for the Mirrors of Reflecting Telescopes. 113 
must now consider the combination of eye-glasses, which will 
cause the axes of the differently coloured pencils from the same 
point to enter the eye parallel, and with which objects near the 
edge of the field of view will not be coloured. The process which 
we shall employ, and which is easily applicable to achromatic 
eye-pieces in general, consists in finding the tangent of the angle 
made by the axis of any pencil with the axis of the telescope, 
and making its chromatic variation equal to nothing. 
(13). Let the focal length of the small mirror =/; the distance 
from the small mirror to the first eye-glass=p; from the first eye- 
glass to the second (or that nearest the eye) = q; let the focal 
lengths of the first and second eye-glasses be g and k. Then the 
axis of any pencil after reflection from the small mirror crosses 
the axis of the telescope at a point whose distance from the small 
1 
Ha? 
=p- ml are ee fold . It crosses again at distance from first 
: 1 b ; 
ra ae rare and whose distance from the first eye-glass 
oa E 4 ov phe = (pt b)fe 
ses aay RF = pb- @+b)f- We fe 
g pb—(p+)f 
second eye-glass 
_,-—pbe-(p+o)fs_ _ voq—q(p+b)f—bgtp)g+ (p+b+ gfe 
~ 1 b= (p+) f—bg+fe po-(p +b) f- bg +fg 
It finally crosses at a distance from the second eye-glass 
1 
< pb - (p+ b)f—bg +fg 
k pbg—q(p+b)f-5(q+p)e+(pt+b+afe 
ASphq-q(p+5)f—bq+p)g+(p+o+ gifs} Melge. , 
~ poq-q(p+o)f-b(q+p)g—pok+(prbtgfgt (pte) fk+b.gk—fgk 
(14). Let m be the distance from the axis of the smal] mirror 
PME vats ; Dor 
at which the axis of any pencil is incident upon it; m x ir 
Vol. I]. Part I. P 
; distance from 
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