CHAP, in.] SIGHT. 49 



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 a vertical line distinctly, a 

 needle held vertically for instance, 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 ot 

 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 surface, 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, such 

 as a horizontal or vertical needle, the eye will neglect the weaker 

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

 object. Hence an astigmatic eye, more convex in the vertical 

 meridian, will see a horizontal 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 hori- 

 zontal 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. 



Kays of light proceeding from a line, which is neither vertical 

 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 presence of these lines 

 accordingly adds to the imperfection of the vision of any object. 



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

 generally with a greater convexity along the vertical meridian. 

 If a set of horizontal or vertical lines be looked at, or if the near 

 point of accommodation be determined by Schemer's experiment, 

 for the needle placed first horizontally and then vertically, the 



4 



