246 Prof. A. Schuster on the Influence of 



radiations corresponding to the temperatures of the bounding 

 surfaces. 



When the steady state is reached, (5) leads to 



B-A=2K, 



where K is some constant which is to be determined. Putting 

 this value of B — A into equation (4 a), we get 



B + A = 2K^r + 2e. 



where c is a second constant. Hence 



B = Ktf t t' + K + c, 



A = Kkx — K + c. 



The values of the constants may now be expressed in 

 terms of the radiations at the surfaces. We find in this way : 



K= F 1 -F ^ FoQrt + lj + Fx 

 tct + 2 ' tct + 2 



The temperature inside the body is determined from F if 

 the law of radiation is known. In the case considered (1) 

 gives 



2F=A+B = 2K/^ + c (8) 



If the temperature variations are comparatively small, 

 Newton's law may be applied, in which case the temperature 

 will be proportional to F, and will vary uniformly in the 

 plate. The important point in the solution of the problem 

 lies in the discontinuities of F, and therefore also of the 

 temperatures at the boundaries. 



To calculate the discontinuities we take the values of F at 

 the boundaries, as obtained from (8) after substitution of K 

 and c. We find : 



F=Fo(<rf+1)+Fl fw 



ret + 2 



Fm *'.("+ i)+fi £or , = , 



/et + 2 



But F is the radiation received from the outside when # = ; 

 the discontinuitv at that surface is therefore 



F( X =o) — F : 



IV-Fo 

 Kt + '2 ' 



The same discontinuity occurs at the other surface. Any 

 radiation I in its passage through the plate is reduced to 

 le~ Kt . When /ct is large the plate is practically opaque, and 



