104 Cadi/ and Arnold — Electric Arc. 



first stage cannot be observed, because the anode is kept at a 

 high temperature from its proximity to the cathode. 



In the curves for 2 and 8 mm the maxima corresponding to the 

 "rotating stage" of the arc are evident (see §33). So unsteady 

 was the arc during this .stage at lengths of 4 and 6 mm that no 

 readings could be taken. The maxima are presumably due to 

 increased voltage caused by a bending or lengthening of the arc. 



§31. Up to the present time, no satisfactory mathematical 

 expression for the mechanism of the metallic arc lias been pro- 

 duced. Steinmetz (I.e.) has derived a formula for the potential 

 difference across the iron arc as a function of current and length, 

 which is in fair agreement with observation over the range 

 experimented on. This formula is open to criticism, however, in 

 that it takes no account of the drop at the anode, and assumes 

 the temperature throughout the arc to be that of the boiling 

 point of the electrodes. 



As for the curves in fig. 5, their range is limited by the 

 comparatively low voltage of the supply. The presence of the 

 critical points and the irregularities due to the rotation of the 

 arc also contribute toward making the observations worthless 

 for analysis. 



§32. Wide discrepancies exist between the values given by 

 different observers as the "constants" of the metallic arc. Thus 

 for the value of a in the equation 



E = a + U . (1) 



v. Lang* gives for iron 25 volts, Lecherf 2.0, and Child (I.e.) 

 25 volts. The value obtained from the experiments of Stein- 

 metz (1. c), who observed the potential difference the instant 

 before the electrodes (magnetite rods) were brought together, 

 is from 2S to 31 volts. 



These differences are inherent in the different methods 

 employed. When the arc approaches the length zero, the anode 

 receives negative ions directly from the cathode and its drop is 

 all but eliminated. Moreover, the resistance of the iron oxide 

 from which the discharge takes place depends upon its temper- 

 ature, and this forms a very appreciable source of error for 

 which it is almost impossible to correct. The value of a ob- 

 tained by this method cannot be compared with one derived, 

 for example, by extrapolation from the Ed curve, nor with one 

 obtained with the use of an exploring electrode. Differences 

 in the currents used by various observers account also for a 

 part of the discrepancies. 



We have made a large number of observations in which the 

 iron terminals were slowly brought together and the last volt- 



* Wied. Ann., xxxi, 384, 1887. f Ibid., xxxiii, 609, 1888. 



