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



the night, and using bars to denote mean values, we 

 have 



-|-(cos\ + ^wr) 



17 ** Jo 



77 



cos A 



(j- - 1 f*in 



— Ti 4 = Bi = — I S cos A, cos d> deb = S 



77 7Tj 



7T 7T J T 7T 



. . . (31) 



When this averaging is taken into account, the approxi- 

 mately isothermal state (T^^To) is found to occur for 

 cosX = ?i/\/2 ; for this value of \, 



ToVT?= i(l+ W2) = 1-055, 



which is sufficientlj near unity. The general run of the 

 change of temperature distribution with latitude has the 

 same features as before. 



§ 9. Comparison with Emden. — The formal problems dis- 

 cussed by Emden in the paper already mentioned and his 

 method of solution are very similar to those discussed above, 

 except that he takes the material to be bounded below by a 

 black surface. Emden considers the radiative equilibrium 

 of an atmosphere subject to external solar radiation in 

 two cases: (1) the case of "grey radiation," by which 

 he means the case in which the mean coefficient of 

 absorption for the solar radiation is equal to that for the 

 atmospheric radiation; this is the case n = l above ; (2) the 

 case in which the radiation spectrum can be divided into two 

 ranges which have different mean coefficients of absorption, 

 the solar radiation being entirely confined to one of them; 

 this is practically our general case in which n is not unity, 

 In each case he considers the solar radiation to be " gleich- 

 massig verteilt," i. e. not as being confined to a parallel 

 beam, but as uniformly distributed over the solid angle 27r ; 

 consequently he does not consider the variation of the state 

 of equilibrium with latitude. The two main results to 

 which he draws attention are : in case (1) the whole atmo- 

 sphere must be isothermal, at a temperature equal to the 

 " effective " temperature T 1 calculated from the incident 

 radiation with allowance for the albedo (see p. 873 above) ; 

 in case (2) the state is not isothermal and the boundary 

 temperature T is connected with the effective temperature 





