and the Achromatism of Microscopes. 251 
ag 
aang 
tend to cross the axis at a distance or from g, or when 
1 1 
q a 
incident on r they are converging to a point whose distance from 
it = -b= S64, they then tend to cross the axis at 
a-q a= 
the distance 
i r(a+b.q—ab) 
SSS Se OE === 
a a—-—q —ab+a+b.q+ar—qr 
r  at+b.q—ab 
from r, or the distance 
r(a+b.g—ab) ae moss a+b+c.qr—at+b.cq—b+c.ar+abe 
—ab+at+b.qt+ar—ab ” —qrt+a+b.qgt+ar—ab 
(=g) from s. They finally cross the axis at the distance 
s fatb+c.gr—at+b.cg—btc.art+abc} hai 
—grstatbt+e.qr+at+h.gst+a.rs—ath.cq-b+c.ar—abs+abe 
from s. And the distance from the axis, at which a pencil -of rays 
meets g, is am: that at r is mx St tga’, that at s is 
. 
e a+b+e.gr—a+bh.cg—b+c.ar+abe 
. ie - 
Hence the tangent of the visual angle is 
a+b a+b @+b.c ‘a.b+c ab _ abc 
mi—-1+4t°te at ge ate ae et: 
$ _? q rs qs qr qrs) 
Vol. If. Part II. Kk 
