I. On the Spherical Aberration of the Eye-pieces of 



Telescopes. 



By GEORGE BIDDELL AIRY, MA. 



FELLOW OF TRINITY COLLEGE, AND OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 



AND LUCASIAN PROFESSOR OF MATHEMATICS IN THE UNIVERSITY 



OF CAMBRIDGE. 



[Read May 14 and May 21, 1827-] 



In a paper on Achromatic Eye-pieces, which was read before 

 this Society about three years since, and is printed in the .second 

 Volume of the Transactions, after giving the equations which mu.st 

 be satisfied in order that an eye-piece may be truly achromatic, 

 I stated my intention of laying before the vSociety, at some future 

 time, investigations of the conditions most favourable for the 

 destruction of spherical aberration. I now proceed to fulfil this 

 promise, by presenting to the Society an investigation, which I 

 hope will be found pretty complete, of the course of a small pencil 

 of homogeneous light after refraction by a lens ; and by pointing 

 out the application of the resulting expressions to the theory of eye- 

 pieces. I have not considered the general case of a small pencil 

 incident in any direction, but have confined myself to the cases 

 in which the axis of the pencil passes through the axis of the lens : 

 a limitation which, however, includes every thing relating to the 

 eye-pieces of telescopes and microscopes. 



The importance of these investigations has been acknowledged 

 by every scientific artist and by every writer who has endeavoured 

 to assist, by practical rules, the common workman. But the com- 

 plication of symbols has prevented most writers from entering upon 



Vol. Ill, Part I. . A 



