the Surface-Temperature of the Planets. 171 



we form the following equation to determine e :— 

 292°- 10° _ ^>(l--425g) 



whence 



Since the radiation by day is greater by about 1*15 than 



— . 292 4 



by night, being as ^- 4 we have more approximately 



i(-40 + *50)« or '45<?, 

 £ (-40 4- -20) ^ or -30 e, 



for a cloudy night under the same conditions. 

 This gives .,„., , 



or substantially what it was before. It changes the final 

 result for the mean temperature of Mars by less than two- 

 tenths of a degree. 



Determination of e { , — Since in the mean the planet radiates 

 as much heat as it receives and 



^=1-10, 



y 



the radiation must be in the same ratio. Whence the loss from 

 radiation in twenty-four hours on Mars, so far as it depends 

 on the heat received, is 



«!=ri« 



= •51. 



or, by the more approximate calculation in the paragraph 

 above, it still =-51 



.Substituting these values in our equation above, we find 

 a, the mean temperature of Mars, = 8°*7 C, 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 energy received*. 



* If we adopt Arrhenius's formula for the temperature T of the Earth's 

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

 paper on the effect of carbon dioxide in the air, 



«A+M+(l-«) A(l+iO + N(l+-) 



y (l+„_/3„) 



where a = atmospheric absorption for solar heat, 



/3 = „ „ Earth-surface heat, 



A= solar constant, less loss by selective reflexion by the air, 



M= heat conveyed to the air from other points, 



N= „ ,, surface from other points, 



*.-.!.. v=l ft- albedo of the surface 

 y = radiation constant. 



