72 M. POUILLET ON SOLAR HEAT, 
and we equally know that this formula has been verified by very 
accurate experiments of MM. Gay-Lussac and Welter, which 
extend for the pressures from 1460 mill. to 144 mill., and for 
the temperatures from 40° above zero to 20° below. 
Thus we may already calculate the capacities of the different 
strata of air up to four-fifths of the height of the atmosphere : it 
would be, however, interesting to continue the experiments of M. 
Gay-Lussac, and to extend them, if it be possible, preserving the 
same precision, down to temperatures of 60° or 80° below zero, 
—a temperature which we can now obtain by means of the ap- 
paratus of M. Thilorier*. 
However, if we admit provisionally that the formula of M. 
Poisson actually extends to a pressure of ;3, of atmosphere, 
we find that the temperature of the corresponding stratum at 
that pressure would be lower by 163° than the mean tempera- 
ture of the stratum nearest the soil, and, as the latter is 27° above 
zero, the other would be 136° below zero. 
Calculating the temperatures of the 100 strata corresponding 
to each of the 100ths of the atmospheric pressure, and taking 
the mean of them, we obtain approximately what we may call 
the mean temperature of the atmospheric column, because it is 
in fact in virtue of this temperature that the entire column emits 
radiant heat: the calculation gives for this mean — 8°. 
There is still another verification possible. We know that 
the barometric formula is exact up to a considerable height, 
and that it establishes a relation between the vertical distance of 
the two strata and the corresponding pressures. This relation 
1s approximately 
z= 18393.1. (4) ; 
on combining it with the preceding, we arrive at this result— 
t—-?}= hel 
224°8 
that is to say, that the difference of the temperatures of two 
strata is 1° for every 225 metres within the extent to which the 
barometric formula can be applied. 
We know that the experiments of M. de Humboldt give 200" ; 
this difference of one-eighth depends doubtless on many causes, 
and particularly on the fact that the formula which connects the 
capacities with the pressures can only be employed for dry air, 
* See my experiments on this subject, Compies Rendus, t. iv. p. 513. 
