350

REMARKS

ON

DOC.

51

Doc. 54

REMARKS

ON OUR

PAPER:

"ON THE FUNDAMENTAL ELECTROMAGNETIC

EQUATIONS

FOR MOVING

BODIES"

by

A.

Einstein

and

J.

Laub

[Annalen

der

Physik, 28 (1908):

445-447]

Mr. Laue

was

kind

enough

to

call

our

attention

to

an

inaccuracy

in

our

[2]

paper

cited in the title.1

We

say

there

(Ann.

d.

Phys.

26(1908):

535):

"It is remarkable that

the

boundary

conditions for the

vectors

(H,

D,

Jq,

93

at

the

boundary

of

two

media

are

the

same as

for bodies

at rest.

This

follows directly

from

equations (1a) to

(4a)."

Apart

from

the fact

that equations

(3a)

and

(4a)

are

irrelevant for the

derivation of the

boundary

conditions, this

statement

is

correct only

if the

component

of the

motion normal

to

the

boundary

surface vanishes,

which

is

actually

the

case

in the

problem

treated

in

§2

of

the

paper

quoted. The

boundary

conditions

of the

general

case are

most

easily found

in the

following

[3]

way,

which corresponds to

the

one

taken

by

Heinrich Hertz.

If

the

boundary

surface,

or,

more

exactly,

the infinitely thin

boundary

transition shell,

moves

in

some

arbitrary

manner,

then,

in

a

point

situated

in

it

and instantaneously at

rest,

the

quantities

determining

the

electromagnetic

field will in

general

vary

discontinuously,

infinitely fast,

with time;

how-

ever,

these

changes

will

be

continuous

for

a

point

moving

with

the

matter.

Thus,

the application

of

the operator

It

+

(oV)

to

a

scalar

or

to

a

vector

will

not

lead to

infinitely

large values

even

in

the

boundary

surface. If

we

then write

equation

(1a)2

in the

form

1

c

if

+ 5

=

curl

S)

+

i(oV)S)

c

[1] 1In

his letter

Mr. Laue

gave

the

correct

boundary

conditions

and pointed

out

a

different derivation

of them.

2loc. cit.