266 Mr. M. Ponton on certain Laws 
and high dispersive power indifferently among the best and the 
worst Cases. 
In the three sets of observations, there are fourteen of the first 
order, in which the agreement with the exponential law may be 
considered perfect ; and there are twenty-one of the second order, 
in which the agreement may be regarded as nearly complete. 
These together amount to thirty-five out of the fifty-one, or better 
than two-thirds of the whole. To these may be added the five 
of the third order, in which the agreement may be considered fair, 
thus making four-fifths of the whole, in which the observed and 
calculated indices agree as nearly as can be reasonably expected. 
The whole errors in Fraunhofer’s twelve observations amount 
to 0:003449, or 0-000287 per medium, and 0-000041 per line. 
In Rudberg’s ten observations, the sum total of the errors is 
0003204, or 0000320 per medium, or 0:000046 per line, so 
that these two sets are nearly equal in quality. In Powell’s 
twenty-nine observations, the total errors amount to 0:034400, 
or about 0:001180 per medium, and 0:000170 per line ; so that, 
in general accuracy, Fraunhofer’s observations are to Powell’s 
nearly in the ratio of 4 to 1. 
That the whole of the discrepancies between the observed in- 
dices and those calculated by the exponential law are due, not to 
any defect or inaccuracy in that law, but solely to inaccuracies 
in the observations, it is not difficult to show. As regards the 
fourteen observations of the first order, there can be no doubt 
whatever. With respect to those of the second order, it fortu- 
nately happens that the two sets of observations on oil of anise, 
at temp. 18°25 and temp. 20°-9, are both of this order, and 
agree very nearly,—the cumulo errors in the former being 
0:000398, and in the latter 0:000387. But the observations on 
the same medium, at the intermediate temperature 15°'1, are of 
only the third order,—the cumulo errors being 0:000748, about 
double of those in the former cases. Now this difference can arise 
from no other cause than a difference in the degree of accuracy 
with which the observations were made; so that there is here a 
difference in the amount of error, arising simply from an inferior 
degree of accuracy in the observations, equal to the total amount 
of error in the two best observations on oil of anise, thus show- 
ing that these latter errors must themselves be due to defestive 
observation. But it is equally clear that the greater errors im 
the worst set must also arise from inaccurate observations; for 
had these been made with the same care as the two first, they 
would have been of the same quality. It may hence be fairly 
inferred, that in all the observations, thirty-seven in number, in 
which the cumulo differences do not exceed 0°000748, these are 
due to incorrect observations. 
