DOC. 16 FOUNDATIONS

OF GRAVITATION

197

Since

only

linear substitutions

are

admissible,

certain

one-, two-,

and

three–

dimensional manifolds

are privileged,

which

may

be

designated as straight

lines,

planes,

and linear

spaces.

[13]

The

theory

sketched here

overcomes

an

epistemological

defect that attaches

not

only

to

the

original theory

of

relativity,

but also

to

Galilean

mechanics,

and that

was

especially

stressed

by

E.

Mach. It

is obvious that

one

cannot

ascribe

an

absolute

[14]

meaning

to the

concept

of acceleration of

a

material

point,

no

more so

than

one can

ascribe it

to the

concept

of

velocity.

Acceleration

can

only

be defined

as

relative

acceleration of

a point

with

respect

to other bodies.

This

circumstance makes

it

seem

senseless

to

simply

ascribe to

a

body

a

resistance

to

an

acceleration

(inertial

resistance

of

the

body

in the

sense

of classical

mechanics);

instead,

it will have

to

be

demanded that the

occurrence

of

an

inertial resistance be linked

to

the relative

acceleration

of

the

body

under consideration with

respect

to

other bodies.

It

must be

demanded

that the inertial resistance

of

a

body

could be increased

by having

unaccelerated inertial

masses

arranged

in

its

vicinity;

and this increase

of

the inertial

resistance

must

disappear again

if these

masses

accelerate

along

with the

body.

It

turns

out

that

this behavior of inertial

resistance,

which

we

may

call

relativity

of

inertia, actually

follows from

equations (5).

This circumstance constitutes

one

of the

[15]

strongest pillars

of the

theory

sketched.