242 Mr. Airy on Achromatic Eye-pieces of Telescopes, 
a positive quantity, and = must not be greater than ,344. If 
1 1 ‘ 
however > were 7 ats, the aperture of the flint lenses would be 
less than that of the crown by the same part: an advantage by 
no means inconsiderable, as flint-glasses of 4 inches diameter can 
be very frequently obtained, while those of 5 inches cannot be 
procured once in several years. 
(11) On the achromatic eye-piece. The defect in tele- 
scopes which occasioned the invention of the achromatic eye- 
piece, and the manner in which it removes that defect, have 
been explained in the Introduction to this Paper. We shall 
merely state in this place, that in all the following instances 
we shall pursue the same course; we shall find the distance 
from the last lens at which the axis of a pencil of rays meets 
the axis of the telescope: we shall then find the distance from 
the center of the lens at which the ray is incident upon it; and 
having found the tangent of the visual angle, by dividing the 
latter by the former, we shall make its variation, depending on 
the variation of ”,=0. 
(12) On the eye-piece with two eye-glasses. Let D be the 
distance of the first eye-glass from the object-glass= 4B, Plate XI. 
Fig. 1: p its focal length: a the distance of the second eye-glass from 
the first= BC: qits focal length. Suppose the axis of a pencil of 
rays coming from the center of the object-glass, to fall upon the 
first eye-glass at EZ: it will, after refraction, tend to cross the 
axis of the telescope at the distance 
: or Dp = BG 
ee 
p D 
beyond that lens, and therefore at the distance 
Dp D+a.p—Da is 
Sa 
D2s or ns = CG 
