324 Professor Airy on a peculiar Defect hi the Eye. 



ficient; but for the facility of grinding, and for the diminution 

 of the curvatures, it appeared preferable to make one surface 

 cylindrical, the other spherical, both concave. Let r be the 

 radius of the cylindrical surface, R that of the spherical, then 

 the refraction in the plane passing through the axis of the cy- 

 lindrical surface being entirely effected by the spherical surface, 

 parallel rays in this plane after refraction will diverge from 



the distance ^—^ : while the refraction in the plane perpendi- 

 cular to the axis being caused by both surfaces, parallel rays 

 in this plane will, in their emergence, diverge from the distance 

 1 



To discover the necessary data I made a very fine hole 

 with the point of a needle in a blackened card, which I caused 

 to slide on a graduated scale ; then strongly illuminating a 

 sheet of paper, and holding the card between it and the eye, 

 I had a lucid point, upon which I could make observations 

 with great ease and exactness. Then resting the end of the 

 scale upon the cheek-bone, and sliding the card on the scale, 

 I found that the point at the distance of six inches appeared 

 a very well-defined line inclined to the vertical about 35°, and 

 subtending an angle of 2° by estimation. At the distance of 

 3| inches it appeared a very well-defined line at right angles 

 to the former, and of the same apparent length. It was ne- 

 cessary, therefore, to make a lens, which, when parallel rays 

 were incident, should cause those in one plane to diverge from 

 the distance 3J inches, and those in another plane from the 

 distance six inches. Making the expressions above equal to 

 these numbers, and supposing n=:1.5S, we find R= 3.18, 

 r = 4.45. To prevent, if possible, the eye from becoming 

 more short-sighted, I fixed upon the values R=z3J, r=r4g. 



After some ineffectual applications to the different work- 

 men, I at last procured a lens to these dimensions from an 

 artist named Fuller of Ipswich. It satisfied my wishes in 

 every respect. I can now read the smallest print at a con- 

 siderable distance with the left eye, as well as with the right. 

 I found that vision is most distinct when the cylindrical sjir- 



