The distribution of temperature along a thin rod electrically heated in vacuo. II. Theoretical (continued)

For a thin rod electrically heated in vacuo the differential equation defining the distribution of temperature in the steady state has been formulated previously. If the rod is not too short, a solution can be obtained by suitably combining the two particular solutions for a similar infinitely long rod heated by the same current, which is applicable over the whole length of the rod. The solution is discussed in relation to some formulae that had been proposed by Stead. The solution also leads to a very useful expression for the temperature at the centre of a finite long rod as a function of its length