DOC.

36

207

Doc. 36

ON A

METHOD FOR THE

DETERMINATION OF THE

RATIO

OF THE TRANSVERSE

AND

THE

LONGITUDINAL

MASS OF

THE

ELECTRON

by

A.

Einstein

[Annalen

der

Physik

21

(1906):

583-586]

Three quantities

concerning

cathode

rays

are

accessible

to

precise

observation: the potential difference

producing

the velocity of the

rays

(generating

potential), the electrostatic

deflection,

and

the

magnetic [1]

deflection.

There

exist

two

independent

relations

between

these three

quantities

whose

knowledge

at

considerable

ray

velocities is of

extraordinary

theoretical interest.

One

of these relations,

namely

that

between

magnetic

and

electrostatic

deflection,

has been examined

for

B-rays

by

Mr. Kaufmann. [2]

In

the

following

I

shall

point

out

that there exists

one

other relation

between

these

quantities

that

can

be measured

with sufficient

accuracy,

namely,

that

between

the

generating potential and

the electrostatic

deflection

of

cathode

rays,

or,

what

is the

same,

the ratio of the

transverse to

the

longitudinal

electron

mass as a

function

of

the

generating

potential. [3]

If the

square

of

the velocity of the electrons is

very

small

compared

with the

square

of

the

velocity

of light, the

motion of

the electron

obeys

the

equations

d2x

e

u0

X,

etc.,

where

e/u0

denotes the ratio

of

the

charge

to

the

mass

of

the

electron,

x,

y,

z

the coordinates

of

the

electron,

and

X,

Y,

Z

the

components

of

the

electric field

strength

if

no

other forces besides the electrostatic

ones

act

on

the electron.

We

assume

that the electrons

move

with

an

initial

velocity

zero

from

some

starting point

x0, y0,

z0

(cathode).

The

motion

is then

uniquely

determined

by

the

equations

given above;

it shall

be

given

by

the

equations

x

=

q1(t)

,

y

=

q2(t)

,

z

=

q3(t)

.