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



radiated from the air (emission-coefficient j3, temperature 6) 

 to space (temperature 0). The second one gives the heat 

 radiated from the soil (1 cm. 2 , temperature T, albedo 1— v) to 

 the air ; the third and fourth give the amount of the sun's 

 radiation absorbed by the air, and the quantity of heat ob- 

 tained by conduction (air-currents) from other parts of the 

 air or from the ground. In the same manner we find for the 

 earth's surface 



/3 7 <T 4 -0 4 ) + (1-£)tvT*= (1-«)vA+N. . (2) 



The first and second members represent the radiated quan- 

 tities of heat that go to the air and to space respectively, 

 (1— a)vA is the part of the sun's radiation absorbed, and N 

 the heat conducted to the point considered from other parts 

 of the soil or from the air by means of water- or air-currents. 



Combining both these equations for the elimination of 0, 

 which has no considerable interest, we find for T 4 



T4 _ aA + M + (l-«)A(l + y) + N(l + l/v) _ K 



y(l + v-/3v) ~ l + v(l-/3) * l ; 



For the earth's solid crust we may, without sensible error, 

 put v equal to 1, if we except the snowfields, for which we 

 assume r> = 0*5. For the water-covered parts of the earth I 

 have calculated the mean value of v to be 0*1)25 by aid of the 

 figures of Zenker*. We have, also, in the following to make 

 use of the albedo of the clouds. I do not know if this has 

 ever been measured, but it probably does not differ very much 

 from that of fresh fallen snow, which Zollner has determined 

 to be 0*78, i. e. j>=0"22. For old snow the albedo is much 

 less or v much greater ; therefore we have assumed 0'5 as a 

 mean value. 



The last formula shows that the temperature of the earth 

 augments with /5, and the more rapidly the greater v is. For 

 an increase of 1° if v=l we find the following increases for 

 the values of v= 0*925, 05, and 0*22 respectively : — 



/3. 



!/=0-925. 



i>=0-5. 



^=0-22. 



0-65 



0-944 



0-575 



0-275 



0*75 



0-940 



0-556 



0-261 



0-85 



0-934 



535 



0-245 



0-95 



0-928 



0-512 



0-228 



1-00 



0-925 



0-500 



0-220 



This reasoning holds good if the part of the earth's surface 



* Zenker, Die Vertheilung der Wdrme auf der Erdoberjlache, p. 54 

 (Berlin, 1888). 



