derived from M. Cauchy’s Theory, 209 
Availing ourselves of this circumstance we may put the re- 
lation (20.) or (21.) under the simpler form 
4 Sptp(l1—-4p) —Sp = 4 (1-26) (25.) 
or, what is equivalent, 
My Pp = Up (up—Hg) + by (un—2 Hy +s) (26.) 
whence ay = — (1—2¢,) = —tp (1-2 ¢p) 
which are wholly functions of the values of +, viz. 
4p — el 7 2 eo (27.) 
fi 1a. ta ~2tp +R" 
by nae eS ae e TA eal = ; (28.) 
Thus employing the values (22.) of T; Tp Ty the follow- 
ing numbers result : 
log (—ap) = 1:80441 
log (—b,) = 1:06281 
Now, to take an example of a particular medium; for flint 
glass, No. 13, Fraunhofer found 
bp = 16277 bp = 1'6483 My = 1°6711. 
Hence by (26.) and the above logarithms, we may calculate 
the value of »,, which will be found to result 
My = 163492; 
by Fraunhofer’s observation it was 
My = 1°6350. 
Such is the method of Sir W. R. Hamilton: he has, how- 
ever, not only calculated this example, but has gone through 
the values of the index, for the same ray D in all the media 
examined by Fraunhofer. These results I will subjoin, add- 
ing a column of the same values as computed by myself, by 
a tentative method with only the approximate formula, from 
my paper in the Philosophical Transactions. 
Third Series. Vol. 8. No. 46. March 1836. 2A 
