302 DOC. 71 PRINCETON LECTURES
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(34)
SPECIAL RELATIVITY
\
c
i
ex
h
i

hz
e
«

~
e
=
eu 
vhz
v/l^T2
ei
~h vhv
vr^T2
h
v
h'z
=
hy
+
v
ez
VF
v*
K
ve"
Vl

v2
If there
exists
with
respect to
K
only
a
magnetic
field,
h,
but
no
electric
field, e,
then with
respect
to
K' there
exists
an
electric
field
e'
as
well,
which would
act upon
an
electric
particle
at
rest relatively
to
K'.
An
observer
at rest
relatively to
K
would
designate
this force
as
the
BiotSavart
force,
or
the Lorentz electromotive
force.
It
therefore
appears
as
if this
electromotive
force
had become
fused
with the
electric
field
intensity
into
a single
entity.
[45]
In
order
to
view this
relation
formally,
let
us
consider
the
expression
for the force
acting
upon
unit volume
of
electricity,
(35)
k
=
pe
+i
X
h
in which
i
is
the
vector
velocity
of
electricity,
with the
[46]
velocity
of
light
as
the
unit. If
we
introduce
J"
and
£"
according
to (30a)
and
(31),
we
obtain
for
the
first
com
ponent
the
expression
+
fyizjî
+
Observing
that
t11
vanishes
on
account
of
the
skew
symmetry
of the
tensor
(/),
the
components
of
k
are
given
by
the
first
three
components
of
the
fourdimensional
vector
(36)
a;
=
tfvj,
and
the
fourth
component
is given by
(37) K4
= 44ljfl
T
t42jf2
"t" 4i3jfz
=
í(exÍx
T
eyíy
T
ez^z)
=
i\.
[42]