72 DOC.

60 MARCH

1915

purpose you specially

choose

H

=

g11,

and

show

that

in

this

case,

the

value calculated

according

to

(72)

and

(73),

1/-gEdguvEuv,

is

not

an

invariant.

On

page 1069,

however,

it

is

pointed

out

that H

must

be

chosen

in

such

a

way

that

it

is

invariant for

linear substitutions. Without

this

precondition,

formula

(65),

which

is

fundamental

to what

follows,

obviously

is

not

valid.[4]

As

g11

is not

an

invariant for

linear

substitutions,

your counterexample

does not

constitute

a

refutation of

my

stated theorem.-

As far

as

the

first

part

of

your

letter

is concerned, I

do not

see

why

the

conclusion drawn from

(71)

ought

not

apply.

Variation calculations

are always

carried out in

the

way

in which

I

have done it.

I

know

that

JdTE(dguv)...

(71)

is

an

invariant

when

the

boundary

conditions for

the

dguv's are

observed, regard-

less of how

the

dguv's are

chosen.[5]

Now,

let

the

dguv's

differ from

zero

only

inside

an oo

small

area

o.

The

Euv’s

may

be

treated

as

constant in

the

integration.

If

you

set

dr

=

t

Ja

and

ƒdguvdr

=

dguvr,

whereby

the

dguv's

signify

spatial

mean

values

of

the

dguv

terms,

then

it

is

possible

to set

instead of

(71)

EdguvEuv.

The theorem

follows

from

this, taking

into consideration

that

owing

to

the

small-

ness

of

area

o,

the

dguv’s

transform

at

one

place

within

o,

like

the

dguv's,

i.e.,

also

like

the

guv's.-

I

urge you earnestly

to

inform

me

of

your opinion

of

the

proof upon

reconsid-

eration.

With

cordial

greetings, yours very truly,

A. Einstein.