upon the Poles of the Electric Arc. 975 



one-half of the current in the arc. The absence of wind- 

 pressure in the body of the arc makes it impossible to suppose 

 that the remainder is carried by positive ions. A further 

 supply of relatively low-speed ions must therefore be available 

 for the purpose. For the same reason, these low-speed ions 

 must be associated with a positive space-charge equal and 

 opposite to their own ; otherwise the drag- on the gas would 

 be enormous — some thousands of dynes per sq. cm. for an 

 arc-length of 1 cm. 



This positive charge is doubtless brought into position and 

 held there by its attraction for the negative ions, from which 

 it follows that the high-speed electrons in shooting across 

 the arc will also be associated with an equal and opposite 

 >space-charge. 



Now, in order to produce a Duffield effect, it would appear 

 that these electrons must retain their original momentum in 

 travelling across the arc ; because, if they exert any drag on 

 the gas, they will very rapidly be pulled up quite close to 

 the cathode, thereby setting up a suction there which will 

 balance the recoil of the electrode and so reduce the Duffield 

 effect to zero. 



On the projected electron view, the arc will thus be 

 traversed by four sets of ions — the slow-moving negatives Ni 

 with their compensating positives M 1? , and the high-speed 

 electrons N 2 with their positives M 2 . Of these, N 2 alone 

 do not drag the gas — a condition which is very difficult to 

 reconcile with the absence of wind in the body of the arc ; 

 for absence of wind implies that, while the proportion of Nj. 

 to N 2 is purely accidental, the space-charges of M x and M 2 

 together are equal to the space-charge of N x alone, though 

 the value of M 2 is determined onlv bv N x and that of M 2 

 byN 2; 



It is, of course, easy to understand how the drags of N x 

 and Mi may neutralize one another, since their mutual 

 attractions tend to equalize their space-charges ; but on 

 that view we should expect to find a wind due to M 2 

 blowing from anode to cathode. The drag of this wind 

 for an arc 1 cm. long is given by the product of the Held 

 in the body of the arc and the ratio of the current carried 

 by the projected electrons to their velocity. Taking a field 

 of 25 volts per cm., a current of 10 amperes, and a velocity 

 of l*4xl0 8 cm. per sec, this gives a 'slope of pressure 

 of 8*9 dynes per cm. of arc-length directed towards 

 the cathode. One half of this, or 4*4 .dynes, would be 

 observed on the gauge attached as it was in the wind- 

 pressure measurements, viz. with one limb to the electrode 



