Mr. Arry on a peculiar Defect in the Eye. 269 
that the refraction of one will not be perceptibly altered by that 
of the other, and that the whole refraction will be the combi- 
nation 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 surfaces, and 7 the refractive index, 
and parallel rays be incident, the rays in one plane after re- 
5 . . 5 a f a 7 
fraction will diverge from a point whose distance is = ae and 
1 
5 3 . . T 
those in another plane from a point whose distance is = 
1 
This construction then was sufficient; 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 cylindrical surface, being entirely effected 
by the spherical surface, parallel rays in this plane after refraction 
will diverge from the distance pbs while the refraction in the 
plane perpendicular to the axis being caused by both surfaces, 
parallel rays, in this plane, will on their emergence, diverge from 
the distance ———1___. 
== (+8) 
J cae 
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 6 inches, appeared a very well defined 
MM 2 
