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II. Researches towards establishing a Theory of the Dispersion of Light. No. II. 
By the Rev. Baden Powell, M.A. F.R.S. Savilian Professor of Geometry in the 
University of Oxford. 
Received Nov. 5, — Read December 17, 1835. 
In my paper inserted in the last part of the Philosophical Transactions, I have com- 
menced a comparison between the results of M. Cauchy’s system of undulations, ex- 
pressing the theoretical refractive index for each of the standard rays of the spectrum, 
and the corresponding index found from observation in different media. This com- 
parison is there carried on for all the results obtained by M. Fraunhofer. But these 
include only a limited range of transparent bodies ; and close as is the accordance in 
these instances, the theory cannot be considered as fully verified, until we shall have 
extended a similar examination to a greater number of media, and especially to those 
of higher dispersive power. In this research I am now engaged : but as it will neces- 
sarily occupy a considerable period to carry it on, from time to time, as data are 
furnished, I venture for the present to submit to the Royal Society the following por- 
tion of my calculations in continuation of the preceding. 
In my former communication I had referred to M. Fraunhofer’s results as afford- 
ing the only precise data which observation had as yet furnished. But through the 
kindness of Prof. Miller, of Cambridge, I have since become acquainted with the 
series of results obtained by M. Rudberg. They are given in Poggendorff’s Annalen, 
band xiv. and xvii., and comprise the indices observed by him for the standard rays, 
or the ratios of the velocities in air to the velocities within the crystal, in a direction 
perpendicular to the axis of the rhombohedron, in a prism of calcareous spar, having 
its edge parallel to that axis ; and in a prism of quartz similarly cut ; in either case, 
both for the ordinary and extraordinary ray : also the ratios of the velocities in the 
direction of the three axes of elasticity respectively, in aragonite and topaz. 
This valuable series of data I have now examined : and the comparison of them 
with theory constitutes the present communication. The calculations are made by 
precisely the same method as those described in my former paper ; and the results 
are here stated in exactly the same tabular form, which will consequently need no 
explanation. The coincidences of observation and theory will be found at least as 
close as those already obtained from M. Fraunhofer’s results, and I think will be 
allowed to afford a satisfactory extension of the theory to the cases here discussed. 
MDCCCXXXVI. D 
