108
MOLECULAR
DIMENSIONS
[11]
(4)
||
=
Ma
{,
=
M»
^
5:
=
Aw,
3?
+
^
+
"
7?
=
0
where
A
denotes the
operator
S2
+
S2
S2
and
p
the
hydrostatic
pressure.
Since
equations
(1) are
solutions
of
equations
(4)
and
the latter
are
linear,
according to
(3)
the quantities
u1, v1, w1
must
also satisfy
equations
(4).
I
determined
u1, v1, w1
and
p by
a
method
given
in
§4
of
the Kirchhoff lectures
mentioned
above1
and found
[12] 1"From equations
(4)
it
follows that
hp
=
0.
If
we
take
p
in
keeping
with
this condition
and determine
a
function
V
that
satisfies
the
equation
AV
=
1\k
p,
then
equations
(4)
are
satisfied if
one
puts
a
-
11
+ a1
w
~
7%
sr
+
,
and
chooses
u', v',
w'
such
that
Au'
=
0, Av'
=
0,
Aw'
=
0,
and
[13]
Now,
if
one
puts
Su'
.
Sv]
,
Sw]
Ip-"
www
6^-
=
2c
8{2
and
in accordance with
this
[14]
6*-
P
+
«
£2
t]2
H
~~ 2
2
u]
=
-2c
v]
=
0,
w]
=
0,
w
[15]
and
then the
constants a,
b,
c can
be
determined
such
that
u
=
v
=
w
=
0
for
p
=
P.
By
superposing
three
such
solutions,
we
get
the solution
given
in
equations
(5)
and (5a).