400 DOC.
11
LECTURE ON
ELECTRICITY
&
MAGNETISM
I
4
induction
for
a
circle
equals
2l
+
l°g-
-
^
I.
These
expressions
reduce
to
the
ones given
by
Einstein
if l'
is interpreted
as
the circumference of the
square
and the
circle,
respectively;
see,
e.g.,
Waitz
1908,
p.
595.
[72]l
is
the self-induction
per
unit of
length.
[73]The
factor
2 in
the
equality
should be 4.
[74]Michael
Pupin
(1858-1930)
was
the
originator
of
the idea
of
"loading" telegraph
or
telephone
lines
with inductance coils
at regular intervals,
in order
to
reduce
attenuation of the
signal;
see, e.g.,
Rellstab
1908, pp.
807-809.)
[75]PE
is
the
electromagnetic
field
energy density, i.e.,
PE
=
e/8n
S2
+
u/8n$2.
[76]§z
is
assumed
to
be
zero.
This
assumption
for the
magnetic field
was
originally
intro-
duced
by
Hertz
(see
Hertz, H.
1889).
Einstein's
treatment
of the Hertzian oscillator
is
very
similar
to
the
one
given
in Planck
1906
(pp.
103-108).
[77]The
last
term in
this
expression
should
be
- y-y;
the second
term
on
the
right
in
the
d2F
expression
for
(5Z
below should
likewise be
- -= .
ox
X2 X2
[78]In the last
term,
x2/r2
should be
x2/r3.
[79]The
following
expressions
are
valid
for
large
distances from the
origin.
[80]Q
is
the
angle
between
r
and the z-axis.
[81]The
integral
represents
the
field energy
on
a
spherical
surface of radius
r,
averaged
over
the
period
T.
It should
be
preceded by
a
factor of
c/4n.
[82]The
apparatus employed
by
Hertz to
generate electromagnetic waves
consisted of
two
large
conducting spheres,
each of which
was
connected to
a
stretch
of
wire.
The
free
ends
of the
wires
were so
close
together
that
a
spark
could
pass
between them. In this circuit
an
oscillation is
produced whereby
the
spheres
are
periodically charged
and
discharged.
The
frequency
of the oscillations
is
determined
by
the self-inductance of the
wires
and the
capaci-
tance
of the
spheres.
The
figures
Einstein
gives
for the
length
of the
wires
(l),
the
capacitance
of
the
spheres
(C),
and the maximum
potential
difference
between the
spheres
(pmax)
are
of the
same
order of
magnitude
as
the
ones
in
Hertz's
experiments
(see
Hertz,
H.
1887).
See Drude
1894, pp.
391-398, 417-420,
for detailed calculations.