upon the Pole's of the Electric Arc. 977 



Take the above figure, and let B now represent a layer of 

 positive electricity giving rise to the cathode dark space. 

 All electrons passing from C to B will be urged forward 

 with a force P, half of which is produced by the charge 

 on B and half by that on 0. C therefore feels a direct 

 backward thrust of ^P,and as the attraction of the electrons 

 for B urges B towards C, a hydrostatic pressure of ^P will 

 also be felt by G. The net effect is that C feels the full 

 recoil of the momentum imparted to the electron with the 

 same result, though not by the same mechanism, as if 

 the electron had been projected from C by forces with 

 C's surface. As before, this recoil will be balanced by a 

 suction if the electrons rapidly lose their momentum on 

 leaving the dark space, with the result that no Duffield 

 pressure will be thereby produced. But it will be un- 

 balanced if they shoot across the arc without drag. Taking 

 Duffield's calculation but substituting the drop of 11*6 volts 

 in the dark space for the 6*1 volts at the cathode face, 

 one obtains for the current carried by these high-speed 

 electrons one-third of the total current instead of a half. 

 The corresponding pressure-slope set up by the compensating 

 positive ions will be 5'9 dynes per cm. instead of 8'9, a 

 quantity which would have been also readily detected in 

 the wind-pressure experiments had it been present. 



In the opinion, therefore, of the author the theory of 

 electrons projected across the arc either from the cathode 

 itself or from its immediate neighbourhood is not in accord- 

 ance with other experimental data. 



On the other hand, if the effects of viscously moving ions 

 are not necessarily ruled out in looking for an explanation 

 of the Duffield effect, there seem to be possibilities therein 

 which, though not affording a theory that is above reproach, 

 are at least worth putting on record. The argument is as 

 follows. 



In a symmetrical field it will be a condition of symmetry 

 that the drag of the ion on the gas shall be everywhere 

 equal to the force with which the field drives the ion. 



But in the act of starting from rest close to one of the 

 electrodes, that drag of an ion on the gas is smaller than 

 the driving force, owing to its lower speed ; its suction on 

 the electrode it is leaving is therefore proportionately 

 reduced. It follows that every ion which starts its motion 

 in the gas close to an electrode ^ives rise to an effect which 

 is equivalent to an unbalanced backward thrust on this 

 electrode, the momentum supplied by this thrust being 

 equal and opposite to that received by the ions. 



