of Chromatic Dispersion. 269 
end of Table VI., and may be regarded as more accurate than 
those calculated from the exponential law alone. It thus appears 
that when observations are made at more than two different tem- 
peratures and with sufficient accuracy, they furnish data whence 
the indices of refraction may be calculated so as to fulfil all those 
three laws, namely, the exponential law, the law of regular ex- 
trusions, and the law of temperature, as affecting the index of 
elasticity. When the indices of refraction fulfil these three con- 
ditions, they may be regarded as nearly quite correct. 
In reference to the law of temperature, it will of course be 
understood that it is the differences of expansion under the in- 
fluence of temperature, rather than the differences of the degrees 
of temperature themselves, to which the differences in the value 
of the index of elasticity must correspond. 
To the effects of the exponential law, in bringing the extrusions 
into conformity with the regular type, a solitary exception is 
presented in the case of the oil of cassia. The singleness of this 
exception, however, raises a strong presumption that all media 
whatever conform to the same regular type as respects their ex- 
trusions, and that the apparent departure in the case of the oil 
of cassia is due solely to errors of observation. This is rendered 
the more probable by the fact of the proved existence of large 
errors in the observed indices of this medium; by the anomaly 
that, at the intermediate temperature, it has a higher exponent 
than at the higher and lower temperatures ; and by the circum- 
stance that the corrections deducible from the exponential law 
tend greatly to reduce, though not quite to remove, the irre- 
gularity in the extrusion of G, in which the departure of this 
medium from the regular type consists. 
It would not be difficult to find for the oil of cassia a set of 
indices of refraction which, while fulfilling the exponential law, 
should at the same time render the extrusions regular, and also 
fulfil the law of temperature as respects the index of elasticity, 
taking advantage for this purpose of the analogies furnished by 
the oil of anise*. Owing, however, to the inherent inaccuracy 
* There seems to be some intimate connexion between the value of n, 
the exponent of least extrusion, and the position assumed by the nodes of 
the extrusions with the first powers of the normals. Thus, in the case of 
the oil of cassia, when the value of » is 3°4 or 3°5, the position of the lower 
node is considerably on the H side of G. But if the exponent be gradu- 
ally lowered, the node will remove further and further from H, until, when 
the value of n is 2°9, the node nearly coincides with G itself. But when 
the exponent is still further reduced, the position of the node gradually 
advances towards F, and the extrusions then present the regular type. 
This is a point which invites further mvestigation ; but for this purpose it 
would be needful to have a more accurate set of observations on oil of 
cassia. 
There seems to be also some probability that the position of the upper 
