DOCS.

180,

181

JANUARY

1916 175

letter-paper

coordinate

system

is

only

a

contrivance.

Always

the

same

points

are

illuminated

on

the

plate.

If

you perform

the distortion

of

the

tracing

paper only

within the

finite realm and in such

a way

that the

image

of

the

star,

the

aperture,

and the

plate

remain unshifted

without

damaging

the

constancy,

then

you

obtain

the

special

case

your question

refers

to.

The

essence

is:

As

long

as

the

drawing paper,

i.e.,

“the

space,”

is

unreal,

both

diagrams

do not differ at

all.

“Coincidences”

are

what

count, e.g.,

whether

the

plate

points

are

hit

by

the

light or

not.

Thus the distinction between

your

solutions

A

and

B

is

merely

a

difference in

presentation

with

physical congruency.

This

will

surely

become evident to

you upon

closer

contemplation.

If

the

equations

of

the

physics

were

not

generally covariant, you

would also

be able

to

make

the

above

consideration;

however,

relative to

the

letter-paper

system,

the

same

laws would not be

valid in the second

diagram

as

in the

first.

To this

extent

then,

both

of

them would not be

equivalent.

This

distinction

falls

away,

however,

with

general

covariance.

I also note

that

I

have

purposefully

left out the

fourth

(time)

coordinate,

which

is

insignificant

in

principle,

however.

Cordial

greetings

to

you

and

everyone, yours,

Einstein.

181. To Karl

Schwarzschild

[Berlin,]

9

January 1916

Highly

esteemed

Colleague,

I

examined

your paper

with

great

interest.[1] I would

not

have

expected

that

the

exact solution

to

the

problem

could be formulated

so

simply.

The mathe-

matical

treatment

of

the

subject

appeals

to

me

exceedingly.

Next

Thursday I

am

going

to deliver

the

paper

before the

Academy

with

a

few

words of

explanation.[2]

Meanwhile,

I

received

another letter

from

you yesterday evening,

which

I

would also

like

to

answer

right

away.

1)

The

theory is

fully developed,

as

far

as

the

fundamental formulas

are

concerned,

so no

other

difficulties remain in

the

treatment

of

the

individual

problems

aside

from

the

computational

ones,

which

are,

however,

inordinately large.

But

you

will gather

from

the

following

reflection

that

no

notable modification

is

made for

the

perturbation problem.

The modifications

that the

theory yields

are

of

a

relative order of

magnitude

determined

by

kM/r.

If

M

is

taken

as

the

solar

mass,

then

this

quantity is

barely