172 ©. 8. Hastings—Color Correction of Double Objectives. 
be regarded as symmetrical with respect to 7 for values not 
differing largely from Py Again, for white tight, ¢, is shown 
by the photometric observations above named to have a single 
maximum corresponding to a certain value of n which we will 
designate as n,, and consequently may be regarded as a sym- 
metrical function of x in the region of this maximum. Finally 
< is never large in practical cases between the limits , and 
0 
n, while P,—P, increases continuously in numerical value 
toward these limits. If then we set ny=n, the two definite 
integrals become sensibly equal and q is a maximum. 
e value n, corresponds to light of a refrangibility greater 
than that of the Fraunhofer line D and less than that of H, 
however, to the former. The only prominent Fraun- 
e€ reasoning given ab : 
forms of radiation transmitted by the lens system if appropriate — 
] x 
Np Should be nearly equal to ng. ‘ 
It will be observed that the term color and all considerations 
relating to color have been entirely omitted from the discussion. 
This is what we might have anticipated as a necessary feature 
from the remarks on page 170. 
One consequence of the solution above developed may be 
here noted, viz: the focal plane is defined by Py and not by 
two like values of P,, greater than this minimum. This is con- 
trary to the doctrine of some writers but in accordance with 
eritical experiments. * 
Ill. Method of applying the results to the practical construction 
of an objective. 
The solution obtained cannot be directly applied as a guide 
in the construction of an objective, for P is by no means the 
simple funetion of n, A and B as implied in equation (1’) when 
real lenses are in question. Even if we confine our attention 
* See paper cited above, pp. 434-435. 
