252 Mr. Atry on Achromatic Eye-pieces of Telescopes, Sc. 
its variation 
=m eae + Lies oe D = Qathe 2ab+e_ Be on 
AIAG ig qs qr. qrs Sn-1 
a+b+c a+b a a+bhe ab+e ab _ abc 
ae ee \ 
+ dm {—1 ~ 
Ss r q Ts qs qr qrs 
Making this = 0, and putting the value of dm in (25), 
a+b+c.qr+at+b.qs+ars—2.a+b.cq—2.b+c.ar—2abs+3abe 
L=p., ——— ————= 
qrs—a+b+eqgr—a+b.qs—ars+at+h.cg+b+c-ar+abs—abe- 
(27). It is usual in practice to place the diaphragm in the 
situation which we have supposed. If it»should be placed on 
the other side of the object-glass, m would be invariable, and the 
investigation would be in every respect similar to those for eye- 
pieces of telescopes. 
(28). In a common microscope, in which the diaphragm was 
at a little distance from p towards gq, it was found that a=5, b=2, 
c=,3, g=2,8, T=1,9, s=1,6. The equation above gives r= —p x,191; 
hence the microscope was not properly constructed. 
To complete the theory of eye-pieces, and to shew what are 
the most advantageous arrangements of their lenses, there remain 
to be considered the effects of spherical aberration. This part 
is equally important with that. we have treated, and far more 
difficult of investigation: and may perhaps form the subject of 
a future communication. 
G. B. AIRY. 
Trinity COLLEGE, 
April 26, 1824. 
