and the Achromatism of Microscopes. 245 
the pencils incident on the first eye-glass, may be supposed 
parallel to the axis of the telescope. Then they will cross, or 
tend to cross, the axis at the distance p from the first lens, or 
a-p from the second. They will again cross it at the distance 
oa or — from the second lens, or 
a—p 
Sle 
p — (64=P) _ ab—bp—a+b.q+pq from the third. 
a—p—4q Ge a cla | 
They will finally cross it at the distance 
1 r (ab—bp—a+b.q+pq) 
or — 
LSS ab—bp-a+b.q—ar+pqtpr+gqr 
1 
rT ab—bp—a+b.q+pq 
from the third eye-glass. And if m be the distance from the 
axis at which a pencil is incident on the first eye-glass, mx o—? 
is the same on the second eye-glass; and ‘ 
ps ee, Boe eins rg Pod Gop, hebns aM gtd 
Pp a—p-q q (4—p) PY 
that on the third eye-glass. Hence the tangent of the visual 
angle 
Taking the chromatic variation of this, as far as the first power 
3 : 5 : 
of —., and making it vanish, we have 
3ab 
a 2b 2(a+b) 2a Mt 1 =A 
pqr qr pr Pq ‘ T 
or 3ab—2bp—2.a+6.q—2ar+pq+pr+qr=0, 
112 
