246 Mr. Airy on Achromatic Eye-pieces of Telescopes, 
the general equation for an eye-piece with three eye-glasses- 
If a,p, 9,7, be given, then 
pe 2aq+2ar—pq-pr—qr 
“a 3a—2p—2q ; 
(17). Suppose, for example, a = p+q. Then 
2¢+pqtpr+qr 7 
j= See eee Ge apt 
This formula is given by Boscevich. 
(18). The eye-piece with three eye-glasses is little used, for 
this reason. The refraction, which causes the final intersection 
of the pencils with the axis, must be effected entirely by the 
last eye-glass; and except its aperture be small, the spherical 
aberration distorts the image very much: so that it is impossible 
to have a large field of view. In the eye-piece imstanced 
above, the course of the axis of a pencil’ is represented in 
Fig. 2. and it is evident that the inclination of the pencil to the 
axis of the telescope at Y, is occasioned entirely by the single 
refraction at X. On this account, the eye-piece with four eye- 
glasses is now universally employed. 
(19). On the eye-piece with four eye-glasses. ‘Taking up 
the investigation of (16), and supposing the focal length of the 
last eye-glass=s, and its distance from the third=c, the pencils 
cross the axis at a point whose distance from the last eye-glass 
r (ab—bp—a+bh.qt+pq) 
= ¢ = — ee 
ab—bp—a+b.q-—ar+pqt+pr+qr 
_ abe—bep—at+b.cq—b+c.artepqtb+c.pr+atb+e.qr—pgr (=8) 
ab—bp—a+b.qg-ar+pq+pr+qr 
They finally cross at the distance 
