Abstract
THE distribution of temperature in a filament electrically heated in vacuo has been studied by several previous authors. The differential equation defining the steady state is: 
in which T is the temperature at a distance x from one of the ends, T
m is the value to which the temperature T
l at the centre tends as the length 2l of the filament is increased indefinitely, keeping the heating current the same, and a is a constant determined by the cross-section of the filament, its thermal conductivity and the emissivity of its surface. Using the boundary conditions T = Θ when x = 0, and dT/dx = 0 when x = l, one obtains1 
the value of T
l occurring in (1) being determined by the condition that, when the upper limit of the integral is made equal to T
l, x should become l.
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References
See Carslaw, H. S., and Jaeger, J. C., “Conduction of Heat in Solids”, 135 (Oxford: Clarendon Press, 1947).
Krishnan, Sir K. S., and Jain, S. C., Nature, 173, 166 (1954); Proc. Roy. Soc., A (in course of publication).
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KRISHNAN, K., JAIN, S. Temperature Distribution in an Electrically Heated Filament. Nature 173, 820–821 (1954). https://doi.org/10.1038/173820a0
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DOI: https://doi.org/10.1038/173820a0
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