Radiation on the Transmission of Heat, 247 



the discontinuities are small: but they do not disappear 

 until the plate is of infinite thickness unless the opacity is 

 complete. If, e. g., the opacity of the plate is such that the 

 light is reduced to 6 -10 times its original value, and the tem- 

 peratures of the bounding surfaces differ by 100 D , there would 

 still be a discontinuity of 8J° at the surfaces. 



According to Melloni's experiments, the absorption of heat 

 in rock-salt is independent of the wave-length, a plate of 

 "26 cm. thick transmitting 92 per cent, of the radiation. 

 From this I calculate the value of k to be *032. If we had a 

 plate of rock-salt 1 cm. thick and placed it between black 

 surfaces at temperatures of 100° and D respectively, a state 

 of equilibrium would be reached in which, if conduction were 

 entirely absent, the rock-salt in contact with the temperature 

 of boiling water would acquire a temperature of 50°" 74, 

 while at the other boundary the temperature would be 49°'26; 

 so that the plate would take up a temperature which nearly 

 throughout its thickness is equal to the arithmetic mean of 

 that of the bounding surfaces. 



For the extreme cases the above equations reduce to 



F=i(F + F 1 ) ; i£ K t=0, 



F = [F («— x) + ¥ ] x]/t, if fct is very large. 



In the latter case the temperature distribution is the same as 

 that established by conduction. 



4. The discontinuities which have been proved to exist 

 when conduction has been neglected show that conduction, 

 however small, must always be taken into account, Before 

 doing so we may extend our calculations to the case that the 

 bounding surfaces are partly reflecting. The surface con- 

 ditions are then : 



A=(l-*)F l} + <rB £ora>=0, 



B=(l-<r)F 1 +o-A lov x = t, 



where g is the reflecting power, which must be taken to be 

 one for perfect reflectors. 



The same reasoning which previously determined K and c 

 now gives the equations : 



[(^ + 2)-a(^-2)]K = (l-o-)F 1 -F , 



[(**+2)-cr(irf-2)]c =(l + <r)F + (l-o-)(/c«F + F 1 ). 



The discontinuities of F at both boundaries are 



(F 1 ~F )(l + o-)/[<l-(r) + 2(l+<7)]. 



