Professor Airy on a peculiar Defect in the Eye. 323 



which I saw distant objects distinctly with my right eye, F' 

 found that to niy left eye a distant kicid point had the ap- 

 pearance of a well-defined line, corresponding exactly in direc- 

 tion and nearly in length to the major axis of the ellipse above- 

 mentioned. I found also that if J drew upon paper two black 

 lines crossing each other at right angles, and placed the paper 

 in a proper position, and at a certain distance from the eye, one 

 line was seen perfectly distinct, while the other was barely vi- 

 sible. Upon bringing the paper nearer to the eye, the line 

 which was distinct now disappeared, and the other was seen 

 very well-defined. All these appearances indicated that the 

 refraction of the eye was greater in the plane nearly vertical 

 than in that at right angles to it, and that consequently it would 

 not be possible to see distinctly by the assistance of lenses with 

 spherical surfaces. I found, indeed, that by turning a con- 

 cave lens obliquely, or by looking directly through a part near 

 the edge, I could see objects without confusion ; but in both 

 cases the distortion produced in their figure was such that I 

 could not hope to make any use of the left eye without some 

 more effectual assistance. 



My object was now to form a lens which should^ refract more 

 powerfully the rays in one certain plane, than those in the 

 plane at right angles to it ; and the first idea was to employ 

 one whose surfaces should be cylindrical and concave, the axis 

 of the cylinders crossing each other at right angles, and their 

 radii being different. To show that this construction would 

 effect my purpose, it is only necessary to imagine the lens di- 

 vided into two lenses by a plane perpendicular to its axis. 

 Then it is easily seen that the refraction of one will not be per- 

 ceptibly altered by that of the other, and that the whole re- 

 fraction will be the combination of the two separate refractions. 

 The rays in one plane will be made to diverge entirely by the 

 refraction of one lens, and those in the other plane by that 

 of the other lens. If then r and r^ be the radii of the sur- 

 faces, and n the refractive index and parallel rays be .incident, 

 the rays in one plane after refraction will diverge from a point 



* whose distance is ~~r,5 and there is another plane from a point 

 whose distance is -. This construction was then suf- 



