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.