Potential at the Electrodes in Vacuum-tube Discharge. 493 



other hand, if there be no loss of energy by impact it will 

 not come to rest at all. 



Considering now V as the drop of potential at the electrode, 

 •and u the velocity with which the ion enters the space over 

 which this drop takes place, it is evident that 



(a) for u = const., T decreases with increasing values of V 



— that is, by increasing the drop at the electrode 

 the discharge of the ion is accelerated ; 



(b) for T = const, V increases with u, which means that 



to maintain the time of discharge the same the drop 

 at the electrode must increase with the velocity with 

 which the ions move into its field ; 



(c) for T = const, and u = const., V must increase with 



{mje) — that is, other conditions being the same, the 

 greater the ratio of the mass of the ion to its charge 

 the greater must be the electrode drop. 

 Referring to (a) we explain the existence of a drop of 

 potential wherever the ions move up to and discharge to a 

 conductor. It also explains the fact that a conductor assumes 

 the potential of the conducting gas, in that for u = 0, T only 

 approaches infinity as V approaches a zero value, (b) ex- 

 plains the simultaneous increase in drop at the two electrodes, 

 in vacuum-tubes, if with the anode in the cathode dark space 

 they are made to approach each other. For, in this case, the 

 ions reaching one electrode are supposed to have emerged 

 from the space covered by the drop at the other, hence a 

 greater drop at the first producing a greater velocity u at the 

 second necessitates thereby a greater drop at the second. 

 The second acts in the same way on the first, so that there is 

 .a mutual increase in the drop at the two electrodes. By (c) 

 the great difference in anode and cathode drops in vacuum- 

 tubes may be explained under the view that the ratio {mje) 

 for the positive ions is much larger than for the negative, 

 and hence the cathode drop (for the .same velocity of approach 

 u at the two electrodes) necessarily much larger at the cathode 

 than at the anode. It is very likely that the difference would 

 be much greater if the gradient (in the negative glow) 

 driving the positive ions into the catho Is field were not 

 much smaller than that (in the positive column) driving the 

 negative ions into the anode field. 



We find in these examples that the above equation for T, 

 though deduced from an ideal case, furnishes an explanation 

 for many of the phenomena, and we may therefore conclude 

 that it contains the controlling factors, those ignored entering 

 as correcting factors. It is very likely that the electric 

 intensity is not constant within the space covered by the 



