114 Wz Harkness—Color Correction of Achromatic Telescopes. 
In any system of infinitely thin lenses in contact, the number 
The color week of an ‘objective depends only upon the 
form of its focal curve; which form is as much under control 
as the nature of the case admits when the es D, By 8, 
etc., of equation (43), are independent of each other. This, 
taken in connection with what precedes, Ben kataies that— 
siehce n objective consisting of a system of infinitely thin 
nses in contact, the color correction cannot be improved by 
reer t the number of lenses beyond the number of different 
powers of 4 involved in the dispersion formula employed. 
This result confirms the conclusion of my former paper, in 
which [ used a dispersion formula involving but two powers of 
the wave-length, and consequently found but two lenses neces- 
sary in an achromatic objective. It also throws a curious light 
upon the general ered of aa be cas If the law of dis- 
spective of any irrationality which may exist in the pid 
With rational spectra, and a law of dispersion involving at 
least two different powers of the wave-lengths, a pair of len 
would suffice for the construction of a perfectly sch eoneele 
objective. In strictness, these statements apply only to objec- 
tives consisting of infinitely thin lenses in contact. Possibly 
they may require modification when the thicknesses and dis- 
tances apart of the lenses are considered. 
The text books teach that the condition of achromatism for 
two thin lenses in contact is 
O=pF,+DS, td 
in which f, and f are the foci, and p, and p, the di rl ea 
powers, of the ApS They further teach that it is sufficiently 
accurate to put 
