662 PROCEEDINGS OF THE AMERICAN ACADEMY. 



the radiation must be in the same ratio. Whence, the loss by radia- 

 tion in twenty-four hours on Mars so far as it depends on the heat 

 received is 



ex = 1.1 e 

 = .51, 



or by the more approximate calculation in the paragraph above, it 

 still 



= .51 



Substituting these values in our equation (page 660), we find 

 a;, the mean temperature of Mars, 



= 8°. 7 a 



or ==47°. 7 F., 



taking into account the heat radiated away as well as the heat received 

 and gauging the temperature by the heat retained ; by the net, instead 

 of the gross, amount of the radiant energy received. 



If we assume clouds to transmit less heat than 20 per cent, we di- 

 minish i/ and increase (1 — .35 e), so that the ultimate result is not 

 greatly altered. 



If we take Arrhenius' formula for the temperature T of the earth's 

 surface as affected by the air-envelope, we have as determined in his 

 paper on the effect of carbon dioxide in the air : 



T' = 



a^-f J/-f(l-a)^(l + i') + iV^M + - j 



y {I + f — ZSv) 



where a = atmospheric absorption for solar heat, 



ft — atmospheric absorption for earth-surface heat, 

 A = Solar Constant, less loss by selective reflection by the air, 

 31 = heat conveyed to the air from other points, 

 N = heat conveyed to the surface from other points, 

 V = 1 — albedo of the surface, 

 y = radiation constant. 



The values for these quantities found bolometrically for a clear sky 

 are a = .50, 



^ = 1 — .79 X .32 = .747 = whole spectrum — albedo of the air X 



visible portion, 

 (3 = a approximately, 

 v= 1 -.11 = .89 



