1874.] Refracted and Diffracted Spectra. 27 
II. ON THE RELATION BETWEEN REFRACTED 
AND DIFFRACTED SPECTRA. 
By Munco Ponrton, F.R.S.E. 
O all workers with the spectroscope, an accurate 
method of determining the relation between the 
indications of that instrument and the normal 
positions of the spectral lines in the diffracted spectrum, 
which correspond to their wave lengths, has long been an 
object of desire. 
The method hitherto followed, in ascertaining the wave- 
length corresponding to any line found in the field of the 
spectroscope, is that of interpolation, by means of the 
formula suggested by Mr. W. Gibbs, in ‘‘Silliman’s Journal,” 
for July, 1870. Reduced to its most simple shape, this 
formula may be stated thus :—Let a, b, c represent the 
given positions of any three lines in the index of the spe¢tro- 
scope, and let x, y, z represent their corresponding wave- 
lengths. Further make 6—a=/, c—b=q, and c—a=r. 
Then, according to the formula of Mr. Gibbs, we have— 
he Bali 
2 ts ae G 
from which any one member may be found if the rest are 
given. 
This formula, however, is applicable only when the three 
lines are very near each other—a proximity not always 
attainable. Moreover, it will be found that, even when the 
three lines are near, the result is much less approximately 
correct in some parts of the spectrum than in others. 
The truth is, that the formula is absolutely correct only 
when thrown into the following more general shape— 
e Pigt Ee — 0) 
ze me oe 
where the exponent « is variable, having diverse values in 
different parts of the spectrum. 
The question thus arises, whether it may be possible to 
ascertain the law, according to which this exponent varies, 
with sufficient accuracy to render the formula available, not 
only for determining unknown wave-lengths, but also for 
correcting those already approximately ascertained by obser- 
vation. Could implicit reliance be placed on an adequate 
number of observations, this task would not be difficult. 
