264 Proceedings of Royal Society of Edinburgh. [sess. 
all cases, the radiation of the soil against the mass of air at tem- 
perature u must be less than it was under the assumption that no 
radiation exists between the two masses. But, on the other hand, 
the mass of air at temperature t arriving at a lower temperature 
by its own radiation, its power of absorption from the soil will he 
increased at the same time. Now, we know that the radiating 
(absorptive) power against the earth’s surface is equal for both 
masses. Thus, the same quantity of heat radiated by one and 
absorbed by the other will affect the earth’s radiation in each case 
in exactly the opposite way. Hence, it follows directly, first, that 
the total amount of heat given by the soil to the air is the same, 
whatever he supposed as to the communication of heat between 
the elements of the atmosphere themselves ; and secondly, in 
making the assumption that all the heat required for maintaining 
the constant temperature, u , is spent by the earth’s surface, we are 
bound, on the other hand, to give the soil the whole advantage of 
the radiation coming from the mass of air at temperature t. 
If we denote by dw' the quantity of heat radiated by the soil 
during the time dz , by die that radiated by the mass of air at 
temperature t , we may represent our result by the following 
equations : — 
~t~ = - n\(t' - u) - n\(t' - t) 
dw 
Tfe = -nMf-t). 
Apparently these equations are true only so long as there are no 
other sources of heat except the soil and the atmosphere, which is 
the case during the night. How they are affected by the solar 
radiation during the day shall be pointed out afterwards. 
The equations in their present form give the total change of 
heat in both the earth’s surface and the air. To find the change of 
temperature we must introduce some further considerations. What 
we really know by the fundamental law of the relation between 
the radiation and the absorptive power of a body only refers to 
the whole quantity of heat radiated or absorbed. Bat, unfortu- 
nately, we do not as yet know what part of this whole quantity is 
absorbed by a distinct element at the surface of the body. Taking 
