1819.] andon the Laws of the Communication of Heat. — 329 
This result may be announced in a manner still more simple, to 
which we are led by the following calculation. 
If we call P the cooling power of air under the pressure p, 
this power will become P (1°366) under a pressure 2 p; P (1-366)? 
under a pressure 4 p; and under a pressure p . 2”, it will be 
P (1:366)". Making p . 2" = p’ and P (1°366)" = P’, we shall 
obviously obtain by eliminating x. 
Log. P’ — log. P __ Log. p’ — log. p 
Log. (1°366) Log, 2 
Hence 
P’ p' 0°45 
sm 
We shall find in the same way for hydrogen 
Pp’ p' 038 
5 ae ey, 
For carbonic acid, the exponent will be 0°517, and for olefiant 
gas 0°501. 
From this we conclude, that the cooling power of a gas is, 
every thing else being equal, proportional to a certain power of 
its elasticity ; but that the exponent of this power vanes from 
one gas to another. Itis 0°38 for hydrogen, 0°45 for air, 0°517 
for carbonic acid, and 0°501 for olefiant gas. These last three 
numbers differing little from 0°5, we may say that in the gases 
to which they belong, the cooling power is nearly as the square 
root of the elasticity. 
If we compare the law which we have thus announced with the 
eens of Leslie and Dalton, we shall be able to judge 
of the errors into which they have been led by the inaccurate 
suppositions which serve as the basis of all their calculations, 
and by the little precision attainable by the methods which they 
have followed. ‘The first by photometrical experiments, calcu- 
lated by the law of Newton, finds the cooling power of air 
pepernons to the fifth root of its density; and Mr. Dalton 
finds it proportional to the cube root, supposing, as he always 
does, the law of cooling the same for all bodies and in all the 
ases. 
Now that we know the influence that the temperature and the 
density of the gas in which it takes place has upon cooling, it 
remains to discover how for a given state of a fluid the velocities 
of cooling depend upon the excesses of the temperature. 
We have already observed, that the law which expresses this 
dependance remains the same for the same gas when its elasti- 
city changes. Letus see now what happens when we pass from 
one gas to another ; and for this purpose let us resume, from the 
preceding tables, the velocities of cooling due to the sole con- 
tact of air, of hydrogen, carbonic acid, and olefiant gases, these 
four fluids being under a pressure of 0°72 metre. 
