512 Prof. A. W. Porter on the 



be made nearly white hot, while those parts which are covered 

 with glass do not even glow. In such a case there are several 

 hundreds o£ degrees difference in the temperature of neigh- 

 bouring portions of the wire. This experimental result 

 accounts for the platinum wire sealed into an ordinary incan- 

 descent lamp remaining as cool as it does. 



The problem in its simplest form. 



A cylindrical wire of good conducting material and radius 

 a is surrounded by a concentric sheath of radius b and thermal 

 conductivity h The wire is heated by means of an electric 

 current or otherwise to a constant uniform temperature by a 

 rate of supply of heat H per unit length of the wire. Then 

 if the thermal emissivity from the outside of the sheath is e 

 we have 



Br 



= e.2irb6 b , 



H= -k . 2W|^) = -A • 2th 



where 6b is the temperature of the outside of the sheath, 



5T- ) is the slope of temperature in the sheath at its 



inner surface. The corresponding solution for the tempera- 

 ture of the wire is 



^=-JH^ loge «}' 



where 6 a is the temperature of the wire. 



To find the effect of changing the thickness of the coating 

 we differentiate this equation with respect to b : giving 



-db 



_ H J 1 1\ 

 -'2tt \We + k~bJ 



The effect then is to increase 6 a (for a given rate of supply 

 of heat) provided that b is greater than kje ; the coating 

 under these conditions acts as a lagger. But if b is less than 

 this critical value the effect of its increase is reversed ; the 

 coating under these circumstances promotes the outward 

 flow of heat. This critical value if it exists is independent 

 of the radius of the wire ; but it must be noted that since b 

 can never be less than a, it is possible that for a particular 

 wire it does not exist. To find out the likelihood of its 

 occurrence we must examine the values of h and e which 

 will probably enter into account. 



