DIOPTRIC MECHANISMS. 757 



Imperfections in the Dioptric Apparatus. 



640. The emmetropic eye may be taken as the normal eye. The myopic 

 and hypermetropic eyes may be considered as imperfect eyes, though the 

 former possesses certain advantages over the normal eye. An eye might be 

 myopic from too great a convexity of the cornea or of the anterior surface 

 of the lens, or from permanent spasm of the accommodation-mechanism, or 

 from too great a length of the long axis of the eyeball. The last appears to 

 be the usual cause. Similarly, most hypermetropic eyes possess too short a 

 bulb. Moreover, in the strongly-marked myopic eye there is frequently hy- 

 pertrophy of the longitudinal (meridional) fibres of the ciliary muscle, often 

 spoken of exclusively as the ciliary muscle, and atrophy or absence of the 

 circular fibres ; in the hypermetropic eye, on the other hand, the circular 

 fibres are well developed and the meridional fibres scanty. The presbyopic 

 eye is, as we have seen, an eye normally constituted in which the power of 

 accommodation has been lost or is failing through increasing weakness of the 

 ciliary muscle or a loss of elasticity in the lens, or through the parts be- 

 coming rigid. 



641. Spherical aberration. In a spherical lens the rays which impinge 

 on the circumference are brought to a focus sooner than those which pass 

 nearer the centre, and the rays proceeding from a luminous point are no 

 longer brought to a single focus at one point, but form a number of foci at 

 different distances. Hence when rays are allowed to fall on the whole of 

 the lens, the image formed on a screen placed in the focus of the more central 

 rays is blurred by the diffusion-circles caused by the circumferential rays 

 which have been brought to a premature focus. In an ordinary optical in- 

 strument spherical aberration is obviated by a diaphragm which shuts off 

 the more circumferential rays. In the eye the iris is an adjustable diaphragm ; 

 and when the pupil contracts in near vision the more divergent rays proceed- 

 ing from a near object which tend to fall on the circumferential parts of 

 the lens are cut off. As, however, the refractive power of the lens does not 

 increase regularly and progressively from the centre to the circumference, 

 but varies most irregularly, the purpose of the narrowing of the pupil cannot 

 be simply to obviate spherical aberration ; and indeed the other optical im- 

 perfections of the eye are so great that such spherical aberrations as are 

 caused by the lens produce no obvious effect on vision. 



642. Astigmatism. We have hitherto treated the eye as if its dioptric 

 surfaces were all parts of perfect spherical surfaces. In reality this is rarely 

 the case, either with the lens or with the cornea. Slight deviations do not 

 produce any marked effect, but there is one deviation, known as regular 

 astigmatism, which, present to a certain extent in most eyes, very largely 

 developed in some, frequently leads to very imperfect vision. This defect is 

 due to the dioptric surface being not spherical but more convex along one 

 meridian than another, more convex, for instance, along the vertical than 

 along the horizontal meridian. When this is the case the rays proceeding 

 from a luminous point are not brought to a single focus at a point, but 

 possess two linear foci, one nearer than the normal and corresponding to the 

 more convex surface, the other further than the normal focus and corre- 

 sponding to the less convex surface. If the vertical meridians of the sur- 

 face be more convex than the horizontal, then the nearer linear focus will 

 be horizontal and the further linear focus will be vertical, and vice versa. 

 (This can be shown 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, 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 prop- 



