DOC.
14
PROOF
OF
AMPERE'S
CURRENTS
177
700
Fig.
1.
Each sharp peak corresponds
to
a
reversal
of the
magnetisation
and
we
have
for each of
them
6dt
2
XI. (8)
Let
the
origin
t
=
0
coincide with
a
point
in
Fig.
1,
where the
current
passes
from
the
negative
to
the
positive
direction. Then
we
may
write
i
=
Attn
cot,
(9)
8
=
2Bco9niot
and
0
may
be
developed
in
a
series
(10)
Of
this series
the
first term
only
need
be considered
here, as
the
effect
corresponding
to it is
the
only
one
that
is
multiplied by
resonance, so
that the other terms have
no
sensible influence
on
the
motion
of
the
cylinder.
Now,
multiplying
(10) by
cos nt
and
inte-
grating over a
full
period
T=2z/w
we
find
CO
3*
8»
jg
6
cos
cot
dt
=
-
Bv
o
ic
On
the
left
hand
side
0
is
different
from
0
only
in the
very
small
intervals
at t
=
O
and t
=
x-00.
For the
first
of
these
we may put
tubes
were
connected in such
a way,
that
a
current
passing through
them flowed
round the tubes
in
opposite
directions.
Under these
circumstances,
the current induced
in
the
windings
is
exactly pro-
portional
to
dI/dt,
the
demagnetizing
action of
the
poles
of
the iron
bar
being
eliminated,
as
well
as
the
induction due to
the
field
of the
coil
K. The
graph
for the
induced current,
and
therefore for
dI/dt
or
0
was
obtained
by
means
of
an
dt
oscillograph
of Siemens and
Halske.
The
alternations of the current i,
repre-
sented
by
the
sinusoid,
were
registered
in the
same
way.