Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/25

260 $\text{W}=1$) about 80 p. c. of the earth's radiation is absorbed in the air, we may as mean temperature of the absorbing layer choose the temperature at the height where 40 p. c. of the heat is absorbed. Since emission and absorption follow the same quantitative laws, we may as mean temperature of the emitting layer choose the temperature at the height where radiation entering from space in the opposite direction to the actual emission is absorbed to the extent of 40 p. c.

Langley has made four measurements of the absorptive power of water-vapour for radiation from a hot Leslie cube of 100° C. These give nearly the same absorption-coefficient if Pouillet's formula is used for the calculation. From these numbers we calculate that for the absorption of 40 p. c. of the radiation it would be necessary to intercalate so much water-vapour between radiator and bolometer that, when condensed, it would form a layer of water 3.05 millimetres thick. If we now suppose as mean for the whole earth $$\text{K}=1$$ and $$\text{W}=1$$ (see ), we find that vertical rays from the earth, if it were at 100°, must traverse 305 metres of air to lose 40 p. c. Now the earth is only at 15° C., but this cannot make any great difference. Since the radiation emanates in all directions, we have to divide 305305 metres [sic] by 1.61 and get in this way 209 metres. In consequence of the lowering of the quantity of water-vapour with the height we must apply a slight correction, so that the final result is 233 metres. Of course this number is a mean value, and higher values will hold good for colder, lower for warmer parts of the earth. In so small a distance from the earth, then, 40 p. c. of the earth's radiation should be stopped. Now it is not wholly correct to calculate with Pouillet's formula (it is rather strange that Langley's figures agree so well with it), which gives necessarily too low values. But, on the other hand, we have not at all considered the absorption by the carbonic acid in this part, and this may compensate for the error mentioned. In the highest layers of the atmosphere there is very little water-vapour, so that we must calculate with carbonic acid as the chief absorbent. From a measurement by Ångström, we learn that the absorption-coefficients of water-vapour and of carbonic acid in equal quantities (equal number of molecules) are in the proportion 81 : 62. This ratio is valid for the least hot radiator that Ångström used, and there is no doubt