196 W. Harkness—Color Correction of Achromatic Telescopes. 
focal curve; and s, is the semi-diameter, at the point where it 
cuts the focal plane, of the cone of rays whose wave length is 4,. 
The exact nature of the color correction of a telescope can be 
determined by placing the focal plane in a number of different 
positions, and observing the corresponding values of 7,, and 7» 
These values being substituted in equation (34), several inde- 
pendent values of 7, can be deduced, the mean of which will 
probably be very near the truth. 
e conclusions reached in the preceding pages may be 
summed up as follows:  - 
Ist. From any three pieces of glass suitable for making a 
corrected objective, but not fulfilling the conditions necessary 
for the complete destruction of the secondary spectrum, it will 
always be possible to select two pieces from which a double ~ 
objective can be made that will be superior to any triple 
objective made from all three of the pieces. 
2 e color correction of an objective is completely defined 
by stating the wave length of the light for which it gives the 
minimum focal distance. 
3d. An objective is properly corrected for any given purpose 
when its minimum focal distance corresponds to rays of the 
wave length which is most efficient for that purpose. For 
example, in an objective corrected for visual purposes the rays _ 
which seem brightest to the human eye should have the mini- 
mum focal distance; while in an objective intended for photo- 
graphic purposes the rays which act most intensely upon silver 
bromo-iodide should have the minimum focal distance. 
4th. In double achromatic objectives the secondary spectrum 
(or in other words, the diameter, at its intersection with the 
focal plane, of the cone of rays having the maximum 
distance), is absolutely independent both of the focal length of 
the combination, and of the curves of its lenses; and depends 
solely upon the aperture of the combination, and the physical 
properties of the materials compdosing it. 
5th. When the focal curve of an objective is known; and 
the relative intensity, for the purpose for which the objective 
is corrected, of light of every wave length is also known; then 
the exact position which the focal plane should occupy caa 
readily be calculated. ; 
6th. It may be remarked incidentally that in an objective 
corrected for photographic purposes, the interval between the 
maximum and minimum focal distances is less than in one 
_ corrected for visual purposes. Hence, a photographic objective 
has less secondary spectrum, and is better adapted to spectro- 
scopic work, than a visual objective. 
Washington, May 24, 1879. 
