62 Professor Airy on the Spherical Aberration 



adopted; the distance between the lenses must, in all cases, be half the 

 sum of their focal lengths. The forms of the lenses, without great error, 

 may be the same as those just given. 



5. If a bright object appears yellow, or a dark one blue, at the edge 

 farthest from the center of the field, the lenses must be brought a little 

 nearer together. 



For a four-glass eye-piece. 



1. For distinctness, let the first and last lenses be crossed lenses of 

 focal length 3, the radii of the surfaces being as 1:6, and the more 

 convex side of each turned to the other. Let the field-glass be plano- 

 convex of focal length 4, its plane side toward the eye ; and the remaining 

 glass a meniscus of focal length 4, the radii of its surfaces as 25 : 11, 

 and its convexity towards the field-glass. Let the distance of the center 

 of the second lens from that of the first be 4 : the distance of the field- 

 glass from the second lens 6, and that of the eye-glass from the field-glass 

 5,13. 



2. The distortion in this eye-piece is very small. 



3. The first diaphragm should be at the distance 3 from the first 

 lens. The last diaphragm, or field-bar, at the distance 3 from the eye- 

 glass. 



4. Any other focal lengths and distances may be adopted, if the 

 following condition be attended to. Let p be the focal length of the lens 

 next the object-glass ; q that of the next lens ; r that of the field-glass ; 

 and s that of the eye-glass. Let a be the distance between the two first 

 (or the length of the second pipe) ; c the distance between the field- 

 glass and the eye-glass (or the length of the Jirst pipe) ; b the distance 

 between the two middle glasses, (or the distance between the two pipes). 

 Then, p, q, r, s, a, and c, may be taken at pleasure, and then b must be 



qr {2 .a+c-p + s)- {g + r) (3 gc-fps-2 .cp + as) 

 3 {c.p + q + a.r-Ys) -4 ac—2 .p -\-q .r + s 



