660 proceedings of the american academy. 



Heat received and Heat retained. 



Such, then, would be the mean annual temperature of the planet, 

 were the heat retained as well there as here. I am far from saying 

 that such is the temperature. For the retention is not the same on 

 the two planets, being, on account of its denser air, much better on the 

 earth. But that such is the amount received is enough to suggest 

 very different ideas as to the climatic warmth from those hitherto 

 entertained. 



Temperature deduced from Heat retained. 



To obtain some idea of the heat retained and of the temperature in 

 consequence we may proceed in this way : 



Let y = the radiant energy received at the surface of the earth. 

 i/i = that similarly received on Mars. 



e = the relative emissivity or the coefficient of radiation from the 

 surface of the earth, giving the ratio of the loss in twenty- 

 four hours to the amount received in the same time, due to 

 factors other than the transmissibility of the air, which is 

 separately considered. 

 ei = the same coefficient for Mars. 



Clouds transmit approximately 20 per cent of the heat reaching 

 them ; a clear sky at sea-level, 50 per cent. Consequently as the sky 

 is half the time cloudy the mean transmission of its air-envelope for 

 the earth is 



.35 e 

 For Mars it is 



.60^1 



To get, then, the mean temperature of the planet in degrees, .r, from 

 the heat retained, which is the daily mean receipt less the mean loss, 

 we have the following equation, the mean temperature of the earth 

 being [519.4°F. Abs.] 288°C. above absolute zero : 



^ _ Vy, (1 -.60gi ) 

 288.5 ~ \X^ (l-.35g) 



Determination of e. 



To find e we have the data that the fall in temperature toward 

 morning on the earth under a clear night sky is about 18° F. or 10° C. ; 



