448
For modification of the functions to achieve an integration instead of s or θ by
(22.3) and (22.5), the following calculation is used to determine the accuracy:
d
dx
r
m c
E
n
s
de
m c
E
τ
π
ϕ
abs
=






∈
∈
( )
∈
( )
 
 
∞
−
∫
0
2
2 4 2
2
0
2 4
,
(22.20)
in which
ϕ
σ
σ
σ
π
s
s s ds
s
s
r
s
0
1
0
2
0
2
∈
( )
 
  =
( )
( ) =
( )
∈
( )
∫
,
(22.21)
The outcome appeared as a dimension variable ϕ in combination with dimensionless cross section σ . To calculate the variable ϕ [s 0 ] a detailed graphical frame
for 1 < s 0  < 10 was employed. Reliability of the functional asymptotic calculation
for ϕ was essential so s 0  – 1 ≪ 1 and s 0  ≫ 1 this is expressed as
ϕ
β
β
ω β ω
ω
β
β
β
ω
ω
s 0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
1
4
1
2
4
[ ]=
+
−
−
−
− −
+
+
+
ln
ln
ln
ln ln
1 1
0
(
) ( )
–
,
L ω
in which
β
ω
β
β
0
2
0
0
0
0
1 1
1
1
=
−
=
+
(
)
−
(
)
s
,
(22.22)
L
d
ω
ω
ω
ω
ω
0
1
1
0
1
( )=
+
(
)
∫
− ln
.
The final integral can appropriately be written as
ω
ω ω
ω
ω
ω
+
(
)=
+






( )=
+ ( )
′
1
1 1
1
2
0
2
0
0
,
l n
,
L
L
with
′ ( )=
+






=
−
−
( )
∫
∑
−
=
∞
− −
−
L
d
n n
n
n
ω
ω
ω
ω
π
ω
ω
0
1
1
2
1
1
2
0
0
1
1
12
1
ln
,
.
(22.23)
The ultimate expression of the water pulled down through the use of the static
electricity force may easily be shown through implementation of the calculations of
22 Global Environmental Equilibrium