﻿the Insolation of an Atmosphere. 893 



close to 60°; and we have seen that the value « = G0° plays a 

 special part in the theory. 



It is therefore interesting to inquire whether the theory 

 developed in the present paper has any bearing on the 

 question of the origin of the variation with latitude. The 

 tacts to explain are that the temperature of the stratosphere 

 increases as the latitude increases, and that the height of 

 the tropopause decreases. Reference to recent books on 

 meteorology and the physics of the air shows that there 

 is no accepted detailed explanation. 



Assuming that a stratosphere is optically very thin, it will 

 be very nearly isothermal and its temperature will be equal 

 to T . Formula [U) shows at once that the ratio of T to T, 

 (the effective temperature of the insolation) increases as 

 X increases, provided n is not zero, and that the increase 

 becomes relatively large for high latitudes. As seen in § 7, 

 this is due to the increased absorption of the solar radiation 

 in the more superficial layers. This does not seem to have 

 been suggested before, and it may in fact be one of the con- 

 tributary causes of the increased temperature in higher 

 latitudes. But the first of formulae (31) shows that the 

 actual value of T decreases as \ increases. All the theory 

 indicates is that T decreases much more slowly than 1\ as 

 X increases, and so the absolute increase of T as observed is 

 not accounted for. The tendency to increase would be helped 

 if it could be shown that n increased with X, i. e. if the ratio 

 of absorption of solar radiation to that of terrestrial radiation 

 increased with latitude. Some effect of this kind there must 

 be : for carbon dioxide is more important as an absorber of 

 solar radiation than of terrestrial radiation, and owing to the 

 decreased humidity in high latitudes the ratio of carbon 

 dioxide to water vapour is there greater. But this, again, 

 would not appear to be sufficient. 



It must now be recalled that we have assumed throughout 

 that any portion of the surface radiates away an amount of 

 energy equal to that incident on it. But we know that this 

 is not true for the earth's surface. Heat is coirvected from 

 the equatorial regions toward the polar regions : otherwise 

 the change of surface temperature with latitude would be 

 much more severe than it is. Hence the equatorial regions 

 must radiate less than they receive, the polar regions more. 

 Now if 7rF is the additional net outward flux (positive or 

 negative), the radiative distribution of temperature is obtained 

 by adding the term F(^ + t) to the right-hand of (28"), and 

 the boundary temperature is given by 



o-V/tt = iF+iS(cosa + in). . . . (41) 



