

during the Absorption of Electrons by Platinum. 195 



appreciable difference to the accuracy o£ alignment of the 

 points. 



§ 12. The Potential Driving the Thermionic Current. 



When the applied voltage is such that the current is 

 saturated, the same number of electrons per unit length will 

 be emitted by every portion of the hot wire. In that case 

 the mean value of the potential which drives the current 

 will clearly be the potential of the middle of the wire. In 

 the stage where saturation has not been attained this will no 

 longer be true, as a greater number of electrons will be 

 emitted per unit length from those parts of the filament for 

 which the negative potential is greatest. In that case, how- 

 ever, the true average potential of all the emitted electrons 

 will be obtained if the current-E.M.F. curves are analysed 

 in the following manner : — 



The thermionic current per unit length of the wire will be 

 different for different parts of the wire and will be greatest 

 where the negative potential of the filament is greatest. The 

 potential will vary from point to point of the wire on 

 account of the difference of potential required to drive the 

 heating current through it. If the potential at any point is 

 Y, we can denote the thermionic current per unit length at 

 that point by /(Y). Then the observed current, i, will be 

 the integrated effect of this over the whole length of the 

 wire. Thus if I is the length of the wire, we shall have 



<)Y 



since ^— , the gradient driving the heating current, is con- 

 stant. Hence 



^-Bvkc/W-AV.)] 



where Yi and Y are the potentials at the two ends of the 



BY 



wire. If Y is less than l^—, then f(Y ) is in general equal 



to since it corresponds to a positively charged part of the 



wire, so that f(Yi) = ^— X — r=. We can thus obtain the 

 Of o v 



value of /(Y) over this range by simply differentiating the 



current-E.M.F. curve with respect to Y, since this curve 



expresses i as a function of Y. 



02 



