﻿894 Mr. E. A. Milne on Radiative Equilibrium : 



A similar formula holds when rotation is taken into account. 

 Since F is positive in high latitudes and negate in low, 

 T should be greater in high latitudes and smaller in low 

 than it would be in the absence of convection. Moreover, 

 for some particular latitude F will be zero, and here the value 

 o£ T will be the same as in the absence of world-wide con- 

 vection. The agreement between calculation and observation 

 for 8.E. England thus implies that in this latitude the amount 

 radiated is about equal to the solar radiation incident. 



But T for high latitudes exceeds that for low. Now 

 7r(F + Scos«) is the total outward radiation to space. 

 Hence (on the assumptions made) the total radiation to 

 space in high latitudes must exceed that in low, unless the 

 change of n is very considerable. This is a surprising 

 result, but not necessarily impossible ; if the stratospheric 

 temperatures are really maintained to great heights under 

 the influence of radiation there seems little escape from 

 it. The difficulty is, of course, not new. Gold dealt with 

 it as follows *. Gold showed that if the absorbing power 

 of the atmosphere increases, then the theoretical height of 

 the tropopause increases. In the notation of § 2, it can be 

 deduced from (4) that t 2 though increasing with n is 

 fairly insensitive to it. Roughly speaking, then, on Gold's 

 theory the isothermal state sets in at a fixed optical depth 

 below the outer boundary ; hence the more absorbing the 

 atmosphere the smaller is t 2 /t^ the smaller is p^lpi, and 

 the greater is the height of the tropopause. The known 

 increased humidity over the equator, with consequent in- 

 creased absorbing power, would thus account for the observed 

 increased height of the tropopause ; and the lower tempe- 

 rature of the stratosphere follows from the increased height 

 through which a convective gradient holds, even allowing 

 for the higher ground temperature. But the above difficulty 

 still remains, for the increased absorbing power implies a 

 decreased outward radiation. 



Gold argued from the improbability of this that " the 

 atmosphere is not a ' grey ' body, but must have nearly 

 perfect transparency for some spectral region." It is well 

 known that the coefficient of absorption varies considerably 

 from place to place in the spectrum, whereas we have 

 assumed it to possess but two values — one for solar radiation 

 and one for terrestrial. But it is very doubtful whether 

 this removes the difficulty. For there still has to be an 

 equilibrium of radiation. One might reason generally 

 that the transparency of the air in certain spectral regions 

 * Geophysical Memoirs, i. p. 128 (1913). 



