DOC. 14
PROOF
OF
AMPERE'S
CURRENTS
181
704
in
the
cylinder
cannot have
any
influence in
our experiment,
their
[12]
sole
effect
being a
slight
retardation of the
magnetic
reversals. So
far
as
we can
see,
the above
effects
are
the
only
ones
that
have
the
same frequency as
the
current
in
the
coil
and
are
therefore
magnified by
resonance.
When
now
the
coil
was
connected to
the
main
alternating
current
conductors the
image
on
the
scale
remained
perfectly
at rest
so
long
as
the
length
of the
suspending
wire
was
not such
as
to
make
the
frequency
of
a
free
vibration of the
cylin-
der
coincide
very
nearly
with
that of
the
alternating
field.
The
resonance appeared
and
disappeared again
by a change
of
length
of
the
wire
by
1
mm,
the whole
length
being
8
cm.
In
order
to find
the
length required
for
resonance
and
to
make
sure
that the
suspended apparatus
did
not
vibrate in
one
of its
higher modes,
we
used
the
following
method
by
which
we
could
also
determine
the moment
of inertia of the
cylinder.
At the
lower end of the iron
cylinder we
sealed
a
short
copper
cross
bar
whose
moment of inertia
was
10,7.
For
the moment
of inertia of the
cylinder
calculation
had
given
0,0045.
It follows from
this that the
period
of
oscillation
of the
cylinder
becomes
10,7
=
48,8
times
greater
by
adding the
small
cross
0,0045
bar.
If
therefore
we
chose
the
length
of the wire
so as
to
have
a
frequency
1
1)
with the
cross-bar,
the
frequency
without it would
be about
48,8.
This is
nearly equal
to
the
frequency
of the alter-
nating
current.
We
were
sure by
this
that
the
suspended system
would
vibrate
in its
fundamental
mode. In
order to determine
the moment
of
inertia
more accurately however,
the
cylinder
was
now
placed
within
the coil
and the
length
of the wire
was
increased
until the
resonance
was
at
its
maximum. Then the
frequency
of the free
vibrations
might
be
supposed
to be
equal
to
that of the
alternating
current which
was
found
to be 46,2.
After
this
the
arrangement
was
removed from the
coil
and the
cross
bar
fixed to
it. We then
found
the
frequency
1,14.
From
these
numbers
we
deduce
__f1,14"__
Q
10,7
(.40,2)
0,0065.
After
these
preparations
it
was
found
that
Effect II,
i.e.
the
oscillation caused
by permanent
poles
in
the
cylinder, was
of
no
[13]
1)
By
frequency we always mean
the number of
complete
oscillations in
a
second.