: ‘ 
| 
aberration to be perfectly corrected for light of all degrees of 
refrangibility ; then the image of a star formed upon the focal 
plane by light of wave length 4, will be a point, and the linear 
semi-diameter of the image of the same star formed by light of 
wave length A, will be the semi-diameter of the cone of rays of 
that wave length at the point where it cuts the foeal plane. 
Therefore we have 
: i Aa ep) fit Be (28) 
in which a is the semi-aperture of the objective, and s,# is the 
required semi-diameter of the cone of rays of wave length 4. 
Combining (28) with (26), we find 
i 2 a\2 N+nP (29) 
8, Se, —y,) L+nM 
This is the expression for a tri le objective. In the case of 
a double one, » becomes zero, ait (29) reduces to 
a2? = aly, i VEY 3 F (30) 
which shows that in a double objective properly corrected for 
any given purpose, the linear gemi-diameter of the secondar 
to the focal 
curve, but places it somewhat further from the objective, in 
such wise that the plane cuts the curve in two points, which 
or these points we must have 
1 
(31) 
1 Bo Oe 
| C+ Dy + Bye C+ Dye + Ryn 
Am. Joor. 8c1.—Tutrp Serres, Vou. XVII, No. 105.— Sept., 1879. 
13 
