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 "." 147
In a second series of observations the approximate value of Q was 100, and in,x' Q+100
this case the formula becomes -= Q23.
x Q -100+ Q -+ 8 '
The actual value of the ratio will vary with the value of îQ in the various
experiments; in most cases it is from one to two per cent. greater than unity: aQ being
negative.
Introducing these the formula for L expressed in terms of quantities which can be
directly observed is
1 1T x Q+100 a lla2 - 8
4=QQ Q+ ( 1 + )Q c 128d2 }
[The coefficient of 8Q in the denominator is in some of the experiments 21.]
THEORY OF THE ACTUAL OBSERVATIONS.
The above simple theory of the experiment assumes (A) that a perfect resistance
balance can be (1) obtained and (2) maintained during the experiment, and (B) that in
measuring a throw the galvanometer needle can be brought to absolute rest before a
reversal of the current. The coil is made of copper wire; slight changes of temperature therefore affect its resistance, the current itself produces a small heating effect in
the wire, and it is practically impossible to maintain an accurate balance. Again to bring
the needle accurately to rest before each throw involves time, while to avoid undue
heating it is necessary to be rapid in observations; it is better therefore to make a
correction for any small swing which may exist at the time of making a reversal. Lord
Rayleigh has shewn how actually to make the observations, provided the reversal takes
place as the needle passes its equilibrium position (Phil. Trans., 1882, Pt. II., p. 680).
The following quotation gives his theory and practice of the method of observation.
"In the simple theory of the method the induction throw is supposed to be taken
when the needle is at rest, and when the resistance balance is perfect. Instead of
waiting to reduce the free swing to insignificance, it was much better to observe its
actual amount and to allow for it. The first step is, therefore, to read two successive
elongations, and this should be taken as soon as the needle is fairly quiet. The battery
current is then reversed, to a signal, as the needle passes the position of equilibrium, and
a note made whether the free swing is in the same or in the opposite direction to the
induction throw. We have also to bear in mind that the zero about which the vibrations take place is different after reversal from what it was before reversal, in consequence
of imperfection in the resistance balance. At the moment after reversal we are therefore to regard the needle as displaced from its position of equilibrium, and as affected
with a velocity due jointly to the induction impulse and to the free swing previously
existing. If the arc of vibration (i.e. the difference of successive elongations) be a0 before
reversal, the arc due to induction be a, and if b be the difference of zeros, the subsequent
vibration is expressed by
S (a + a0) sin nt + b cos nt,
19-2