Radiation on the Transmission of Heat, 255 



and hence 



— s— =*(b-a)=-«, 



A + B = - sex + d. 



If the boundaries are at a considerable distance, it cannot 

 matter what their reflecting properties are, and we may take 

 them to be black radiators of temperatures XJ («r — 0) and 

 TJ< (# = £). Writing therefore A = Rw for # = 0, and B = Rw* 

 for x = t, the two equations for A and B determine c. It is 

 found that 



_ 2R(i/ — ut) 



C ~~ 8t+2 ' - 

 or for a great thickness t 



__ 2RK-M,) 



The heat transmitted is 



dx t V sA./* 



Comparing this with (23) it is seen that as regards its 

 effect on the transmission of heat, scattering has the same 

 effect as absorption. 



7. It remains to discuss how far the two assumptions made 

 in this investigation may affect the results. In the first 

 place equation (2) is not strictly correct, and the value of /c 

 will not be the same as that obtained by the measurement of 

 the absorption of radiations passing through the plate. Con- 

 sider unit area of the surface and let the radiation incident 

 on the plate be equal in all directions. The radiation enter- 

 ing unit-area normally will be Adco, and that entering in a 

 direction forming an angle Q with the normal will be 

 A cos 6 dco, where dco is a small solid angle which, in the case 

 under consideration, will be 27r sin 6d6. If dx is a small 

 thickness of the absorbing plate, the length of path of a ray 

 through it will be dx/cos Q. Hence the total absorption in 

 the plate will be 



2vAx?dx \ ~ 2 sin 0d0 = 27rAfc'dx, 

 Jo 



the total incident radiation is 



2irAdx I § sin 6 cos 6 d0=nrA, 

 Jo 



Hence the ratio of absorbed radiation to incident radiation. 



