Volume 1: The Early Years, 1879-1902 (English translation supplement) Page 18 (40 of 220)

Since in the
case
of both
figures
(the circle from the system and the
ellipse)
the
highest
value for
x
has the ordinate 0
(as
the 1st
differential
quotient shows),
and the centers of all circles lie
within
the
ellipse,
we
only
have to examine
whether
for
y
=
0
one
of
the two
points
of the circle lies outside the
ellipse.
Since the
entire
figure
under examination is symmetrical with respect to the
y-axis,
we
need to consider
only
one
(the
positive)
side.
[Note
in
margin:]
The
proof
is
not sound.
We
must make
a
direct
comparison
of the
equations
for the
circle
and
for the
ellipse
and
identify the
x
and
y
of both.
Ellipse
Ax2
+ y2
=
r2
I
Circle x2
-
2px
+
y2
-
r2
+
2p2
=
0
If
we
eliminate
y:
^ x2 -
2px
+
2p2
=
0
x2
-
4px
+
4p2
=
-4p2
+
4p2
The
expression 4-4p*
+
4p*
x
=
2
p
Substituted in I
2p2
+y2
=
r2
y
=
+
4
r*
-
2p*
.
For the root to be
real,
we
must have
r2
2p2
p
42
r
p
-Ü-
J
2
there is
no more
contact with the
ellipse.
r
If
p
,
/
2
24.
MATURA EXAMINATION (D) PHYSICS: "TANGENT
GALVANOMETER AND
GALVANOMETER"
[19 September
1896, 2:30-3:45
P.M.]
Albert Einstein
TANGENT GALVANOMETER AND GALVANOMETER.
Each electric current is surrounded
by circular, concentric
magnetic lines
of force that lie in
planes perpendicular
to
the
18

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Extracted Text (may have errors)

Since in the
case
of both
figures
(the circle from the system and the
ellipse)
the
highest
value for
x
has the ordinate 0
(as
the 1st
differential
quotient shows),
and the centers of all circles lie
within
the
ellipse,
we
only
have to examine
whether
for
y
=
0
one
of
the two
points
of the circle lies outside the
ellipse.
Since the
entire
figure
under examination is symmetrical with respect to the
y-axis,
we
need to consider
only
one
(the
positive)
side.
[Note
in
margin:]
The
proof
is
not sound.
We
must make
a
direct
comparison
of the
equations
for the
circle
and
for the
ellipse
and
identify the
x
and
y
of both.
Ellipse
Ax2
+ y2
=
r2
I
Circle x2
-
2px
+
y2
-
r2
+
2p2
=
0
If
we
eliminate
y:
^ x2 -
2px
+
2p2
=
0
x2
-
4px
+
4p2
=
-4p2
+
4p2
The
expression 4-4p*
+
4p*
x
=
2
p
Substituted in I
2p2
+y2
=
r2
y
=
+
4
r*
-
2p*
.
For the root to be
real,
we
must have
r2
2p2
p
42
r
p
-Ü-
J
2
there is
no more
contact with the
ellipse.
r
If
p
,
/
2
24.
MATURA EXAMINATION (D) PHYSICS: "TANGENT
GALVANOMETER AND
GALVANOMETER"
[19 September
1896, 2:30-3:45
P.M.]
Albert Einstein
TANGENT GALVANOMETER AND GALVANOMETER.
Each electric current is surrounded
by circular, concentric
magnetic lines
of force that lie in
planes perpendicular
to
the
18

