270 



Mr. A. W. Porter on the Influence of the 



where h is the radiation-constant and 6 a is the temperature at 

 the surface of the body. 



The remainder, which is to include both true conductive 

 and also convective loss, will be proportional to the tem- 

 perature-gradient in the medium close to the surface of the 

 body. It may on this assumption be represented by 



dd 



~ c T~ 

 ar 



w 



'here 



dO 



dr 



is the temperature- gradient in the medium at 



the bounding surface of the body, and c is a positive constant 

 which will be referred to as the convection-conductivity. 

 The total rate of loss is hence 



hd—c 



d6 

 dr 



which may be written 



del 



[*-?]«- 



The expression inside the brackets is the quantity called the 

 " emissivity " in the usual treatment of the problem. On the 

 above assumption, far from being a constant, it is seen to be a 

 thing whose value will vary with every modification of the 

 experiment by which it is sought to be determined. 



To fix ideas, take the case of a cylindrical rod or wire of 

 radius " a " heated uniformly at all points and maintained at 

 constant temperature by mechanism the nature of which is of 

 no consequence. Let it be surrounded by a coaxal cylindrical 

 sheath of radius R maintained at a constant temperature, which 

 will be taken as the zero of temperature, the intervening space 

 being filled with conducting or pseudo-conducting material. 

 The differential equation to be satisfied by the temperature in 

 the medium is 



d*0 1 d6 A 

 r dr 



dr* 



since with the above conditions everything is symmetrical with 

 regard to, and uniform parallel to, the axis of the cylinder ; 

 and the solution of this which satisfies the boundary con- 

 ditions is 



a log R— loga ' 



