254 Prof. A. Schuster on the Influence of 



familiar with this kind o£ opaqueness, due to reflexions 

 within convection currents set up by the solar heating of a 

 valley. It is advisable therefore to extend the foregoing 

 investigation to include the effects of scattering and irregular 

 reflexions. 



If sAdx is the proportion of the incident light A which is 

 intercepted by the layer dx, ^sAdx will pass out of the layer 

 in either direction. Hence A will be diminished by j>sAdx, 

 and B will be increased by the same amount, if B is the 

 radiation in the opposite direction. Adding the effects of 

 absorption, already discussed, we have 



dA = K (F-A)+ls(B-A 

 dx 



g=<B-FRMB-A) 



from which we obtain an equation corresponding to (4«) viz.: 



^(A + B) = (« + »)'(B-A), .... (25) 



while (4 IS) remains the same. 



Proceeding as in § 3, we obtain the differential equation 



a d 2 F / d 2 , \ / da , dhi\ A 



This equation, which includes (10) for the special case 

 s = 0, is one which can be discussed in the same manner. 



For steady temperatures the solution is of the same form 

 as (12), the value of a now satisfying the relation 



« 2 A = 2/cR + k(k + s) A- 



It is of interest to deal with the special case when there is no 

 absorption properly speaking. Putting a = in (12) we may 

 write the solution 



u = ax + e, 



which shows that in the absence of absorption but the presence 

 of scattering the temperature gradient is constant. 



To determine the effect of radiation on the transmission of 

 heat we use the fact that for k = equations (4 b) become 



£<A-B)=0. 



Putting 



A-B = c, 



