DOC.

47

263

The

formula

v=v0

1

- v2/c2

permits

a

very

interesting application.

Mr.

J. Stark

showed

last

year1

that the ions

constituting

canal

rays

emit

line

spectra

by

observing

a

shift in spectral lines

which

he interpreted

as a

Doppler

effect.

Since the oscillation

process

that

corresponds to

a

spectral

line is

to

be

considered

an

intra-atomic

process

whose frequency

is determined

by

the

ion

alone,

we may

consider

such

an

ion

as a

clock

of

a

certain

frequency

v0,

which

can

be

determined, for

example,

by

investigating

the light emitted

by

identically constituted ions

which

are

at rest

relative

to

the observer.

The

above

consideration

shows,

then,

that the effect of

motion

on

the light

frequency

that is

to be

ascertained

by

the observer is

not completely

given

by

the

Doppler

effect.

The

motion

also reduces the

(apparent)

proper

frequency

of the

emitting

ions in accordance with the relation

given

above.2

[24]

S5.

The

addition

theorem

of

velocities

Let

a

point

move

uniformly

relative

to

the

system

S'

according to

the

equations

x'

=

u'

t'

x

y'

=

u't'

y

y

z1

=

u't'

z

If x', y',

z',

t'

are

replaced

by

their

expressions

in

x, y, z,

t

with

the

help

of

transformation

equations

(1),

one

obtains

x,

y,

z as

functions of

t, and

thus also the point's

velocity

components

w, w,

w

x

y

z

with

respect to

S.

We

thus

get

1J.

Stark,

Ann. d.

Phys.

21

(1906): 401.

2Cf.

§6,

equation (4a).

[23]