Help

log
cos
y =
9.95226
-
10
7
=
26°
2
3'
Calculation of side
a
Since
*
a
is
an
obtuse
angle,
a
=
2r*sin
(180°
-
a)
log
a =
log
20
+
log
sin
(64°43'38")
=
1.30103
+
9.94884
-
10
=
1.24987
a
=
17.77
PROBLEM
2
If
p
denotes the distance between such
a
circle of the
given
system and its center, then its radius will be
=
Jr2
-
p2
.
Its
equation
is
(x
-
p)2
+
r2
-
p2
y2
=
r2
-
p2
x2
-
2px
+
p2
+
y2
=
r2
-
p2
x2
-
2px
+
y2
=
r2
-
2p2
We
now
search for the
equation
of the
envelope, i.e.,
the intersection
of
two
such circles whose
p
differ
infinitesimally
from each other.
For the
intersection, in the
case
of
an
infinitesimal increment
d(p),
the
increments
of
x
and
y
as
well
as
the
equation
must
identically
equal
0.
Hence:
x2
-
2px
+y2-r2+2p2
=0
xz
-
Zpx
+ y*
-
r2
+
gp2
+
(-2x
+
4p)c/p
=
Q
Subtr.
4p
-
2x
=
0.
We
now
substitute this
value in the above equation
x2
-
2px
+ y2
-
r2
+
2p2
=
0
x2
~x2
+
y2
-
r2
+ix2
=0
^-x2
+
y2
=
r2
For
x
=
0
y
=
+
r
For
y
=
0
x
=
+
rJ
2
We
now
have to consider the condition under which
a
circle of the
system
touches the
ellipse
1/2
x2
+
y2
=
r2.
17

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current circuit. At
any
given
point
in the
surroundings
the
magnetic
force present
is inversely proportional
to the
square
of the distance
from the
(rectilinear) conductor,
and
directly proportional
to
the
current in the conductor.
The latter
proportionality
determines is used for the
relative
determination of the current in
a
conductor from the
magnitude,
because in two
different
measurements
the currents
are
proportional
to
the magnetic forces. This is done
using
the
tangent galvanometer.
The setup of the latter is
as
follows: On
a
stand there is
mounted
a
metal
ring
in
a
vertical
plane which
can
rotate around
a
vertical axis. Around it
can
is
fixed
an
insulated wire which
can
be
connected with the
current-producing
apparatus by two conducting
setscrews. In the
middle of the
ring
there is
suspended
a
magnetic
needle
on
a
very
fine
thread; the needle
can move
freely
in
the
horizontal plane.
Of
course,
one
can
also
use
magnets
in forms other
than
a
needle (e.g.,
a
small
mirror
of
magnetized
steel such
as
is
used for
reading
with
a
telescope and scale). Around the mobile
magnet there
are
two
mobile
copper
casings
which
serve
for
damping
its
oscillating
motion.
[Fig.]
The
apparatus
is set
up
for
use
in such
a
way
that
the
metal
frame lies in the
plane
of the meridian. If
a
current
is passed
around the metal
ring,
then
two
forces
act
on
each
pole
of the needle.
1) the
horizontal
component
H
of
the terrestrial
magnetic
force
in the direction of the meridian
2)
perpendicularly
to
the
latter,
the
magnetic
force of the
current circuit K, which is
proportional
to the current I, i.e.,
equals
I.K
(a constant value for the instrument).
[Fig.]
The
diagonal
of the force
parallelogram
represents the
magnitude
and direction of
the
resulting magnetic
force. Hence the needle will
assume
its
direction.
If
we
denote
by
Y
the
angle
of deflection
(the
angle
between the
needle
and the
magnetic meridian),
then
it follows
directly
from the diagram
tang
r
=
magnetic
force of the current
terrestrial
magnetic
force =
Ik
H
A
second measurement
yields
an
analogous
equation:
tang
r
'
=
.....
I '
k
H
Division
yields
tang
?
tang
?'
I
.
7
Thus the currents
are
proportional
to the tangents of the
angles
of
deflection.
The
magnitudes
of the
magnetic
forces of the earth and of the
needle do not affect this kind of
relative
measurement
(the
magnitude
of the needle's
magnetic
force has been taken to be
equal
to 1,
because it does not affect the
magnitude
of
deflection,
since it would
have only furnished
a
proportionality factor to both magnetic force
19

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Page 15483. MILEVA MARIC TO HELENE SAVIC, WITH A POSTSCRIPT BY EINSTEIN click to expand contents

Page 193138. PAULINE EINSTEIN TO PAULINE WINTELER click to expand contents

Page 194139. TO CONRAD HABICHT click to expand contents

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