252 Prof. A. Schuster on the Influence of 



shows the variations in the plate when placed in contact with 

 two perfectly black surfaces. The effect of increased radia- 

 tion is shown in Curve III., which gives the temperature 

 variation for totally reflecting surfaces, and with a value of 

 R=10~ y corresponding to a temperature of about 360° C. 

 The curve for the higher temperature and black surfaces has 

 not been drawn, as it would confuse the figure, being nearly 

 coincident with Curve I. The temperature scale is of course 

 arbitrary. The curves show very clearly that radiation 

 destroys the uniform temperature slope which is obtained 

 when conductivity alone is taken into account, and that the 

 deviations from uniformity are greater when the surfaces are 

 reflecting than when they are black. 



To investigate the effects of radiation on the transmittance 

 of heat it is best to take the two extreme cases : one in which 

 the plate is so thin that very little heat is absorbed in it, and 

 the other in which the plate is so thick that very little radia- 

 tion can traverse its whole thickness. For small thicknesses 

 we may in equations 23 a and 23 b expand the exponential, 

 retaining only the terms as far as at in the numerator, and 

 uH 2 in the denominator. After the necessary transformations 

 we find for the case of black surfaces 



a= ?-K 1+ v> 



Hence for the heat transmitted according to (16) 



a 2 \ UX pTT 

 ti = a ., = -- +liu. 

 kT t 



The first term represents the heat calculated according to the 

 laws of conduction, and the second term gives the effect of 

 radiation. In the case of a very thin plate we are justified 

 therefore in taking the two effects separately and adding the 

 result. A similar calculation shows that for the case of 

 reflecting boundaries the heat transmitted by a thin plate is 

 that calculated from the known laws of conductivity, viz., TJX/t. 

 A different result is arrived at when absorption within the 

 plate cannot be neglected. If we transform equations 23, 

 taking e at as large com] tared to one, we find for black 

 surfaces 



t \ k\ 1 \ tc-\t) 



and for reflecting surfaces : 



t \ KA. / \ (C\xt J 



