DOC.

49

317

d

Tr

! #

d

JeT

and

w t

i

+

i£

u

t

On

p. 462

the subscripts

in the

quantities

u

^

and

u^

have to be

added.

Also, in about the

middle

of this

page a

mistake

in

sign

should

be

corrected: the

equation

should read

Va

i

-4

A

letter

by

Mr.

Planck

induced

me

to add

the

following supplementary

remark

so as

to prevent

a

misunderstanding

that could arise

easily:

In

the

section

"Principle of

relativity

and

gravitation",

a

reference

system

at

rest

situated

in

a

temporally constant,

homogeneous

gravitational

field is treated

as

physically

equivalent to

a

uniformly

accelerated,

gravitation-free reference

system. The concept "uniformly

accelerated"

needs

further clarification.

If-as in

our

case-one

considers

a

rectilinear

motion (of

the

system

E),

the acceleration is

given

by

the

expression

dv/dt,

where

v

denotes

the

velocity.

According

to

the kinematics in

use up

to

now,

dv/dt

is

independent

of

the

state

of motion of the

(nonaccelerated)

reference

system,

so

that

one

might

speak

directly

of

(instantaneous) acceleration

when

the

motion

in

a

certain time

element

is

given.

According

to

the kinematics

used

by

us,

dv/dt

does

depend

on

the

state of motion

of the

(nonaccelerated)

reference

system.

But

among

all the values of acceleration that

can

be

so

obtained for

a

certain

motion

epoch,

that

one

is

distinguished which

corresponds

to

a

reference

system

with

respect to which

the

body

considered

has

the

velocity

v

=

0. It

is

this value of acceleration

which has

to

remain constant in

our

"uniformly

accelerated"

system.

The

relation

v

=

jt

used

on

p.

457

thus holds

only

in

first

approximation; however,

this is

sufficient,

because

only

terms

linear

in t and

r,

respectively, have

to

be taken into

account

in

these

considerations.

(Received

on

3

March

1908)

[3]