20 
PROFESSOR POWELL’S RESEARCHES TOWARDS ESTABLISHING 
I conceive, in general, the indices deduced may be relied on as exact, to at least three 
places of decimals. Some exceptions are noticed in the tract as less certain, viz. the 
oils of Angelica, Cummin, and Pimento, and the balsam of Peru. Such as they are, 
however, these results form (as far as I am aware) the only existing data for pursuing 
the comparison with theory. But I trust they may not be thought insufficient, when 
we consider that in the present stage of the inquiry the object to be aimed at seems 
chiefly such a general comparison as may enable us to see whether the main principle 
of the undulatory explanation of the dispersion is applicable, with a sufficient ap- 
proach to precision, to encourage us to pursue the theory, or whether it must be aban- 
doned, and some new principle sought. 
With respect to media of low dispersive power, little doubt can exist. I have 
therefore not thought it worth while to go through the calculations for many of this 
class, but have confined my examination in the present instance chiefly to the higher 
cases to which my observations have extended. 
It may be necessary to premise a notice of the method of calculation adopted in 
the present communication, as it differs from that employed in my two former papers. 
That method consisted in finding, in the first instance, by a tentative process, (vir- 
tually equivalent to assuming the two extreme indices from observation,) the funda- 
mental arc A from which the others were derived on dividing by X for each ray, so as 
to fulfill the conditions of the approximate formula 
It also appears from the investigations given in several consecutive papers in the 
London and Edinburgh Journal of Science, &c., that this formula is in fact obtained 
by supposing the sum of a series of analogous terms collected into one, with a com- 
mon constant coefficient II. This simplified hypothesis (from the accordances already 
obtained) is evidently very near the truth for the whole range of media hitherto 
examined. 
Professor Sir W. R. Hamilton afterwards pointed out (besides a direct process for 
performing this approximate calculation) a method of investigating the exact expres- 
sion when we do not allow the above assumption as to the coefficients, viz. 
This is explained at large in the journal just named* ; and in a subsequent number f- 
Method of Calculation. 
t August 1836. 
* March 1836. 
