compound lenses and object-glasses. 
2.5 5 
quiry, and I shall accordingly confine myself to the equation 
N = o, or A/ =; o. 
If we develope this equation, it will assume the form 
o=S + T.D+U.D 2 
where S, T, U are functions of the curvatures and powers of 
the lenses. Now as the telescope may be directed to objects 
at all different distances, D is arbitrary and independent, and 
in consequence, the above equation must be satisfied, if pos- 
sible, independent of D. This gives the three equations S = o, 
T = o, U = o, or, obtaining the values of these quantities 
from our equation ( o ) 
o = |x'LA ~j 
+ {A'~ B'L+ C'L*} 
+ L"{ A"— B" ( L + L') + C" (L +L')‘ } j 
+ &c. J 
» = n‘LB-)-|i'’L'{ B' — 2 C' L } A 
•f B"— 2 C"(L + L') ; 
+ &C. 3 
o =[x 2 LC-f \d' U C+ [x"‘ L"C"+ &C. 
l g. Let us first consider the equation (t). If we put for 
A, A', B', &c. their values in terms of r , r , r , &c. and more- 
over if we suppose 
>; 
(*) 
(u) 
(V) 
r==r, r^=r', r=z r", See. 
and 
r — r =p, r 
1 2 S’ 
3 r + =e'> r 5 - r 6=e"> &c - 
(X 2 ( a -f- a'-j- ex,") — a, (x* ( d -f- 2 a,") = 6, |x* d'~C 
[S{0 + &) = e, ^ff=f 9 ^=zg 
and similarly for the other lenses, accenting the letters a } b, 
c, &c. the equation will become 
