HI.

meridian of the eye. The diffusion of the rays proceeding from each dark point upwards and downwards, on the surface of any vertical line, will be superimposed on the adjoining dark points of the surface, and the general blackness of the whole line will not be interfered with. The only visual defect as regards lines in the. direction of the defective myopic meridian will, therefore, be the shadowy prolongation of the vertical ends of the lines; the re mainder of the dark lines, and of the white interspaces, will be clear and defined. But as regards lines parallel with the Emc. meridian, or approaching it in parallelism, the diffusion being still in the direction of the vertical Mc. meridian of the eye, the upper and lower boundaries of the horizontal lines, both the black and the white lines, will become diffused vertically on the retina, while there will be no diffusion as regards the ends of the lines. The

vertical diffusion of their images on the retina will thus cause the series of black and white horizontal lines to appear to be mixed up together, not only rendering their upper and lower borders undefined, but causing also a general greyness of colour over the whole series. The ends of the lines will, however, remain sharp and distinct, because there is no diffusion of their images in the horizontal direction. The same explanation is applicable to the cases in which both principal meridians are ametropic though in different degrees; the relative visual defects depend equally on the causes just explained.

3. By the Astigmatic Fan.-The same remarks will apply to lines when they are arranged in the form of the astigmatic fan (see fig. 54). The line which appears to be blackest, and to have the most sharply defined borders, indicates the direction of the chief ametropic meridian of the astigmatic eye; while the line perpendicular to it will be the most defective in definition, and will indicate the meridian of the eye which is least ametropic.

If the Astc. fan be extended so as to form a wheel-like circle of spokes or radii, while the central portion is filled up by a series of concentric and equidistant circles, similar effects to those described with the Astc. fan will be manifested, and if the figure be rotated the alternating displacement of the focal adjustment on the retina of different parts of the central circles will produce the effect of a revolving movement in them (see fig. 55).

4. By a Circular Point of Light.--When a small round opening is made in a dark screen and light admitted through it, if looked at

the cone

by an astigmatic eye at a distance of a couple of feet or so, of light appears elliptical in form, the direction of the ellipse varying as the eye approaches or recedes from the opening. Whatever may be the direction in which at one distance the hole in the screen appears to be elongated, at some other distance from the eye the hole will appear to be elongated in another and generally in a contrary direction.

The variations in the apparent form of the small opening depend on the differences of distance for which the eye is accommodated. If the astigmatic eye is accommodated to the distance at which the

small opening is placed, so as to bring the rays of light proceeding from it to a focus on the retina in one meridian, the opposite meridian will be relatively ametropic, and diffusion of the rays passing through it will result. Thus, taking for example an eye that is Mc. in its vertical meridian and Emc. in the opposite meridian, when the small hole is so placed that the light traversing it is brought to a focus on the retina in the Emc. meridian, diffusion of rays will occur in the direction of the Mc. meridian, and the point of light will appear to be elongated in that direction: the opening will be elongated vertically. If, however, the distance be such that the rays of light are brought to a focus on the retina in the line of the Mc. meridian, the opposite Emc. meridian will practically be rendered for the time ametropic, deficient in refractive power, and diffusion will occur in that direction. If the eye in its horizontal Emc. meridian be accommodated for focussing on the retina rays of light coming from the distance point of the Mc. meridian, the Mc. meridian will have its distant point shortened, and diffusion will occur in that direction. The point of light will appear to be elongated vertically.

5. By a Stenopoeic Hole.-When the stenopoeic opening is placed in the visual line near the centre of the cornea, and the astigmatic eye looks through it at the vertical and horizontal lines of Snellen, they appear as sharp and defined, or nearly so, in all directions, as they do to an Emc. eye.

6. By a Stenopoeic Slit.-When an astigmatic eye looks through a stenopoeic slit at an object, the rays of light proceeding from the object and passing through the slit will be acted upon by the dioptric media of the eye according to the refractive quality of the particular meridian the slit coincides with. If the case be one of simple Mc. or Hc. Ast., and the slit be placed in the direction of the Emc. meridian, both vertical and horizontal lines will appear equally clear. If the slit agree with the ametropic meridian, there will be diffusion of rays in the direction of that meridian, and lines corresponding with the meridian perpendicular to it will be rendered visually dim and obscure. The proper correcting or lens, according to the kind of ametropia, will at once remove the confusion. If the slit be applied to any intervening meridian similar effects will occur in a modified degree, according to the position of the meridian. If the case be one of compound Mc. or Hc. Ast, and the slit be placed so as to correspond with either of the principal ocular meridians, the visual effect will be the same as if the case were one of simple Mc. or Hc. Ast. of amount corresponding to the degree of ametropia of the particular meridian to which the slit is applied. If it be a case of mixed Ast., objects will be seen as they would appear if they were regarded by an eye with simple Mc. or Hc. Ast., according to which meridian the fissure is applied to. In all cases a correcting spherical lens will remove the astigmatic

effect produced by the application of the stenopoeic slit. It should, however, be remembered that effects similar to those last described would ensue if the stenopoeic slit were applied to a myopic or hypermetropic eye of the same degree of M. or H., but without any

Ast.

