1897.] Electrification in an Electric Field, etc. 293 



Again, Wiedemann, in Die Lehre von der Elektricitat, Band II., 

 asserts that the flame removes the apparent electrification & ', and 

 produces a real electrification of opposite sign depending on the 

 action of the apparent electrification on the interior of the body. 



There seems to be some obscurity as regards what is meant by 

 removing the apparent charge. Prof. Gray, however, clearly states, 

 and I think the same thing is implied in the Appendix to the 

 chapter in Maxwell above referred to, that it means reducing the 

 surface to zero potential. It would, I think, be impossible to do 

 this unless for the portion of the surface affected by the flame at 

 one instant : if the flame be taken to another portion of the 

 surface the real electrification produced there will alter the 

 potential of all parts of the field and, therefore, of that part which 

 has already been reduced to zero potential. To reduce the whole 

 surface to zero potential, a flame large enough to affect all parts 

 of it at once would be necessary. But, if this is what is meant 

 by removing the apparent electrification, the real electrification, 

 as will be shewn presently, is not necessarily either equal in 

 amount or opposite in sign to the apparent electrification. Another 

 way of putting it, used by Mascart and Joubert, is ' reducing the 

 surface to the neutral state.' It is not clear what this means, 

 unless it be making the electric stress zero at every point of the 

 surface, on both sides of it. But this by Gauss's theorem is 

 impossible if a real electrification is produced by the flame. 



What seems to be properly implied by removing the apparent 

 charge is making the surface density of this charge, as defined by 

 Maxwell, zero ; that is to say, a real charge must be given to the 

 surface which will make the normal force at any point of it 

 continuous. But, generally, this could not be done by means of 

 a flame. 



Let a denote the apparent electrification, and a x the real 

 electrification necessary to remove the apparent charge. Also 

 let V denote the potential at any point before and V after the 

 apparent charge is removed, and V x the potential due to the real 

 electrification of the surface. Then, V = V+ V lf and we have 



dV dV . , n 



, + j- + 47TO- = 0, 



dn Y dn 2 

 „dV ir dV . 

 dn Y dn» 



also £i ~ (F+ V,) + K,j f) (V + V,) + 4x«, = 0, 



