260 Prof. S. Arrhenius on the Influence of Carbonic Acid 



W = l) 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-coeffi- 

 cient 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 K = l 

 andW = l (see Table VI.), 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 305 by 1*61 and get in this way 

 209 metres. In consequence of the lowering of the quantity 

 of water-vapour with the height f 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 w 7 ith it), which gives neces- 

 sarily 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 b}^ Angstrom J, 

 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 Angstrom used, and there is no doubt 



* Langley, "Temperature of the Moon," p. 186. 

 t Hann, Meteor oloyische Zeitschrift, xi. p. 196 (1894). 

 % Angstrom, Bihang till K. Vet. -Ah. Handl. Bd, xv. Afd. 1, No. 9, 

 pp. 11 and 18 (1889). 



