168 @. S. Hastings—Color Correction of Double Objectives. 
a function of n and has an infinite number of values, all in- 
cluded in practical cases, however, within limits nearly ap- 
proached. ‘Thus, since the last equations cannot be satisfied 
for all —_— of n, the problem is reduced to finding that 
value of © < which substituted in (8) will make the combina- 
tion the oe advantageous one. 
e first efforts to find a solution of ibis problem were 
wended by one of -. most brilliant discoveries in physical 
optics. Only in objectives of considerable size does the ques- 
tion become of great importance, and as Fraunhofer was the 
first to attempt such objectives, so he was first confronted with 
the problem. ‘'’o solve it he performed an elaborate series of 
experiments on the optical properties of various glasses, during 
which he discovered the lines in the solar and certain stellar 
spectra universally known by his name. Moreover, as it was 
evident that the accepted value of 5 — should depend upon the 
relative intensity of lights of different refrangibilities, he made 
a photometric determination of the brightness o the various 
parts of the solar spectrum. With data thus derived his theo- 
Se method of determining the best value of the coefficient 
r was to deduce various values by observation, multiply each 
value so obtained by the relative brightness of the correspond- 
ing region of the spectrum, and divide the sum of these products 
by the sum of the numbers denoting the brightnesses. For 
example, if n, 1 2g, My, ete., are the indices of refraction for the 
first medium heroin to the Fraunhofer lines a, ?, 7, ete. 
n'y Ng, n',, etc., the corresponding quantities for the sec cond 
medium, and q,, q., Js, ete., are the relative quantities of light 
contained in the solar spectrum between the lines af, fy, etc., 
then the accepted value of the coefficient is given by the equa- 
tion 
41+, +ete. 
Fraunhofer found, however, that for a combination of crown 
ty flint glass this method always gives too large a value for 
= —, that is to say, that an objective so constructed would be 
notably under-corrected. Nor is it difficult to recognize that 
the theory is imperfect, for it implies that light of all refrangi- 
bilities is of value in ‘the formation of the image exact y in 
