1895 - 96 .] Dr J. Halm on the Temperature of the Air. 
265 
such an infinitely small element, we are sure that only a compara- 
tively small part of the whole radiation received by the surface 
will he actually absorbed within the element, which allows the 
larger part to enter the neighbouring elements, where it is again 
partly absorbed, and partly carried to deeper layers according to 
the laws of conduction. Owing to the fact that radiation of a 
solid like the earth must be a mere action of the surface, the 
question we have to consider is, How much heat is lost or gained 
by an infinitely small element of this surface ? All the other heat 
passing through this element without absorption is of no import- 
ance to our question, because it does not change the temperature, 
t', of the surface. 
The general problem, how much of a given intensity of radiation 
is absorbed by a certain element of a resisting medium, was first 
solved by Bouguer, who gave a formula for representing the extinc- 
tion of light in the atmosphere. There is no obvious reason why 
the same considerations should not apply to the radiation of heat. 
Let us call a the coefficient of absorption for a given substance, 
p its density, dV the volume of an infinitely small element, cr the 
intensity of radiation falling upon the surface of this element, 
da- the quantity of radiation absorbed, then we have the well- 
known formula 
da~ — — aa-pdY . 
From this formula we learn that two different bodies with the 
same absorptive power, but different densities, absorb different 
quantities of radiation in equal elements of their surfaces, which 
are represented by the relation : 
dcr l p 1 
da-. 2 p 2 
As the absorptive power of the soil against the two masses of air 
must necessarily be the same as the power of radiation of these two 
masses against the soil, and vice versa , this last relation must exist 
between equal elements of volume of the soil and the air at their 
surfaces. 
How we have the two equations 
dv dt' , dv 7TT 
CiPidv.-^tmd — = c 2 p 2 dY 
VOL. XXI. 
dz 
2 / 3/97 
dt 
dz 
