C. 8. Hastings—Triple Objectives with Color Correction. 429 
Art. LIV.—On Triple Objectives with complete Color Correction ; 
by CHarues S. Hastines. 
THE prime defect in the large refractors of the present day 
is the secondary spectrum. This, arising from the irrationality 
in the spectra produced by the crown and flint glass, hardly 
noticeable in small apertures, detrimental in telescopes of medium 
power, is positively obnoxious in the large instruments and will 
speedily put an end to farther increase in dimensions. On this 
account there have been many efforts to produce two kinds of 
glass differing sufficiently in dispersive power, which would 
still yield mutually rational spectra. As far as I know we are 
© nearer success in this direction than when Brewster 
curvatures shall be moderate, the conclusion is not so ready : 
On entering the discussion we will assume three as the limit- 
ing number of lenses and +, the focal length as the minimum 
radius of curvature. : 
The formula for the focal length F of three thin lenses in 
contact is, if we set =>: 
' 1 4 A 
r= (+ te or—n(irg) to” —0(r+7) 
Where n’, n”, n’”” are the indices of refraction for the three 
materials used, and r,, r,, r, are the radii of curvature 
for the six surfaces successively. We may write this more 
Concisely for our end, as follows: 
p=(n'—1)A +(n"—1)B +(n’””—1)G, 
calling A,B and C the curvature sums of the first, second and 
third lens respectively. 
. The problem then, succinctly stated, is to find values of A, 
and C, no one of which shall be more than thirty when g=1 
ae Which shall make gy independent of the wave length of 
ight transmitted. : 
n can be expressed as a function of any variable « of the 
form | 
ae n= A+ Be) +172) 
the problem has its mathematical expression in the equations: 
