C. S. Hastings— Color Correction of Double Objectives. 169 
proportion to its intensity, whereas, in reality, light of the 
extremes of refrangibility instead of assisting in defining an 
image is absolutely harmful. Fraunhofer was driven, there- 
fore, to a purely empirical determination of the quantity uader 
discussion; and from his time to the present, the only way for 
an optician to determine the relative foci of the two components 
of an achromatic objective is by a laborious process of altering 
the curves and testing the result until the outstanding color. 
about the image of a bright star is such as experience has shown 
1s attended with good definition. A few of the more scientific 
opticians determine the coefficient by means of prisms instead 
of lenses, and thus, by a knowledge of the mathematical rela- 
tions involved, save a great deal of manual labor. Still, even 
in the case where a pair of prisms combined to form a diasporo- 
meter is used, instead of a pair of lenses, the accepted value of 
the coefficient depends upon an exercise of the judgment 
alone, and hence this ‘process yields no unambiguous solution. 
Il. A Vheoretical Solution. 
In order to investigate the best theoretical value for the 
4 n' : j ‘ 
coefficient da? We may begin by expressing n’ either directly 
or indirectly as a function of xn. The most naturally suggested 
course is to express each as a function of the wave-length o 
n'’=a+fn+yn*; 
and the equations above become 
p= P=(n—1) A+(a—1+fntyn*) B (1) 
Poo=A+ (B+2yn) B (2') 
A=—B (B+ 2yn). (3’) 
The problem is to determine the particular value of which 
can be most advantageously substituted in the last equation. 
* On Triple Objectives with Complete Color Correction. This Journal, vol. 
Xvili, p. 429, 1879. 
