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.

148 M5ESSRS GLAZEBROOK AND LODGE, EXPERIMENTS ON THE OSCILLATORY
in which t is measured from the moment of reversal, and the damping is for the
present neglected. The actually observed arc of vibration is therefore
2 {(a + ao)2 + b2},
-or with sufficient approximation
2b2
a + ca + -,
so that
2b2
a = observed arc + a - -
"In most cases the correction depending upon b was very small, if not insensible.
The 'observed arc' was the difference of the readings at the two elongations immediately
following reversal. As a check against mistakes the two next elongations also were
observed, but were not used further in the reduction. The needle was then brought
nearly to rest, and two elongations observed in the now reversed position of the key,
giving with the former ones the data for determining the imperfection of the resistance
balance. As the needle next passed the position of equilibrium, it was acted upon by
the induction impulse (in the opposite direction to that observed before) and the four
following elongations were read."
To find then the correct double throw a, if a, be the observed throw, a0 the throw
at the time of reversal, and b the difference between the equilibrium positions before
and after reversal, we have
2b2
(a = aC1 + ao --
The sign to be attached to a0 depends on the directions of a, and a0.
After two throws right and left respectively have been observed, and the equilibrium
position is taken with the battery key in one position-denoted by R, say, in the
table-then Q is altered by 3Q and the new equilibrium position is found. This was
done by bringing the needle approximately to rest near the new position, by the proper
use of the battery key (Maxwell i.) and an auxiliary damping circuit, and reading
three elongations in the usual way. From these the position of rest was found. The
difference between the two equilibrium positions gives ci the deflexion to the right;
the battery key is then reversed and a deflexion to the left found; the resistance
3Q is then removed and a second zero reading taken; from these two, we find the
deflexion c2 to the left.
The sum of cl and c, gives c the double deflexion required.
The values of Q and Q + IQ are calculated from the resistances on the multiple
arc in the arms of the bridge.