490 Proceedings of the Royal Society 
p 
R 
s 
V 
Difference. 
+ 
+ 
+ 
195 
4- 56 
*> 
+ 
0 
0 
139 
PQ= 7 mm. 
+ 
+ 
0 
163 
+ 27 
RS= 28 mm. 
+ 
0 
0 
136 
J 
It appears very clearly from these experiments, that the presence 
of an independently charged body affects considerably the potential 
required to produce rupture. When the neighbouring body has a 
similar charge to the discharging one, a higher potential is required; 
and, when it has an opposite charge, a lower potential is required 
than when the neighbouring body is neutral or absent. The effect 
becomes smaller, ceteris paribus , when the distance PQ is dimin- 
ished, and increases when the distance RS is diminished. If we 
bear in mind that it is the surface density at extremity of P, 
which determines the rupture, and not the difference of potential 
between P and Q merely, this result is precisely what we ought to 
expect. 
If we assume that in the cases above quoted the charging of R 
and S affected the whole charge on P without sensibly altering its 
relative distribution, which must have been approximately true since 
the mere presence of R and S in the neutral state did not affect the 
discharge, then the surface density at every point of P will be 
proportional to its whole charge. Let p be the capacity of P 
depending almost entirely on the presence of Q ; — q the coefficient 
of induction between R and P, which is the same as that between 
S and P ; V 0 the potential of P corresponding to rupture when R 
and S are at potential zero, V the corresponding value when R and S 
are at potentials U and IP respectively. Then we have, since the 
surface density at the point of rupture is the same in both cases, and 
therefore by our assumption the whole charges also the same, 
l>V,=jpV-s(U + XT'), 
V-V 0 = J(U + U'). 
