564 
Proceedings of the Royal Society 
inductively upon another insulated spherical ball which is in con- 
nection with the electrometer. 
Before proceeding with the investigation proper, I tested the 
accuracy of the method by applying it to determine how the in- 
duced potential of the ball in connection with the electrometer 
depends on the distance between the centres of the balls. I found 
that the equation 
V = 6081 r" 1 - 42-26, 
where Y denotes the induced potential, and r the distance, between 
the centres of the balls, satisfies all the observed values of Y for 
values of r greater than twenty-four centimetres, but for smaller 
values of r the function requires to be corrected by being multiplied 
by 
/(?•) = • 524 + -02 r. 
Our method, when applied to measure the difference of potential 
required to pass a spark through air at the atmospheric pressure 
between parallel metal plates at different distances, gave a result 
agreeing well with that which Sir William Thomson discovered to 
be true for small distances. The function for V, the difference of 
potential in terms of s, the length of the spark is 
Y = 66*94 J{s 2 + '205 s} 
the equation of an hyperbole, whose semi-transverse axis is *1025 
centimetres, and semi-conjugate axis 6*8623 centimetre-gramme- 
second units. We observed, for lengths of spark, up to 1*2 centi- 
metre. 
From the above equation we infer that — 
R = 66*94 + -205 
where R denotes the electrostatic force ; from which it is evident 
that as s becomes smaller, R becomes greater. But when the discs 
were heated well, immediately before the taking of the observations, 
the curve obtained satisfies the equation — 
Y = 87*04 s- 19*56 s 2 
a parabola ; from which we deduce 
R = 87*04- 19*56 5. 
