194 W. Harkness—Color Correction of Achromatic Telescopes. 
which gives 
ea : 
: — HH Ve + Yn (32) 
_ But by (9) we have 
eae (33) 
Yo ame Ay 
Combining this with (82), we find 
Vo =4(¥m + Yn) (34) 
which gives the relation between 7, and any pair of points at 
which the focal plane may cut the focal curve. 
e have next to consider how the value of ,, can be found; 
and for that purpose a method partly arithmetical, and partly 
graphical, seems most convenient, The data required are, the 
values of Jf for a number of different values of 7, and the 
relative intensity of the light at each of these values of 7. 
The values of 4f must be computed by means of equation 
(26); and the relative intensity of the light may either 
determined experimentally, or taken from published tables. 
or visual intensity, the table given by Fraunhofer may be 
employed; and for photographic intensity, the curves pub- 
lished by Captain Abney contain all that is required. For the 
sake of definiteness, let us suppose that the value of 7, is to 
be determined for an objective corrected for visual purposes. 
We begin by laying down an axis of abscissas, and graduating 
it into a scale of wave lengths. Here, however, it must be 
observed that the brightness of any part of a spectrum depends 
not only upon the inherent brightness of the light at that 
point, but also upon the degree of dispersion employed. As 
Fraunhofer’s determinations of the relative brightness of dif 
ferent parts of the spectrum were made with a flint glass prism 
having a refractive index of 1°63 for the ray D; and as such 
an instrument produces much greater dispersion at the violet 
end of the spectrum than at the red end; it follows that our 
seale of wave lengths must be, not a scale of equal parts, but 
such a scale as existed in the spectrum employed by Fraunhofer. 
The wave length of the brightest ray is approximately 5688, 
and through that point in the scale, and at right angles to the 
axis of abscissas, the axis of ordinates must be drawn. Then, 
from the computed values of Jf, a sufficient number of points 
must be laid down to determine the focal curve, and that curve 
ust t the points whose wave lengths correspond 
_ to the principal Fraunhofer lines, lines must be drawn through 
the focal curve, parallel to the axis of ordinates; the length of 
each line being proportional to the relative brightness of the 
spectrum at the point where it is situated, and the center of 
each line coinciding accurately with the focal curve. Through 
