254 Prof. S. Arrhenius on the Influence of Carbonic Acii 



III. Thermal Equilibrium on the Surface arid in the 

 Atmosphere of the Earth. 



As we now have a sufficient knowledge of the absorption 

 of heat by the atmosphere, it remains to examine how the 

 temperature of the ground depends on the absorptive power 

 of the air. Such an investigation has been already performed 

 by Pouillet*, but it must be made anew, for Pouillet used 

 hypotheses that are not in agreement with our present 

 knowledge. 



In our deductions we will assume that the heat that is con- 

 ducted from the interior of the earth to its surface may be 

 wholly neglected. If a change occurs in the temperature 

 of the earth's surface, the upper layers of the earth's crust will 

 evidently also change their temperature ; but this later pro- 

 cess will pass away in a very short time in comparison with 

 the time that is necessary for the alteration of the surface 

 temperature, so that at any time the heat that is transported 

 from the interior to the surface (positive in the winter, nega- 

 tive in the summer) must remain independent of the small 

 secular variations of the surface temperature, and in the 

 course of a year be very nearly equal to zero. 



Likewise we will suppose that the heat that is conducted 

 to a given place on the earth's surface or in the atmosphere 

 in consequence of atmospheric or oceanic currents, horizontal 

 or vertical, remains the same in the course of the time con- 

 sidered, and we will also suppose that the clouded part of the 

 sky remains unchanged. It is only the variation of the 

 temperature with the transparency of the air that we shall 

 examine. 



All authors agree in the view that there prevails an equi- 

 librium in the temperature of the earth and of its atmosphere. 

 The atmosphere must, therefore, radiate as much heat to 

 space as it gains partly through the absorption of the sun's 

 rays, partly through the radiation from the hotter surface of 

 the earth and by means of ascending currents of air heated 

 by contact with the ground. On the other hand, the earth 

 loses just as much heat by radiation to space and to the 

 atmosphere as it gains by absorption of the sun's rays. If 

 we consider a given place in the atmosphere or on the ground, 

 we must also take into consideration the quantities of heat 

 that are carried to this place by means of oceanic or atmo- 

 spheric currents. For the radiation we will suppose that 



* Pouillet, Comptes rendus, t. vii. p. 41 (1838). 



