34 Frauenhofei? on the R^r active and Dispei'slve Power 
The brightest part of the spectrum is nearly at one-third or 
one-fourth of DE from D. Its position cannot be determined 
more exactly, nor is it of any great importance. 
The curve in Fig, 5. Plate VII. Vol. IX. represents the inten- 
sity of the light in the different- colours. The above values are the ' 
ordinates, and the measured arcs BC^ CD, in the Table, p. 27., 
from flint-glass No. 13, the abscissae. We may suppose that the 
quantity of the light in the different coloured spaces, is repre- 
sented by the areas of the curve BC, CD. If we call this 
quantity 1 for the area of the space DE, then we shall have, 
Area of BC = 0.021 
CD 0.299 
DE 1.000 
EF 0.328 
FG 0.185 
GH 0.035 
On the supposition that with an achromatic object-glass the 
aberration of the brightest rays is more injurious to distinct 
vision, in the ratio of their intensity, than the aberration of the 
fainter ones, the distinctness will be the greater if the ratio of 
dispersion, which we may call a?, is taken, such that 
+ cy-j-d^ 4-^sq-y’l -f ^ ' 
where /3, y^ &c. express the quantity of light in the spaces 
BC, CD, DE, &c., and 6, c, d, &c. the quotients 
— B/f T>n' — B?z' ^ 
G« — B«’ D?i — B/i’ 
This ratio is consequently for flint-glass. No. 30, and for crown- 
glass, No. 13, equal to 1 to 2.012. I have, however, found, 
that with the object-glasses of these two kinds of glass, the dis- 
tinctness is a maximum, when this ratio is taken, equal to 1 to 
1.98., This proves, that if the distinctness ought to be a maxi- 
mum,, the aberration of rays of least intensity ought to be greater 
than it is,, in the inverse ratio of the intensity. 
Having several object-glasses of the same aperture, the' same 
focal length, and the same kind of glass, we may determine in 
* In this case we have, ipc — b) /3 + ix—c) y + {pc — dy^ + (x — e) s + 
