W. Harkness—Color Correction of Achromatic Telescopes. 189 
Art, XXX.—On the Color Correction of Achromatic Telescopes ; 
by Wm. HARKNESS. 
ALTHOUGH much has been written on the. theory of the 
are usually composed of two lenses, rarely of three, and hardly 
ever of a greater number; it has been thought sufficient to 
Our fundamental equations are 
I 1 1 | 
Fau-n{5+s} (1) 
poatdy?+ey (2) 
in which 
J =the principal focal distance of any lens. 
f= the refractive index of the lens. 
r =the radius of curvature of the first surface of the lens. 
p =the radius of curvature of the second surface of the lens. 
A = the wave length of the light. 
— l “ek 
y=1-A, 
a, b, c= certain coefficients, determined from not less than three 
properly situated values of y. 
Equation (2) is Cauchy’s dispersion formula. Now put 
2 ae (3) 
+ i 
and suppose a series of lenses, such that 
1 1 He 
ef —" (4, 1)A, > J, tis (Hy ) L 
These lenses being very thin, let them. be placed in contact with 
- each other; and Tet de equivalent focal distance of the whole 
