76 THE ROYAL SOCIETY OF CANADA 



the surrounding gas until the losses by conduction and convection 

 (i.e. by "free convection"), equalize the gain by radiation. At other 

 temperatures the thermo-element may be losing more heat by radiation 

 than it receives, with the result that its temperature will fall below 

 that of the surrounding gas. 



The following method was used to estimate the correction to 

 be applied to the temperature indicated by the thermo-element. It 

 has been shown by Langmuir^ that the free convection of heat from 

 small wires can be calculated correctly by assuming that the heat 

 flows by conduction alone through a stagnant layer of gas around 

 the wire. If T2 be the temperature of the wire, Ti that of the surround- 

 ing gas, and 



<^2 = f^' Kd^ 



01 = f^' Kd^ 



then by Langmuir's theory the heat loss by free convection per centi- 

 meter length is 



S(02 — 0l) 



where S is the "shape factor" given by the equation 



a 5 -iTt/S 



B Tl 



a being the diameter of the wire and B=-43cm. at atmospheric 

 pressure. We may thus write 



S(02-0i)=W, 



where Wr is the heat due to radiation gained by one centimeter of the 

 wire. Wr may be calculated from the dimensions and radiation con- 

 stants of the plates. Thus knowing S and 02, 0i may be calculated, 

 and finally Ti, the temperature of the surrounding gas. 



The corrections thus involved were found to be quite large, 

 varying from +12°C. near the upper plate to — 14°C. near the bottom 

 plate in the extreme case of blackened glass at 8-42 amperes current 

 input. The unbroken lines in Fig. 2 are curves corrected for radiation 

 by the method outlined above. 



1 Langmuir, I., Phys. Rev., 34, p. 401, June, 1912. 

 Trans. A.I.E.E., p. 1229, 1912. 

 Trans. Am. Elect. Chem. Soc., p. 299, 1913. 



