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." 155
V.-V V- -Vz' == Q2
^-T/=|1, 7,- |,,.L. 21~ + 2Rsx = V,- r1'-(V2- V I') Q2
Now if L', R' denote the inductance and resistance of the two wires joining the
plates of any two consecutive condensers, then
L'= 2L, R'= 2R.
Then if R is the whole resistance, L the whole inductance,
R = nR', L = L'.
And the equations to find the period are
L'd2 + R'lx = -
L'd + R'x = Q2 Q
-L/ ~Xi2 - ~- - - S 7 1/
dQ2
-1 =i
dQ9
ct'
d Q
xn-l-1 xn= dt
Hence we have
L'"x + R',X + (- + yS x-S-, 2x, = 0,
X i L+ x + R'C' +, x2 - X-, = 0
-S x- + L ''2 + -RR'2, + 2-,= O.
Put x - X eiÀt,
and let
S' XL'-R'X- - 1 = P,
S' {x2L'-R't\} -2 = Q,
S' {2L'- R'x} - 1 = R.
Then the equations become
PX, + X2 = o,
X, + Qx, + x, = o,
X2 + QX2 + X4 = 0,
Xn-_ + RX2T = 0.
20-2