DOC. 29 DETERMINATION OF STATISTICAL VALUES

301

00

(2)

I(0)

=

f

aw

(A)

cos 7r

dA.

[4]

0

^

Mechanical devices that

can

carry

out

the

integration

indicated in

(2)

are

already

known.

Moreover, my

friend

Mr. P.

Habicht has shown

me

that the determination of

the

averages

in

(1)

can

readily

be done with the

help

of

an

easy-to-handle

mechanical

integrator.

Thus,

the

practical

execution of the method does

not

seem

to

present any

particular

difficulties.

Let

us

also

note

that

an

integrator permitting

the formation of

averages

of

type

(1)

can

also be used for

answering

the

following question:

Does

or

does

not

a

cause

and effect relation exist between

two

quantities

F1

and

F2,

both of which

are

determined

empirically

as

functions of time?

Indeed,

if

one

forms

SK(A)

= F, (f)F2(f

+

A)

as a

function of

A,

one

obtains

a

horizontal

straight

line for

9W(A)

if there

are no

cause

and effect relations. If such

a

relation does

exist,

without

an

appreciable

retardation,

one

obtains

a curve

that has

an

extremum

for

A

=

0.

If there

is

an

appreciable

retardation,

the

curve

has

an

extremum

corresponding

to

another value

of A.