266
THE
RELATIVITY PRINCIPLE
sin
to
!
,,
_
Vx
+
mxyx
+
nx zx
c
with
respect
to
S'.
The
transformation
equations developed
in
§3
require
the
following
relations
between
the
quantities
w,
l,
m, n
and
w',l',
m',
n':
w'
=
uß
I
m1 =
ä'
=
1
ill
i

m
ß
ß
llC
1
n
(I
c
1

^
c
(4)
We
will interpret the formula for
w'
in
two
different
ways,
depending
on
whether
we
consider
the observer
as moving
and
the
(infinitely
distant)
source
of
light
at
rest,
or
vice
versa.
1.
If
an
observer is
moving
with velocity
v
relative
to
an
infinitely
distant
source
of
light
of
frequency
v
in
such
a
way
that the
connecting
line
"source
of light

observer"
forms
an
angle
Q
with the observer's
velocity
as
referred
to
a
coordinate
system
at rest
relative
to
the
source
of
light,
then the
frequency
v'
of
the
source
of
light
perceived
by
the
observer is
given
by
the
equation
v v
1

cos
^
c
1

vz
2.
If
a
source
of light of
frequency
v0
relative
to
a
comoving
system
moves
such
that the
connecting
line "source of light

observer"
forms
an
angle
Q
with
the velocity of
the light
source as
referred
to
a
system
at
rest
relative
to
the
observer,
then the
frequency
v
of the
source
of light
perceived
by
the observer is
given
by
the
equation
[31]