48 ASTIGMATISM. [BOOK in. 



length of which must depend on the amount of accommodation 

 still possessed by the eye ; it must give the rays just so much 

 convergence that the weakened mechanism is able to bring them 

 to a focus on the retina, the convexity or refractive power of the 

 glass being increased, that is to say its focal length diminished, as 

 the loss of accommodation increases. 



733. Spherical aberration. In a spherical lens the rays 

 which are refracted by the circumferential parts are brought to a 

 focus sooner than those which pass through the more central 

 parts ; in consequence 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 

 instrument 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 proceeding from a near object, 

 which tend to fall on the circumferential parts of the lens, are cut 

 off. The lens however, as we have seen, is not uniform in 

 structure, and the refraction which it exercises does not, as in 

 the case of the ordinary lens, increase regularly and progressively 

 from the circumference to the centre, but varies most irregularly , 

 hence the purpose of the narrowing of the pupil cannot be simply 

 to obviate spherical aberration ; and indeed the other optical 

 imperfections of the eye are so great, that such spherical aber- 

 rations as are actually caused by the lens produce no obvious 

 effect on vision. 



734. 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 from the spherical shape do not produce 

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

 astigmatism, which, present to a certain extent in most eyes and 

 very largely developed in some, frequently leads to very imperfect 

 vision. This defect is due to one or other of the dioptric surfaces 

 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 with the dioptric 

 surface of an optical system 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 focus and corresponding to 

 the more convex surface, the other farther than the normal focus and 

 corresponding to the less convex surface. If the vertical meridians 

 of the surface be more convex than the horizontal, then the nearer 

 linear focus will be horizontal and the farther linear focus will be 



