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