CHAPTER III 



A. THEORY OF THE RADIATION OF THE ATMOSPHERE 



The outgoing effective radiation of a blackened body in the night 

 must be regarded as the sum of several terms : (i) the radiation from 

 the surface toward space (E c ) given, for a " black body," by Stefan's 

 radiation law; (2) the radiation from the atmosphere to the surface 

 (E a ) , to which must be added the sum of the radiations from sidereal 

 bodies (E s ), a radiation source that is indicated by Poisson by the 

 term " sidereal heat." If / is the effective radiation, we shall evi- 

 dently have : 



J = E C — E a — E s 

 For the special case where the temperature of the surface is con- 

 stant and the same is assumed to be the case for the sidereal radiation, 

 we can write : 



J=K-E a 

 K being a constant. Under these circumstances the variations in the 

 effective radiation are dependent upon the atmospheric radiation 

 only, and the problem is identical with the problem of the radiation 

 from a gaseous body, which in this case is a mixture of several 

 different components. As is well known from thorough investiga- 

 tions, a gaseous body has no continuous spectrum, but is charac- 

 terized by a selective radiation that is relatively strong at certain 

 points of the spectrum and often inappreciable at intermediate 

 points. The law for the distribution of energy is generally very 

 complicated and is different for different gases. The intensity is 

 further dependent upon the thickness, density, and temperature of 

 the radiating layer. 



Let us consider the intensity of the radiation for a special wave 

 length A, from a uniform gaseous layer of a thickness R and a tem- 

 perature T toward a small elementary surface dr. To begin with, 

 we will consider only the radiation that comes in from an elementary 

 radiation cone, perpendicular to dr, which at unit distance from dr 

 has a cross-section equal to d£l. One can easily deduce : 



R 



e k e~ a ^r drdQdr 



h 

 which sfives for unit surface : 



j\ — 

 18 



J x =^.dn(i-e- a xR) ' (1) 



