1819.] and onthe Laws of the Communication of Heat. 173 
sufficient approximation at low temperatures ; but that it deviates 
further and further from the truth as the difference between the 
temperatures increases. ' 
If in the concise history of these labours we havenot mentioned 
the mathematical researches of M. Fourier, on the laws of the 
- distribution of heat, the reason is, that all the results of his 
analysis are deduced from the law of Newton, admitted as a 
truth founded on observation, while the sole object of our expe- 
riments is to discover the law that ought to be substituted for it. 
But the very remarkable consequences to which this profound 
mathematician has been led, will preserve all their precision it 
the circumstances and within the limits in which the Newtonian 
law is true; and to extend them to other cases, it will be suffi- 
cient to modify them conformably to the new laws which we 
shall establish. 
Of Cooling in general. 
When a body cools in a vacuum, its heat is entirely dissipated 
by radiation. When it is placed in air, or in any other fluid, its 
cooling becomes more rapid, the heat carried off by the fluid 
being in that case added to that which is dissipated by radiation. 
It is natural, therefore, to distinguish these two effects; and as 
they are subject in all probability to different laws, they ought te 
be studied separately. We shall examine then successively the 
laws of cooling in a vacuum and in elastic fluids. But as the 
lan which we have followed in each of these researches is 
founded on the same principles, it will be proper to explain 
these principles in the first place. 
The most simple case of cooling will be that of abody of sosmall 
a size that we may suppose at every instant all its pomts at the 
same temperature. But to arrive at the object which we proposed, 
the discovery of the elementary law of cooling, it would have 
been to add an useless complication to the question, and would 
have rendered it almost insoluble to have observed, in the first 
place, the rate of cooling in solid bodies ; because in that case 
the phenomenon includes an additional element, namely, the 
interior distribution of the heat, which is a function of the con- 
ductibility. Obliged by the nature of the problem to have 
recourse to liquids, the mercurial thermometer itself appeared to 
us the body best adapted for these experiments. But as it is 
necessary to be able to observe at high temperatures to give to 
the body on which the experiment is made such a size that the 
cooling shall not be too rapid for following its rate with accuracy, 
. it was necessary, in the first place, to examine what influence the 
Rusa or smaller mass of liquid contained in the bulb of the 
ermometer had upon the law of cooling. It was not less 
important to examine whether that law depends on the nature of 
the liquid, or the nature or form of the vessel in which it is con- 
tained. These first comparisons were the object of a series of 
experiments, which we shall state, after haviag explained the 
