128 DOC. 7 GRAVITATIONAL INDUCTION

L

=

-a2

Lp 2q

(

1 +

kM\

Rc,o

and hence for

an

inertial

mass

m' influenced

by

K

m'

=

m +

.....(2).

Rco

The result is of

great

interest in itself. It shows that the

presence

of

the inertial shell

K

increases the inertial

mass

of

the material

point

P

inside the shell. This

suggests

that the entire

inertia

of

a mass

point

is

an

effect

of

the

presence

of

all

other

masses,

which is based

on

a

kind

of

interaction with the

latter.1

The

degree

to which

this

conception

is

justified

will become known when

we

will be fortunate

enough

to

have

come

into

possession

of

a

serviceable

dynamics

of

gravitation.

It is clear

that,

in the

same

way,

the

presence

of P

increases the inertial

mass

of

K.

By means

of

an

argument totally analogous

to the

one

just

presented,

one

obtains

for the inertial

mass

M' of

K influenced

by

the

presence

of

P,

M

=

M

+

kmM

Rco

.....(3)

3.

We

now

seek the forces

F

and ƒ

necessary

to

impart

the

accelerations

T and

Y

to

the

masses

M

or m

in

a

given

direction.

If

A,

a,

and

a

denote coefficients that

are

unknown for

the time

being,

then

we

will have

to set

F

=

AT

+

ayl

ƒ

=

ay

+

alf

1

(4)

The coefficients

of

the second

terms

(a)

are

chosen to be the

same

in the

two

equations,

since the reaction

of

K

on

P

when

only

K is accelerated

must

obviously

be

equal

to

the reaction

of

P

on

K

when

only

P

is accelerated.

The coefficients

A,

a,

and

a

follow from the consideration

of

the three

special

cases

to

which

equations (1), (2),

and

(3)

refer.

In the

first

case,

K and

P

have the

same

acceleration. Let this

common

acceleration be

y.

From

(4)

and

(1)

one

obtains

or

F

+

f

= (A

+ a +

2a)y

+ m

kMm

\

He2)

Y

1This

is

exactly

the

same point

of

view that E. Mach advanced in his astute

investigations

on

this

subject.

(E. Mach,

“Die

Entwicklung

der

Prinzipien

der

Dynamik.

Zweites

Kapitel.

Newtons Ansichten über

Zeit,

Raum und

ewegung.”

[“The

evolution

of

the

principles

of

dynamics. Chapter

2.

Newton's views

on

time,

space,

and

motion.”]).

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