872 ASTIGMATISM. [BOOK in. 



horizontal, then the nearer linear focus will be horizontal and the 

 farther linear focus will be vertical and vice versa. (This can be 

 shewn much more effectually on a model than in a diagram in 

 which we are limited to two dimensions.) Now, in order to see 

 distinctly a vertical line, it is much more important that the rays 

 which diverge from the line in a series of horizontal planes should 

 be brought to a focus properly than those which diverge in the 

 vertical plane of the line itself ; for the former contribute to a far 

 greater extent than do the latter to the sum of rays which go to 

 form the retinal image of and so to excite the sensation of the 

 line. Similarly, in order to see a horizontal line distinctly it is 

 much more important that the rays which diverge from the line 

 in a series of vertical planes should be brought to a focus properly 

 than those which diverge in the horizontal plane of the line itself. 

 When a horizontal line is held before an astigmatic dioptric sur- 

 face, more convex in the vertical meridian, it will give rise to a 

 strong image of a horizontal line at the nearer focus where the 

 many vertical rays diverging from the line are brought to a linear 

 horizontal focus, and to a weak image of a vertical line at the 

 farther focus where the fewer horizontal rays are brought to a 

 linear vertical focus. Similarly, a vertical line held before the 

 same surface will give rise to a strong image of a vertical line 

 at the farther focus where the horizontal rays diverging from the 

 vertical line are brought to a linear vertical focus, and to a weak 

 image of a horizontal line at the nearer focus. But in the case 

 of an astigmatic eye trying to see a horizontal or vertical line or 

 rod such as a horizontal or vertical needle, the mind will neglect 

 the weaker image, and take the stronger image as the only image 

 of the object. Hence if a horizontal and a vertical needle be 

 placed at the same distance before an astigmatic eye, which is 

 more convex in the vertical meridian, that eye will see a hor- 

 izontal needle distinctly when the nearer, and a vertical needle 

 distinctly when the farther of the two foci falls on the retina ; 

 it will require a different accommodation to see the one and the 

 other distinctly. If the astigmatism is such that the horizontal 

 meridian be the more convex, the vertical needle will be seen 

 most distinctly at the nearer, and the horizontal at the farther 

 focus. In both forms of astigmatism the horizontal and the 

 vertical lines which go to make up the features of the surface 

 of an object will fail of being seen distinctly at the same time ; 

 and the vision of the object will be imperfect. 



Rays of light proceeding from a line, which is neither ver- 

 tical nor horizontal but oblique, give rise in an astigmatic 

 system to a number of foci arranged in so complex a manner 

 that no distinct image can be formed on the retina ; the pres- 

 ence of these lines accordingly adds to the imperfection of the 

 vision of any object. 



Most eyes are thus more or less ' regularly ' astigmatic, and 



