Discharge of Electricity from Glowing Carbon. 371 



required for arcing is less when the hot carbon is vertically 

 below the cool one than when it is vertically above, or than 

 when the two carbons are in the same horizontal plane. 



5. Distribution of Potential between the Carbons. 



It is well known that from the surface of hot carbon, 

 •electrons and positive ions are projected. The rate of emis- 

 sion of the latter is small, and its consideration may be 

 neglected in the discussion of the present experiments when 

 the hot carbon is negatively electrified. The electrons collide 

 with molecules of the surround i no- o-as, at somewhat various 

 distances from the hot carbon surface, the average of which 

 maybe called the average range of projection. The collisions 

 result in the creation of molecular negative ions, which, if 

 they are not removed, accumulate near the surface of the 

 carbon, thus establishing a potential gradient through the 

 average range of projection and a consequent movement of 

 the ions towards the hot surface. Such a distribution of 

 potential can be realized with the apparatus previously 

 described by applying between the carbons the potential- 

 difference requisite, at any temperature, to make the 

 •current in the circuit zero, the hot carbon, in this case, 

 being positive relatively to the cool one. This distribution 

 may be represented, from a merely illustrative point of view, 

 by the curve 1 in fig. S, where V is the potential and x the 

 distance from the cool carbon, the hot carbon rise of potential 

 ah being supposed to take place through a distance comparable 

 with the average range of projection of the electrons. 



If the hot carbon is made slightly less positive than the 

 value required for zero current, ac in curve 1 will slope a 

 little upwards ; those few molecular negative ions formed near 

 the surface of the hot carbon beyond the point a will be drawn 

 by the field to the cool rod, though the great majority will 

 still go to the hot carbon. A farther stage, with the hot 

 carbon negative with respect to the cool one, is illustrated by 

 curve 2. As the potential-difference between the carbons 

 increases, the hot carbon rise of potential ah becomes less 

 and less, and the proportion of the negative ions carried to 

 the cool carbon becomes greater. If the potential-difference 

 rose to such a value that the hot carbon potential rise dis- 

 appeared, the current would be saturated ; in our experiments 

 an arc forms long before this stage is even approached. 



The deduction of an analytical expression for the relation 

 between potential-difference and current, in the case under 

 consideration, presents difficulties ; it involves a statement 

 of the circumstances of the appearance of the molecular 



