44

DOC.

37

OCTOBER

1914

Your

integrating apparatus

appeals

to

me

very

much.

Although,

as

it

is

described,

it

only

delivers

y

dx;

but

you

intended-if

I

have

understood

you

correctly-to turn it into

a

measuring

device for

J

y1y2dx

which

you

activate

through

engaging a

second

adjustable

friction clutch

so

that

the rotation of

the

planimeter

disk

is not

simply

proportional

to

dx,

but

propor-

tional

to

y2dx;

then,

of

course,

the

rotation of

the little

counter wheel becomes

proportional

to

y1y2dx.

Another

possibility

with which

you

could

manage

with

a

friction element

but

which would

require

two

integral operations

instead

would be

the

following:

You

have

an

instrument

in which

the

distance of

your

friction roll to

the

center

of

your

counter disk is

proportional

to

y2

(whether

this

is

easily realizable,

I

do not

know).

With

such

a

device

you

could

measure

f(y1+y2)2dx

and

ƒ(y1-y2)2dx,

thus

also

the

difference[6]

2/y1y2dx.

The construction

of

such

a

device

does

not

appear

to

me

to

be

particularly dif-

ficult.

When

we

meet

again,

we

could,

if

you

have

the

inclination

and the

time,

weigh

the

various

possibilities against one

another.

I

ask in advance for

your

forbearance, knowing

well

that

I

am a low-grade

dilettante

in such matters.

With

regards

from

your very

devoted

colleague,

A.

Einstein.