Diagnosis of Astigmatism. Objective Method.

The existence of Ast. may be determined objectively by the changes of form it produces in the ophthalmoscopic appearance of the optic papilla. When the fundus is observed by the direct mode of examination the optic papilla appears elongated in a direction corresponding with that of the most refractive ocular meridian; when the fundus is observed by the indirect mode of examination, and the image is inverted, the optic papilla appears elongated in the direction corresponding with the least refractive meridian.

Varieties of Regular Astigmatism.-All cases of regular Ast. belong to one or other of six varieties of the three kinds of Ast. before mentioned. They are the following:

1. Simple Myopic Ast. (Am.)-One ocular meridian is Mc., the contrary meridian Emc. Parallel rays passing through the former meridian are brought to a focus in front of the retina; through the latter meridian, in the plane of the retina.

2. Simple Hypermetropic Ast. (Ah.)--One meridian is Emc., the contrary meridian Hc. Parallel rays passing through the former meridian are focussed in the plane of the retina; through the latter meridian, have not attained their focus on reaching the retina.

3. Compound Myopic Ast. (M. + Am.)- Both principal meridians. are Mc., but in different degrees. One meridian presents a maximum of M., the meridian at right angles to it a minimum. Parallel rays traversing the two principal meridians are all brought to a focus in front of the retina, but at different distances in front of it.

4. Compound Hypermetropic Ast. (H.+Ah.)—The two principal meridians are Hc., but in different degrees. One meridian presents a greater deficiency of refractive power than the other. Parallel rays traversing each meridian would, if practicable, be brought to a focus at a distance beyond the retina, but the focal distances beyond the retina would be different.

5. Mixed Ast.; Myopia Predominant (Amh.)-Both principal meridians are ametropic, but the anomalies of refraction are opposite in kind. M. in one meridian is mixed with H. in the contrary meridian, but the M. predominates.

6. Mixed Ast.; Hypermetropia Predominant (Ahm.)-This variety is similar to No. 5, with the exception that H., instead of M., predominates.

The amount of Ast. in each of the foregoing six varieties will vary according to the difference between the maximum and the minimum of refraction in the two principal meridians. Such variations are very numerous. Of the three kinds of Ast. to which the six varieties belong, i.e. the simple, compound, and mixed kinds of Ast., the compound is most frequently met with in practice. Examples of Regular Astigmatism.-The following will serve as examples of the six varieties of Ast. Their correction will be explained afterwards.

M. +2 D.

Horizontal

1. (Am.)-Vertical meridian Mc. meridian Emc. Amount of Ast., or the difference in refraction of the two principal meridians, or Am. = 2 D.

2. (Ah.) Vertical meridian Emc. Horizontal meridian Hc., H. being 2 D. Amount of Ast. or Ah. = 2 D.

3. (M. + Am.)-Vertical meridian Mc. = +4 D, horizontal meridian Mc. = +2 D. Difference in refraction between the two meridians, or the amount of Ast. or Am. = +4 D−2D = 2 D.

4. (H. Ah.)-Vertical meridian Hc. H. = 2.50 D; horizontal meridian Hc. 7 D. Difference in refraction between the two meridians, or the amount of Ast., or Ah. = 4·50 D.

D)

=

= —

- (7 D −2·50

5. (Amh.)-Vertical meridian Mc. +1:50 D, horizontal meridian hypermetropic, H. being 10 D. The amount of Ast., or difference in refractive power of the two meridians, or Amh. 150 D added to 1·0 D, 2.50 D.

=

=

6. (Ahm.)-Vertical meridian Mc. +10 D; horizontal meridian Hc. = −1·50 D. The difference in refractive power of the two meridians, or the amount of Ast., or Ahm., is, therefore, the same as in example No. 5, viz. 1.50 D +10 D = 2·50 D.

In the foregoing examples, the vertical and horizontal meridians have been named as the two principal meridians of refractive defect, because it is in these directions, or nearly in them, that the refractive anomalies in Ast. are most frequently found. But the anomalies of refraction may be found in any other of the ocular meridians, and it is essential to determine the precise inclination of the astigmatic meridians in every instance under notice before the correction of the Ast. becomes possible.

To Determine the Direction of the Principal Ametropic Meridians in Ast. and their Degrees of Ametropia.- Various descriptions of test objects have been arranged for determining the direction of the principal ametropic meridians in cases of Ast. Of these probably the most convenient are, firstly, circles, or semicircles such as the one represented in fig. 54 having radii of lines disposed at certain intervals, and marked by figures at the circumference which indicate the number of degrees into which the circumference is divided by them; or, secondly, series of letters