170 ©. 8. Hastings—Color Correction of Double Objectives. 
This value will be designated as n) and the corresponding focal 
distance as P». 
To accomplish the solution we must first find a criterion of 
excellence in an objective. This we may easily do, after de- — 
fining the sense in which we here use certain terms, as fol- 
ows :— 
Light, for the purpose of this investigation, is defined as that 
form of radiant energy which affects the retina; its quantity is 
measured, not by the value of the energy, but by the physio- 
logical effect which it is capable of producing. 
The intensity of light of refrangibility n is measured by the 
quantity of light contained between the refrangibilities n and 
n+dn divided by dn. Thus, if g, equals the quantity of light 
so defined and ¢, its intensity, then 
Gn== 1,0. 
In what follows we shall consider only such light as is given 
out by a very hot solid body. is light is composite and 
contains light of all refrangibilities from a little less than that 
of the Fraunhofer line A to, practically, a little more than that 
of the line H. e let », and n, represent these limits of 
refrangibility. Then, if Q is the total amount of light falling 
upon a given area, e. g. upon an objective, we have evidently 
Ny 
Q= x=[ z dn. 
Ny 
In this expression ¢ is an unknown function of n, but we know 
enough of the properties of this function for the present pur- 
ose. 
2 A perfect objective would concentrate all the light incident 
upon it from a distant point in its axis to a very small circular 
area in the focal plane, which area would be constant for all 
telescopes of the same angular aperture. The most perfect 
attainable objective then would be that which concentrates the 
greatest attainable amount of light within this area. ‘To inves- 
tigate the conditions which must be satisfied to this end we 
must determine the amount of light falling within a small cir- 
cular area a at Po, the radius of which we will set as a tg $4, 
where a is the angular aperture of the objective. It is evident 
that all the light of such refrangibilities as substituted in (1’) 
would yield values of P contained between Py—a and Pot+a 
would fall within the area a. These limiting refrangibilities 
shall be denoted by n_, and ,,. Only a portion of the light 
of refrangibilities less than n_, and greater than Nea however, 
falls upon this area, the amount for light for the refrangibility 
n being clearly, : 
Qu7p _ Pp \2 
a . 
(P,—P,)* 4 
