112 Mr. Airy on the use of Silvered Glass 
these values in the equation da+<dF=0, and dividing by 26n it 
becomes a’(p + p') + F° (r+ R)=0. 
When this condition is satisfied the second image is free 
from colour. 
(11). That the spherical aberration may be destroyed, we 
must have for the same reason da+dF=0, or adz+ F°d3 =0. 
Substituting for these their values from (7), and putting # for the 
semi-aperture of the small mirror, we find 
Bettas Cae ate in 
n 
aed (aera (2.241.p' pees ~p-=7*D)} 
Be as 
4n.n—1. )-@: n+l. R+2"=1,)h <0, 
But it is easily seen that for the same ray B = nie sub- 
stituting 
a 
$n.nai. (ap 42", DY (:. Paps) sg aaa aa -*=*p)} 
(n— or enRy 
n 
+n.n—l. (2R+ = ry. ae a —r)} =0. 
When this equation holds, the spherical aberration is cor-- 
rected. i 
(12). We have found then the conditions which must be 
satisfied in order that all the rays in each pencil may converge 
to the same distance from the small mirror, and that an object 
in the center of the field of view may be distinctly seen. We 
* (p + D).(p+n+1D) + 29" Smee ie 
+ Fee Py OR. 
