DOC.
11
LECTURE ON ELECTRICITY
&
MAGNETISM
397
[4]In
contrast to
the
usage in
the
text, in
the
figure
e
=
e(x,y,z),
e1 =
e1(a,b,c).
[5]In
the
following
formula,
as
well
as
in many
instances
below, a subscript
1
denotes
a
dummy
summation-index.
[6]The
words "Hier
[...]
geben"
are
in Mileva Einstein-Maric's
handwriting.
[7]The quantities
df1
and
df2
below
denote
surface
elements; n1z
and
n2z are
the
angles
between
n1
and
n2
and the
z-axis.
[8]In
the
following
formula
dx
is
a
volume element and ds is
a
surface
element.
[9]The
words "einen
Spezialfall
des
sog." are
interlineated.
[10]These
remarks, as
well
as
the
ones
concerning
theoretical
constructs in
the
next
para-
graph, may
derive from Pierre Duhem
(see, e.g.,
Duhem
1906).
See
Howard
1990 for
a
discussion
of Einstein's
reading
of Duhem.
[11]In
this
integral
the
integration region
K
is
the "continuum"
where
p
is
non-zero,
minus
a
sphere
with radius
R
around the
point
(a, b,
c).
[12]In
the
following integrals
the
integration region is
a
cylinder
of radius
R,
with its
upper
and
lower
surfaces
on
either
side
of the
charged
surface; a
factor of
rj0
(the
surface
charge
density) is missing
on
the
right side
of the
last
equality.
[13]A
minus
sign
is missing
in
the
left-hand side
of
the
following equation.
a
is the surface
charge density.
47c5
[14]The
last
equality
should
be C
=
-jr.
[15]In
the
following equation
2a12
should
be
a\2.
[16]The
whole
line is
interlineated.
[17]In
the
last
three
equalities below,
a
minus
sign
should be added
on
the
left.
[18]In
the
second
equality below,
2d
A
should
be
-
2dAm.
[19]In the
following,
b1b2
should
be
b11b22
and
D
should
be
D2.
[20]A
minus
sign is
missing
on
the
right in
the last
equality.
[21]In the second
equality,
(a11
-
a22)
should
be
(a11
-
a12),
or, alternatively,
(a22
-
a12).
[22]In the formula
below,
2D' should be
(2D')2.
[23]In
the
following,
5
is
the distance between the
plates,
f
is
their
surface,
and
A(p
is
the
potential difference
between the
plates.
[24]The first
equality
should
be
0
=
2nE2j.
[25]The
"Schutzringelektrometer" (originally
devised
by
William
Thomson;
see
Thomson
1867b)
is
essentially
a
large condenser,
the
plates
of which
are
held
at different potentials.
The
potential
difference between the
plates
is
determined
by
measuring
the
force
on
a
loose
section
in
the middle of
one
of the
plates
(see
also the
figure).
For
more details,
see, e.g.,
Chwolson
1908, pp.
325-329,
or
Graetz
1905b, pp.
68-70.
[26]Thomson's
quadrant electrometer
(see
Thomson
1867b)
consists of
four
quadrants
(see
the
figure)
and
a
"needle"
(a piece
of aluminum
foil
or
something
similar)
that
hangs on
two
threads
above
or
inside them.
Opposite quadrants
are
usually
kept
at
the
same potential;
the needle
is
grounded
or
kept
at
a
fixed
potential.
A
potential difference
between the
pairs
of
quadrants, or
between the needle and the
quadrants
will
result
in
a
rotation of
the
needle.
For
more
details,
see,
e.g.,
Chwolson
1908,
pp.
318-324,
or
Graetz
1905b,
pp.
63-65.
See
also the
following
note
and Einstein's
description
of the instrument in
his
ETH student
notes,
H. F. Weber's
Lectures
on
Physics,
ca.
December 1897-ca. June
1898
(Vol.
1,
Doc.
37),
pp.
156-158.
[27]The
electrometer
is
treated
as a
system
of
two condensers,
each formed
by
a pair
of
quadrants
and the
part
of the needle that
lies
above the
pair
(or
inside of
it; see
the
figure).
In
the
expression
for the total electrostatic
energy
I,
P1
and
P2 are
the
potentials
of
the two
pairs
of
quadrants,
p
is
the
potential
of the
needle,
a
-
x
and
a
+
x
are apparently proportional to
the
area
of the needle above
(or
inside)
each of the
pair
of
quadrants,
and
k
is
a
constant.
The
derivative of
O
gives
the
torque D
that
is
exerted
on
the
needle.
[28]The
"Maschinchen"
is
Einstein's invention for
measuring
small
potential
differences
or
charges.
For
a description, see
Einstein
1908a
(Vol. 2,
Doc.
48).
A
charged
conductor
with
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