170

DOCS.

176,

177 DECEMBER 1915-JANUARY

1916

in which

B/r3

is

a (dimensionless) number,

thus

requires

that

ß

be

equal, apart

from

a

numerical

factor,

to

(km/r)3.[3]

I

am very

satisfied with

the

theory.

It

is not

self-evident

that

it

already yields

Newton’s

approximation;

it

is

all the

more

gratifying

that

it also

provides

the

perihelion

motion and line

shift,

although

it

is not

yet sufficiently

secure.[4] Now

the

question

of

light

deflection

is of

most

importance.

With

my

best

regards

and wishes for

the

New

Year, yours,

Einstein.

177. To Hendrik A. Lorentz

[Berlin,] 1

January 1916

Highly

esteemed

Colleague,

Your

enticing

invitations

make

it hard

for

me

to

stay

put here.[1] I

can

visualize

a

visit in

your midst,

can

depict

for

myself

the

very

interesting

conversations,

can

imagine

that

for

a

few

days

I

was

allowed

to

walk

around without

a

muzzle,

so

to

speak,

and

can see

myself

sitting

in Ehrenfest’s

cozy

little

home.[2]

But

I

must

forgo

all

this

because

I

cannot

easily get away

for

a

number of

reasons.

With

all of

your permissions, however,

I

am going

to extend

the date

set for

me

to

a

time when I

really

can

travel;

I

shall

certainly

not

postpone

it

for

longer

than

is

necessary.

Trying

times awaited

me

last

fall

as

the

inaccuracy

of

the

older

gravitational

field

equations

gradually

dawned

on me.

I

had

already

discovered earlier

that

Mercury’s perihelion

motion had

come

out

too

small. In

addition, I

found

that

the

equations

were

not

covariant for

substitutions

corresponding

to

a

uniform

rotation

of

the

(new)

reference

system. Finally,

I found

that the

consideration

I

made

last

year

on

the

determination of

Lagrange’s

H

function

for

the

gravitational

field

was

thoroughly

illusory,

in

that

it could

easily

be modified such

that

no

restricting

conditions

had

to

be

attached

to H,

thus

making

it

possible

to choose it

completely

freely.[3]

In

this

way

I

came

to

the

conviction

that

introducing adapted

systems

was on

the

wrong

track

and

that

a more

broad-reaching covariance,

preferably

a

general

covariance,

must

be

required.

Now

general

covariance has

been

achieved, whereby

nothing

is

changed

in

the

subsequent specialization

of

the

frame of

reference.[4]

I

had considered

the

current

equations

in

essence already

3 years

ago

together

with

Grossmann,

who had

brought

my

attention

to

the

Riemann

tensor.

But

because

I

had

not

recognized

the

formal

importance

of

the