270 Mr. M. Ponton on certain Laws 
* 
of the observations on oil of cassia, those indices could be regarded 
only as approximations to the truth; and such a result would 
hardly justify detention from a more important branch of this 
inquiry, namely, the institution of a comparison between the laws 
brought to light by the foregoing investigation, and the well- 
known hypothesis of M. Cauchy. 
Suffice it meanwhile to have shown the high probability that 
in every case the extrusions and the laws governing them are of 
one uniform character,—a circumstance adding greatly to their 
interest and their importance as one of the means available for 
checking the accuracy of the indices, seeing that any departure 
from this normal type may be regarded as a very strong pre- 
sumption of inaccuracy in the indices, 
It remains, then, to compare the results obtained from the 
exponential law of the indices with those deducible from the 
hypothesis of M. Cauchy, “that the differences between the 
refractive indices of the medium are to each other very nearly as 
the differences between the reciprocals of the squares of the 
normal wave-lengths; or the refractive indices are each com- 
posed of two terms, whereof one is constant for the medium and 
temperature, the other reciprocally proportional to the squares 
of the normal wave-lengths.” 
It is on the basis of this law that the indices in Powell’s 
Tables have been calculated. Those of the three lines B, F, and 
H are assumed from observation ; and those of the four lines C, 
D, E, and G are thence calculated by means of formule based 
on the above law. 
In order to exhibit more perfectly the differences between the 
results thus obtained and those derived from the law of a variable 
exponent, whose value depends on the proportion which the 
irrationality bears to the dispersion, the indices, as calculated 
from the law of M. Cauchy, are given in Table IX., being ex- 
tracted from Powell’s Tables ; and the sums of the errors are 
compared with those arising under the exponential law. 
Fully to appreciate the superiority of the latter, it is well to 
select a case in which the law of M. Cauchy wholly breaks down. 
For this purpose the highly dispersive medium, bisulphuret of 
carbon, will suffice. In this medium, the discrepancies arising 
under the law of M. Cauchy, between the observed and the cal- 
culated indices for the four lines C, D, H, and G, are 
#C _0-000800, “D—0-001700, “E—0-002000, “G0-004400, S+0-008900. 
The discrepancies arising on the seven lines under the exponen- 
node between C and D may be found to coincide with that of the mean 
wave M, whose refractive index is that for white light; but this, too, is a 
point requiring further research. 
