and the Achromatism of Microscopes. 2438 
beyond the second eye-glass. After refraction therefore at the 
second eye-glass, it will meet the axis of the telescope at the 
distance 
1 i tL 
: q (D+a.p—Da) ‘ 
_ D-p 1 pg + Dq+ D¥a.p—Da 
D+a.p—Da q 
And if k be the tangent of the angle BAEZ, then BE=Dk; 
CF=BE = i pi. Pt4 | dicen 
. tan c= i. —Pg+ Dq+D+a.p—Da ¥ 
PY 
=k{-1 g Seat Somes 
P q Pq 
Taking the variation of this to the first power of — and 
De 
making it = 0, we have 
D Dt+a 2Day sn 
por, pig Moai 
=0, 
whence a=—-*4 Or if D be very great, a = Pet This is 
the rule of opticians. If p= 3q then a = 2q: this is the 
Huygenian construction before mentioned. 
(13). If a =q, we must have 
ena. cee ae 
29 — Fy = PAG OF a=g = Da = BG. 
In this case the lens CF is placed at G: and since its focal 
length equals the distance between the two lenses, the image, to 
be distinctly seen, must be formed upon the lens BE. This is 
inadmissible; because the particles of dust on the glass, since 
the smallest substance will now intercept an entire pencil of 
Vol. If. Part If. Ir 
