THE EYE AS AN OPTICAL INSTRUMENT. 193 



united, a lens with other than spherical surfaces must be used, 

 and this cannot be made with sufficient mechanical perfection. 

 Now the eye has its refracting surfaces partly elliptical ; and 

 so here again the natural prejudice, in its favour led to the 

 erroneous belief that spherical aberration was thus prevented. 

 But this was a still greater blunder. More accurate investi- 

 gation showed that much greater defects than that of spherical 

 aberration are present in the eye, defects which are easily 

 avoided with a little care in making optical instruments, and 

 compared with which the amount of spherical aberration becomes 

 very unimportant. The careful measurements of the curvature of 

 the cornea, first made by Senff of Dorpat, next, with a better adap- 

 ted instrument, the writer's ophthalmometer already referred to ,. 

 and afterwards carried out in numerous cases by Donders, Knapp, 

 and others, have proved that the cornea of most human eyes is 

 not a perfectly symmetrical curve, but is variously bent in different 

 directions. I have also devised a method of testing the ' center- 

 ing ' of an eye during life, i.e. ascertaining whether the cornea 

 and the crystalline lens are symmetrically placed with regard 

 to their common axis. By this means I discovered in the eyes 

 I examined slight but distinct deviations from accurate centering. 

 The result of these two defects of construction is the condition 

 called astigmatism, which is found more or less in most human 

 eyes, and prevents our seeing vertical and horizontal lines at the 

 same distance perfectly clearly at once. If the degree of astig- 

 matism is excessive, it can be obviated by the use of glasses with 

 cylindrical surfaces, a circumstance which .has lately much 

 attracted the attention of oculists. 



Nor is this all. A refracting surface which is imperfectly 

 elliptical, an ill-centered telescope, does not give a single illu- 

 minated point as the image of a star, but, according to the sur- 

 face and arrangement of the refracting media, elliptic, circular 

 or linear images. Now the images of an illuminated point, as the 

 human eye brings them to focus, are even more inaccurate : they 

 are irregularly radiated. The reason of this lies in the con- 

 struction of the crystalline lens, the fibres of which are arran- 

 ged around six diverging axes (shown in Fig. 31). So that the 



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