TRANSACTIONS OF THE SECTIONS. 15 
The present object is to remark the bearing of this point on the 
theory of heat. If this theory be true, all refraction of heat ought to 
fall within this limit, and probably a considerable portion of the heat- 
ing rays would have an index not far removed from it. It will be parti- 
cularly interesting to calculate it for rock-salt, and other diathermanous 
media, and compare it with the index of the heating rays. The data 
for rock-salt are given in Professor Powell’s report on Refractive In- 
dices, British Association Reports, 1839. 
This consideration also explains a difficulty which occurred to Prof. 
Forbes, who in his Third Series of Researches (§ 2. No. 45—46), 
having arrived at the conclusion that a wave of heat has a length nearly 
three times that of red light, regards this as a startling inference, and 
difficult to reconcile with the small difference existing between the in- 
dex of refraction for heat and for light. This is just what should re- 
sult in the above theory. 
On the Conduction of Heat. By Professor KELLAND. 
The author’s object in bringing forward this subject at the present 
time, he explained to be, to point out the state of our experimental 
knowledge of the transmission of heat, and to exhibit its total inade- 
quacy to serve as the test of any precise and accurate theory. The 
following is a brief sketch of the history of the subject. Little had 
been done before the time of Lambert, who, in 1755, solved one of the 
most simple problems. Afterwards appeared the writings of Euler. 
But it was left for Fourier, at the commencement of the present cen- 
tury, to exhibit a theory having about it the characters of truth, ade- 
quacy, and extension. For along time Fourier’s memoir was known 
only to a few, and, as it was based on the Newtonian hypothesis, that 
radiation is proportional to the difference of the temperatures of the 
radiating body and of the surrounding air, it happened that the 
interval which elapsed between its production and its publication, to 
a great extent destroyed its utility. In 1813 Dulong and Petit, by an 
admirable series of experiments, established another law, taking the 
indications of the air thermometer as the measure of temperature. 
This law is, that the cooling of a body depends, not as Newton sup- 
posed, on the difference of temperature of the body, and the space into 
which it cools, but on the difference of exponential functions of the 
temperatures. The difficulty of the appearance of this law deterred 
philosophers from attempting its application to any but ove of the pro- 
blems. This one was that of the ring. M. Libri read, in 1825, to the 
Institute, and afterwards published at Florence and in Crelle’s Journal 
in Germany, his analysis of this problem. No one appears to have 
doubted the accuracy of this solution, until, in 1837, the author ex- 
pressed his conviction that the whole was founded on an erroneous 
hypothesis relative to the resulting equation. The following year M. 
Liouville read a paper on the subject to the Institute, which he subse- 
quently published in his own journal. In this paper he points out 
