162
ELECTRODYNAMICS
OF
MOVING
BODIES
It remains
now
to
find the
amplitude
of the
waves
the
way
it
appears
in
the
moving
system.
If
A
and
A1
denote the electric
or
magnetic
force in
the
system
at rest
and in
motion,
respectively,
we
get
[30]
A'2
=
A2
1
~
J COS
ip
1
V
V
Y
which
for
p
=
0
simplifies
to
V2
=
P
1
- H
V
V
1
+
v
V
It follows
from
the
equations
derived
above
that
to
an
observer
approaching
a
light
source
with
velocity
V,
this
source
would appear
to have
infinite intensity.
§8.
Transformation of
the
energy
of
light
rays.
Theory
of
the
radiation
pressure
exerted
on
perfect mirrors.
Since
A2/8i
equals
the
energy
of
light
per
unit
volume,
according
to
the principle of
relativity
we
have
to
consider
A2/8i
as
the light
energy
in the
moving
system. Hence
A'2/A2
would be
the ratio of the
energy
of
a
[31]
given
light
complex
"measured
in
motion" and
the
same
energy
"measured at
rest," if
the
volume
of
a
light
complex
were
the
same
whether measured
in
K
or
k. However,
this is
not
the
case.
If
a,b,c
are
the
direction cosines
of
the
wave
normal of
the
light
in the
system
at
rest,
then the
surface elements
of
the spherical surface
(x
-
Vat)2
+
(y
-
Vbt)2 +
(z
-
Vct)2
=
R2,
which
moves
with
the velocity of
light,
are
not
traversed
by
any
energy;
we
may
therefore
say
that this surface
permanently
encloses the
same
light
complex.
We
ask
for the quantity
of
energy
enclosed
by
this surface
as