370 
On the Measure of Temperature, 
[Dec. 
that the quantities of heat 3 carried off by a gas from any body, form a geometric 
progression, the excesses of temperature being also in geometric progression. The 
ratio of the latter being 2, that of the former will be 2,35, and by a similar trans- 
formation to that before given, this truth resolves itself into the following more 
general one, that is to say, that the loss of heat , due to the contact of a gas, is as the 
excess of temperature raised to the 1,233 power . 
To give an idea how well this law represents the phenomena, we give, in the 
following table, the cooling effect of common air, under a pressure of O m ,72, the 
second column containing the observed results, and the third the calculated ones 
derived from above the law. 
Excess of tem- 
perature. 
Rates of cool- 
ing observed. 
Rate of cooling 
calculated. 
200° 
5°, 48 
5°, 45 
180 
4 ,75 
4 ,78 
160 
4 ,17 
4 ,14 
140 
3 ,51 
3 ,51 
120 
2 ,90 
2 ,91 
100 
2 ,27 
2 ,31 
80 
1 ,77 
1 ,76 
60 
1 ,23 
1 ,24 
40 
0 ,77 
0 ,75 
20 
0 ,33 
0 ,32 
It would he useless multiplying these comparisons, as derived from observations 
made with the other gases, and at various pressures, for we have already shown 
that each gas follows exactly the same law, and this whatever the pressure. And 
the com pardons to which we allude, have given us equally satisfactory results with 
the preceding, a fact which may be easily verified on any of the series we have 
registered. 
To have a general expression for the rate of cooling, as affected by the con- 
tact of a gas, it is necessary to collect together the several particular laws which 
we have established. The first teaches us, that the state of the surface of the body 
has no influence on the quantity of heat abstracted by the g as; the second 
shows, that the density and temperature only affect the cooling process, inasmuch 
as they alter the pressure ; so that the cooling power of this fluid depends simply 
on its elasticity. This elasticity, and the excess of temperature, then, are the only 
elements by which the rate of cooling is affected. If the first be expressed by p, 
and the second by t , we shall have, for the expression of V = rate of cooling 
V — m p£ 
b being for all bodies and all gases = 1,233; c being constant for all bodies, but 
varying with the gas ; and m depending for its value not only on the nature of the 
gas, but also on the dimensions of the cooling body. The values of c are, as we 
have already’ found, 0,45 for air, 0,33 for hydr gen, 0,51“ for carbonic acid, and 
0,501 for olefiant gas. The values of m depend, as we have already’ said, on the 
dimensions of the cooling body, and on the nature of the gas. For the thermometer 
we used, m is equal to 0,00919 in air, 0,0318 in hydrogen, 0,00887 in carbonic acid, 
and to 0,01227 in olefiant gas. These values of m, suppose p to be expressed in 
metres, and t in degrees of the centigrade scale. We may, by means of this 
expression for V calculate the ratios between the cooling powers of the several gases, 
and for each pressure. Thus, in taking unity to represent the cooling power of air, 
and supposing the pressure = 0 m ,7fi, we have for the cooling power of hydrogen 
, 5, and for that of carbonic acid 0,965. These numbeis would change with the 
e asticity of each of the gases — a fact not perceived by Messrs. Dalton and Leslie, 
lough easily deducible from our formula ; their determination, however, for the 
ension 0 m ,76, differs but little from those we have just calculated. We shall return 
presently to this accidental agreement between their experiments and ours. 
D u simplicity ot the general law we have just explained made us very desir- 
° ' eri *ymg it on higher temperatures than any we could command in the 
8 T> 
motnet^r^ 11 TV' ,ieS °^ ,ie . at > \ s meant, loss of temperature, i. e. depression of the ther- 
— £n. Gl, iiie ex P resslon > however, is objectionable, and eminently unphilosopbical. 
