RADIATION AND ABSORPTION. 51 
it would equally give at the surface of the earth, if the atmo- 
spheric air did not absorb any of the incident rays. 
6. The preceding values of p indicate the proportions of solar 
heat which have been transmitted in the different days to which 
they correspond, and the values of 1— p indicate, on the con- 
trary, the different proportions of solar heat which have been 
absorbed at the same periods. These values, however, corre- 
spond to « = 1, that is to say, they indicate the proportions of 
solar heat which would have been transmitted and absorbed at 
those places where the sun was in the zenith, supposing there 
the same atmospheric state as at Paris at the moment of the 
experiment. It results that in the vertical passage the atmo- 
21 
sphere absorbs at least ;4', of the incident heat, and at most 
ja5, Without the sky ceasing to be serene. I must however 
add, that on the 28th of June, to which corresponds the ab- 
sorption of ,%%,, a light white veil was visible on the vault of the 
sky. Moreover other observations, the series of which could 
not be completed, indicated only an absorption of 1°; we may 
thus say that the atmospheric absorption is comprised between 
18 and 24 or 25 hundredths, without its being possible to di- 
stinguish in the sky vapours which disturb its transparence. 
7. By means of this datum, and of the law according to which 
the transmitted heat diminishes in proportion as the obliquity 
increases, we may calculate the proportion of incident heat 
which each instant reaches the illuminated hemisphere of the 
earth, and that which is absorbed in the corresponding half of 
the atmosphere. This calculation depends on an integral of the 
form 
om 
of is, 
which cannot be obtained exactly; but by various methods of 
approximation, it is easy to recognise that for p = 0°75 the pro- 
portion which reaches the ground is comprised between 0°5 and 
0°6, and consequently the proportion absorbed by the atmosphere 
is itself comprised between 0°5 and 0°4; but very near 0-4. 
Thus, when the atmosphere has all the appearance of per- 
fect serenity, it still absorbs nearly the half of the total quan- 
tity of heat which the sun emits towards the earth, and it is the 
other half only of that heat which falls upon the surface of the 
ground, and which is there variously distributed, according as it 
has traversed the atmosphere with greater or less obliquities. 
E 2 
