154
ELECTRODYNAMICS OF MOVING
BODIES
£ =
W^T,
V
=
MqT,
c
=
o,
where
wt
and
w
denote
constants.
We
seek the motion of
the
point
relative
to
the
system K.
Introducing
the
quantities
x, y,
z,
t
into the
equations
of motion of
the
point
by
means
of the transformation
equations
derived in
§3,
we
obtain
U)£
+
v
x
i,
vwc
1 +
V
V
y =
V»
vw
t
i
+
jr
3-
z
=
0.
Thus,
according
to
our
theory,
the
law
of the
parallelogram
of velocities
holds
only
in
first
approximation.
We
put
2
V2
=
dx
+
\dy]
if
St
V. -
W'
A
+
w2
£
V
a
-
arctg
WJL
.
w
x
and
[20]
a
should then
be
considered
as
the
angle
between
the velocities
v
and
w.
After
a
simple
calculation,
we
obtain