is rare. 

 According to Donders, if the astigmatism amount to -fa or more, it is to be 

 considered abnormal ; which simply means that beyond this point the aber- 

 ration interferes with distinct vision. 



From the simple definition of regular astigmatism, it is evident that this 



