The galvanometer.
Let
a
steel
ring
of the indicated form be
exposed
to
a
magnetic
field of the indicated direction.
[Fig.]
It
then will become magnetized, i.e., the magnetic
masses
in it will
become
permanently separated.
It is then
possible (which
cannot
be
proved here)
to
specify
two
magnetic
masses
of different
sign
in
diametrically opposite
points of the center, at
a
distance
A
from it,
which
can
completely replace the ring magnet
as
far
as
magnetism
is
concerned. These points
are
called the poles of the magnet.
Let this
ring
be
suspended
for torsion
so
that the connection
m
-
m
always remains horizontal.
Let the
ring
be surrounded by
a
circular
current
of radius
R,
whose dimensions should be
very
large compared
with those
of the ring
magnet.
The
plane
of the circuit shall be vertical.
Y runs
from
[Fig.]
0
to 2tt
ds
:
x
=
0
y
=
R
sin
Y
z
=
R
cos Y
m
:
x
=
A
sin
u
y
=
A
cos
u
z
=
0
r
=
j a2 sin2
u
+ (R
sin
Y
-
a
cos
u)2
+ R2
cos2
Y
=
J
R2 +
A2
-
2RA
sin
Y cos u
=
R
J
1-2-4
sin
Y cos u
(neglecting the 2nd
power
of
4)R
R
=
R
(1
-
4
sin
Y
cos
u).
The direction cosines
(r)
:
a
b
c
-A
sin
u
R
sin
r
-
/
cos u R
cos
y
r
r
(ds):
a'
p'
c'
0
cos Y
-
sin
Y
,v
mi
ds
R
f
. .
a
o
dx
=
-
-
(sin
Y
-
-
cos
u)',
sin Y +
cos2
Y\1
r2
r
R
j
119