Electron Theory of the Carbon Are. 363 



4. Ihe Anode Fall of Potential— Let A'B', in figure 1, 

 represent the trace of the anode surface ; from this surface 



Fig. 1, 

 A 



electrons are projected in great numbers, owing to the high 

 temperature of the crater, and with a considerable initial 

 velocity. These electrons collide with molecules of the gas at 

 somewhat various distances from the anode surface; ihe 

 average range may be represented by a length S, and the 

 collisions may be considered, for the purposes of general 

 •description, to take place about a plane parallel to the anode 

 surface at a distnnce S from it, whose trace is given by the 

 line AB in the figure. The electrons travel through the 

 distance S with negatively accelerated motion, as they are 

 moving in opposition to the force in the field, and the out- 

 come of their collisions with molecules is the production, at 

 AB, of molecular negative ions. As all the ions so made 

 travel to the anode, but, on account of their greater mass, 

 with a movement so much slower than that of the electrons 

 which created them, negative ions accumulate between A'B' 

 and AB. Further, as the projected electrons move with 

 negatively accelerated motion towards AB, while the 

 molecular ions travel with a positive acceleration from it, the 

 accumulation will be at a maximum about that section. 



The number of positive ions emitted from the anode surface 

 is small compared with the number of electrons projected, the 

 electrification to the right of AB is therefore negative^, and 

 its density far greater than that in the vapour column to the 

 left of that plane. 



By Poisson's equation it is known that this accumulation 

 of negative ions near the anode surface is associated with a 

 steep potential gradient, so that the well-known anode fall o£ 

 potential is thus accounted for. 



The negative ions accumulate until the anode fall of 

 potential is sufficient to bring the projected ions to rest at 

 the end of their average range S. The fall cannot be greater 

 than this, otherwise some of the electrons would be brought 

 to rest before collision with molecules, in which case few 



