the Surface-Temperature of the Planets. 169 



up the radiant energy received from the whole spectrum for 

 the two planets, thus : — 



Heat received at the Surfaces of Mars and the Earth. 



Percent, of heat received 

 Percent, of to whole energy of its 



whole energy. part of the spectrum. 

 Mars. Earth. 



Visual spectrum 32 73 23 



Invisible „ 65 60 50 



Total 64 41-5 



Insolation. — But this is not all. The above deduction 

 applies only to such sky as is clear. Now the Earth is 

 cloud-covered to the extent of 50 per cent, of its surface on 

 the average, Mars, except for about six Martian weeks, at the 

 time of the melting of the polar cap and over an area extending 

 some fifteen degrees from the pole, stands perpetually unveiled. 

 The surface thus fog-enveloped is 0*034 of its hemisphere 

 and the time 0*23 per cent, of the half year, whence the total 

 ratio of cloud to clear the whole year through over the whole 

 surface is less than 1 per cent. 



The albedo of cloud being 0*72, its transmission, including- 

 absorption re-given out, cannot exceed 0*28 and may be taken 

 at 0*20. Consequently the effective heat received on this 

 score by the Earth is about as *20 X \50 x *50 = 60 per cent.,, 

 and for Mars 99 per cent.; the ratio that of '60 to "99. This 

 agrees with Arrhenius's estimate of the heat transmissibility 

 of cloud. 



Taking now Stefan's law that the radiation of a body is as 

 the fourth power of its temperature, which is now generally 

 accepted, and since its enunciation by Stefan has been deduced 

 from theoretic considerations by both Boltzmann and Gralit- 

 zine, and remembering that, since the two planets maintain 

 their respective mean annual temperatures, they must radiate 

 as much heat as they receive, we have the following equation 

 from which to find the mean annual temperature of Mars, x, 

 in which 459°'4 + 60 G or 519°4 F. on the absolute scale 

 denotes the mean annual temperature of the Earth : — 



x : 519°-4 : : t/l 2 X-64x'99 : v'i'524 8 X "415 X '60, 

 or &' = 519°*4 



,o.„ 892 



872 

 531°-4abs. = 72°F. of 22° C 



