Evaluating the Surface-Temperatures of the Planets. 759 



thin layer close to the surface at the higher level. It, too, 

 radiates half up and half down. But of the half going up- 

 wards a less fraction will be intercepted since the superin- 

 cumbent layers are now less absorbing. Thus D/A will be 

 greater at the lower than at the higher level*. We should, 

 therefore, compare the results for any value of D/A in 

 Table I. with the results in Table II. for a somewhat lower 

 value. 



We may exclude the extreme cases of ?i = 2 and n=l, as 

 the true value is certainly between these, and confine our 

 examination to intermediate values. 



Suppose, for example, that D/A = 4/5 at the lower level, 



while it is 3/4 at the upper level. Then $/# = 088 from 



Table I. at the lower, while 0/0 = O'83 from Table II. at the 

 upper level. Or if D/A = | at the lower level, while it is | 



at the upper level, 0/0 = 0'86 below, while 6/0 = O'Sl above. 

 Or in each case the mean temperature is higher at sea-level 

 by about 5 in 87 or by about 17° in 300°. 



It is to be observed that the lower mean temperature at a 

 higher level must hold good if the higher level is so much 

 higher that there is practically no atmosphere above. For 

 then £ = 1 and a 1 = 0, so that Rtf=S and R re = 0. Therefore 



rf /0=land 6 J 6 = and 0\0=\. 



The lower mean temperature of elevated parts of the 

 earth's surface is a well established fact. Perhaps if it were 

 only observed in the case of mountain peaks it might be 

 ascribed to the cold air blowing against them. The fall of 

 temperature in free air as we go upwards tends towards that 

 given by convective equilibrium, though recent observations 

 show that it is not so great as that given by the adiabatic 

 law. Thus for a rise of 3500 metres the adiabatic law would 

 give a fall of about 32° C. if the sea-level temperature were 

 300° A. ; whereas the observations of Teisserenc de Bort at 

 Trappes show a mean annual fall of about 16° C. for this 

 rise (Encyc. Brit. xxx. Meteorology, p. 695). A continual 

 blast of air thus cooled might of course reduce the tempera- 

 ture on the mountain peaks, even if radiation did not tend 

 to any such reduction. But we can hardly account in this 

 way for the equally well established lower temperature of 

 elevated continental plateaus. According to Abbe (loc. cit. 



* Another consideration leading- to the same conclusion is that the 

 atmosphere acts like a plate with its lower surface much warmer than 

 its upper. When we only have the part above an elevated region the 

 difference of temperature between the surfaces is much less than for the 

 whole air, and the radiations up and clown are more nearly equal. 



3E 2 



