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.

146 MESSRS GLAZEBROOK AND LODGE, EXPERIMENTS ON THE OSCILLATORY
of the mirror was east and west, while the scale itself ran north and south. By taking,
however, throws and deflections on both sides of the zero which was at the centre of
the scale, the effect of any small error in setting was eliminated from the result.
GENERAL THEORY OF THE METHOD.
In making the observations the double amplitude, i.e., the distance between an
extreme elongation to the right and a corresponding one to the left, was noted. Let
a be this double amplitude in scale divisions for the induction throws, c for the deflection
due to the alteration îQ, and let d be the distance between mirror and the scale.
Then tan 2a =, tan 20=-, and from this we find
"d' d'
2sin l a 1 lla2-Sc2)
tan = c 1 28d28 )
neglecting higher powers of a/d and c/d. The values of (lla2-8c2)/128d2 varied for the
different arrangements from '00173 to '00023.
The value of the ratio x'/x was obtained as follows:
Let E and E' be the values of the potential difference between the points where
the current enters and leaves the bridge, in the two cases when the values of Q are
Q and Q +SQ respectively.
e the E.M.F. of the battery, which we suppose does not alter*.
Let X and X' be the resistances between the points A and D where the current
enters and leaves the bridge in the two cases, and Y the battery resistance.
Then putting P= Q= 200 in the small terms, and R =S= 100, we find
E'='(Q+ Q+ 100 + 'O Q),
E =x (Q+ 00),
Y
E l+
also E =
E- Y=
1 +X
if a term of the order YSQ/90,000 be neglected. Y is of the order 1 ohm, and îQ of
4 or 5 ohms.
x _= Q + 100
Hence
x Q+100+37Q'
* A combination of large Daniell's cells was used. themselves will afford a test of this. A small change in
Except for the correction now discussed, the results are the E.M.F. would only produce a first order change in the
independent of changes in the battery E.MI.F., provided value of the correction, and therefore a second order change
such (if they occur) go on uniformly, and the experiments in the whole result; it may therefore be omitted.