Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

DISCHARGE OF AN AIR CONDENSER, WITH A DETERMINATION OF "v." 161
original equation; thus, supposing the coil to consist of n parts, so that nS' = S = 16 metres,
we have
tan = cotnb, n = +
2n2
X2LSX = 2n2 (1 - cos ) = (2+ 1)2
4 I- n eglecting l/n2
= 238 if n= 31.
The case of a continuous coil of uniform capacity s and inductance I per unit of
length may be treated as follows.
We assume the frequency to be such that the current across each section of the
wire is the same at any given moment.
Let V be the potential at one end, that at the other being zero, a the length of
the wire, v the potential at a distance x from the end at which the potential is zero.
Vx
Then v=-.
a
The charge on an elelnent dx at x is
s Vxdx
q = svdx =
/a
V2x"
Energy -= qv = s a2 dx.
The total electrostatic energy of the coil is thus
1 sV2 fa
and thus = - x - V sa = 1 VIS,
if Si is the capacity of the whole coil.
Hence the total electrostatic energy of the coil and condenser is
i1 (S+ 1Si).
The electrokinetic energy is ~Lu2 if u is the current.
Hence 2 =
L (S + Si)'
This agrees with the result already found for a large number n of condensers
connected by wires. (See equation (D), p. 159.)
In some of the earlier experiments described in Part IV. in which the whole coil was
VOL. XVIII. 21