SURFACES OF DISCONTINUITY 707 



MN, fading off to zero. P and Q are points of inflection in the 

 curve where the sign of (P4'/dz^ changes, that quantity being 

 zero at each of them, so that p is zero at the planes L and M. 

 Also, since 



4:Trp{z) d^\p(z) 



D dz" 



it follows that 



Jz = z, \dz /, 



\dz 



\dz Jz = z, 



where Ei is the intensity of electric force at the plane L, OL being 

 equal to Zi, and OM to 22. (It is well known that the electric 

 intensity is measured by the gradient of the potential, and has 

 the direction in which the potential is decreasing. We are 



Zl 



assuming the graph to start from zero slope.) Now / pdz 



is the charge per unit area between the planes 2 = and 2 = 2i. 

 Hence this charge is DEi/iir. The charge between L and M 

 per unit area is negative and is equal to 



/. 



22 



pdz, 



Z\ 



which works out as D{Ei + E^l^ic numerically, where Ei is the 

 numerical value of the intensity of force at the plane M (directed 

 towards the plane at 0.) Finally the charge beyond the plane 

 M is positive and numerically equal to DE^/^tt. The theory 

 attributes the positive charge DEi/4:Tr to the mercury surface. 

 To do so we imagine that OL is very small and that the graph 

 turns down very suddenly and steeply at first, so that this 

 portion of the graph is really in the mercury. The changes in 

 the solution may be more gradual. The graph we have drawn 

 would suit a picture in which there is a layer of negative ions in 

 the region LM and a layer of (fewer) positive ions beyond it; 



