I
KINETIC ENERGY OF ELECTRICITY IN MOTION [1]
7
circuit consisted of one Daniell cell and a ballast resistance of
from 3 to 80 Siemens units. Further, if the resistances of
the bridge are not exactly adjusted, and if in consequence a
fraction of the inducing current also passes through the
galvanometer, this fraction will yet be continually reversed in
the galvanometer; so that, if the want of balance be only
small, the error due to it almost entirely vanishes.
Again, since the connection of the galvanometer with the
remaining wires of the combination is constantly changing its
direction those electromotive forces which exist in the bridge
or are generated by the current, and which are not reversed
when the current is reversed, are without influence on the
needle. It is a circumstance of great value, that for the
greater part of a swing the galvanometer is withdrawn from
all disturbing influences.
In consequence of these favourable conditions the observa-
tions agreed together very satisfactorily when we consider the
smallness of the quantities to be measured: the deviation of
the results obtained from their mean was in general less than
30 of the whole. Here also the proceeding was repeated each
time the needle passed through its position of rest. But the
multiplication could not be carried so far as to obtain a con-
stant deflection; for to the constant small damping of the
needle due to air-resistance was added the damping which
was produced whenever the galvanometer was put in circuit
with the bridge, and which lasted only for a very short time.
The time during which connection was made was not always
exactly the same, and thus the damping produced could not
be exactly determined. As, however, its effect became very
marked with large swings, the method was limited to smaller
deflections, and generally only from 7 to 9 elongations were
measured. The method which was used to deduce the most
probable value of the extra-current from the complete arcs of
vibration thus obtained will now be explained.
Let T be the period of vibration of the galvanometer
needle, λ the logarithmic decrement constantly present, q = e^
the ratio of any swing to the preceding one, and let, for
shortness,
T
-ta
tan-17
π
λ=K.