634 Prof. Skinner on the Drop of Potential 



pressure is increased without limit. This value with disk- 

 electrodes seems to be the same as the drop found by War- 

 burg for wire electrodes, though, the conditions differing in 

 the two cases, a rigid comparison cannot be made. 



A Plane Cathode in General. — The foregoing observations 

 allow some general conclusions to be drawn with respect to a 

 plane cathode when the stream-lines are straight and the 

 walls of the discharge-tube sufficiently removed. From the 

 observed similarity in the conducting qualities of the various 

 gases the observations on the cathode drop may, in quality, be 

 extended to gases in general. The relation between drop of 

 potential at cathode V, current-density i, and gas-pressure p r 

 may be expressed by the equation 



y=c+ -(i-a), 



p v J 



where C is the limiting value of the drop at the cathode, as. 

 the gas-pressure increases without limit, depending both on 

 the kind of metal and kind of gas used ; c a constant depend- 

 ing on the kind of gas used ; and a a constant (approximately 

 independent of metal used as cathode). For steel and 

 aluminium cathodes in nitrogen, the values obtained from the 

 foregoing observations are 



0. c. a. 



Steel 245 24'4 -0*6 



Aluminium 210 24*4 -06 



when Y is given in volts, i in milliamperes per sq. cm., and 

 p in millimetres of mercury. 



Our present knowledge of the quantities involved in the 

 equation does not furnish us with means for analysing it. I£ 

 the drop of potential at the cathode be a function of the 

 velocity of impact of the discharging ion, we conclude at 

 least that when the drop is constant with current the velocity 

 of the ions approaching the cathode does not change as the 

 current increases, and hence, the number in unit volume 

 must be proportional to the current. This condition is 

 approached as the gas-pressure is increased, so that, at high 

 gas-pressure, we conclude that the ionization at the cathode 

 is, as at the anode, practically proportional to the current. 

 As the pressure is reduced, since the drop increases, the 

 velocity of impact must increase, and the ionization at the 

 cathode is therefore no longer proportional to the current. This 

 conclusion suggests a means of comparing more searchingly 

 cathode and anode drops, in that by reducing the gas-pressure 



