A THEORY OF THE DISPERSION OF LIGHT. 
23 
General Conclusions. 
With regard to some of the first media above compared, the agreement of obser- 
vation and theory is sufficiently near ; but they are low in the scale of dispersion. 
The cases before mentioned as being somewhat uncertain do not allow of a close 
comparison. The balsam of Peru (though only from approximate data) and the 
kreosote, present higher numbers, and the agreement is therefore the most satisfac- 
tory. This is also the case with oil of anise seed, though perhaps not to the same 
degree ; but the differences are probably not greater than what may reasonably be 
allowed. 
In all these cases, however, we trace some uniformity in the character of the dif- 
ferences ; theory being always in defect for the ray E, and in excess for G. When 
we proceed to the sulphuret of carbon this becomes more apparent ; and the dif- 
ferences increase for the more refrangible rays. And lastly, in oil of cassia the same 
regular order of deviation is more marked, and the differences much greater, espe- 
cially in the rays E and G. This regularity of character, as well as increase in the 
amount of the discrepancy, at once shows that it is at least partly due to some other 
cause than errors of observation. Yet we must remark, that even in these cases there 
is a sort of general accordance preserved between observation and theory, the agree- 
ment being still accurate to the second place of decimals. 
The following considerations, then, suggest themselves : 
1 . It is to be observed that in all these cases closer accordances might be obtained 
if we took slightly different values for the assumed indices of B, F, and H ; such as 
would be consistent with the probable errors of observation. In oil of cassia, how- 
ever, I have found that the errors, even when thus distributed among all the indices, 
are still too great. 
2. The constants a and b are derived solely from the values of \ for each ray, taken 
from the well-known determinations of Fraunhofer from interference. It is doubt- 
less possible that these determinations may be affected by errors. In computing, by 
the method here used, some of Fraunhofer’s indices, in which small discrepancies 
were found, Sir W. R. Hamilton undertook to investigate what amount of alteration 
in the values of \ would account for those differences. He communicated his re- 
searches in a letter to myself, with the values of X, and consequently those of a and b, 
thus altered. I have repeated the calculation for oil of cassia, but find this change 
quite insufficient to remove the discrepancy ; and that, in fact, a much larger altera- 
tion than could for a moment be allowed in Fraunhofer’s data, must be supposed, 
in order to produce any sensible effect. 
3. The entire method of computation here followed, though founded on the exclu- 
sion of those approximate suppositions which are allowed in the simpler formula, is 
yet dependent on the omission of terms in the series for p beyond the three first*. 
* See London and Edinburgh Journal of Science, &c., March 1836, eq. 9 and 13. 
