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
+y2r2+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