262 Proceedings of Royal Society of Edinburgh. [sess. 
Now, let us assume the temperature of the lowest layer of the 
new atmosphere to he identical with the observed temperature of 
the real one, we do not alter by this supposition the conditions 
of heating this layer. For we can easily prove that any change of 
heat in it cannot hut depend on its own temperature, the tempera- 
ture of the soil, the mean temperature, T, and its coefficient of 
total radiation — factors which are supposed to remain unaltered by 
the new supposition. 
We again assume the substituted atmosphere to contain 2 n 
layers, the temperatures of which are as follows : 
T + rcA; T + (w-l)A; T + («-*2)A; T+A; T-A; ' 
T — (n — 2)A ; T - (n - 1)A ; T - nA, 
where A is an extremely small increment of temperature. All 
these layers must be supposed to have the same coefficient of 
radiation, X, and, besides, there exists the condition 
T + n A = t, 
where t is the observed temperature of the lowest layer of the 
atmosphere. 
Considering two of these layers, of which the temperatures are 
T + (n - 7c) A and T — (n - 7c) A, we know that the quantities of 
heat received from the earth’s surface are respectively 
-X{t' -T - (n-7c)A) and - A{f - T + (n - 7c) A} . 
But apparently the sum of these quantities is not altered by 
assuming the first layer to have the temperature, T + nA = t, and 
the second one, T - nA. Thus we come to the general conclusion, 
that we may assume the radiation of the soil to be directed 
towards two masses of air with the respective temperatures, T + nA 
and T - nA, in all their elements , each of which masses has the 
coefficient of radiation, nX ; and that the total amount of this radia- 
tion is equal to the whole radiation against the real atmosphere. 
Of course we know nothing about the temperature, T-nA, of 
the upper limit of our supposed atmosphere. But it has been 
shown, with some approach to certainty, by the very few observa- 
tions made, as well as by theoretical considerations, that, at a 
