3(34: Prof. J. A. Pollock on the 



molecular ions would be formed, and the fall of potential 

 would decrease as the density of the electrification diminished. 

 From this point of view one would expect the anode fall of 

 potential to be equal to the surface difference of potential 

 responsible for the velocity of projection. 



In the case considered, the back electromotive force at the 

 anode is 16*7 volts. This is the value of the discontinuity of 

 the potential due to any heat effects which have an influence 

 on the passage of the electrons through the surface layer, 

 including the part represented by the energy with which the 

 electrons emerge into the gas. According to the above 

 argument the latter is equal to the anode fall of potential,, 

 which in this case is 16 volts. The difference between this 

 value and that of the back electromotive force being but 0*7 

 volt, seems to justify the assumption underlying the whole 

 discussion, that in the expression for the surface discontinuity 

 of potential the term representing the translational energy of 

 the projected electrons is predominant. 



5. Ute Cathode Fall of Potential. — Let figure 1 now 

 represent the negative carbon ; from the surface A'B' 

 electrons are projected with a velocity of 1*5 X 10 8 centi- 

 metres per second, due to a surface difference of potential of 

 6*1 volts. The velocity of the electrons increases after pro- 

 jection, owing to the electric force in the field, and assuming 

 that the cathode fall of potential of 11*7 volts occurs in the 

 distance S, corresponding to their average range, the electrons 

 collide with the molecules of the gas at AB, with a velocity 

 of 2'ijx 10 8 centimetres per second, equal to that acquired bv 

 the free fall through 17*8 volts. 



In the hot gas collisions under such circumstances result 

 in ionization, so that both positive and negative ions are 

 produced at the section AB, the negatives moving to the 

 left in the figure, while the positives travel slowly to the 

 cathode. 



Those electrons which collide with molecules, after a flight 

 less than the average range, may not have sufficient energy 

 to ionize, in which case some negative molecular ions are 

 produced between AB and the cathode surface, to be lost, 

 perhaps, by recombination with incoming positives. As 

 ionization certainly takes place about AB, there is between 

 this plane and the cathode a maximum density of positive 

 electrification ; this, by Poisson's equation, means a steep 

 potential gradient which corresponds to the well-known 

 cathode fall of potential. 



It may be considered that in the development of the arc 



