Geography Reference
In-Depth Information
Table 22.15
Polynomial representation series expansion:
y
(
q
)=
h
=0
γ
h
q
h
+
O
(
N
+1)
N
=5
E
2
B
0
0
γ
0
=
A
1
1
dB
−
(
Table
22.12
)
(22.91)
E
2
sin
2
B
)
3
/
2
(1
−
A
1
cos
B
0
A
1
cos
lam
−
1
Q
0
γ
1
=
√
1
=
1
(22.92)
−
E
2
sin
2
B
0
−
E
2
sin
2
lam
−
1
Q
0
A
1
cos
B
0
sin
B
0
2
√
1
γ
2
=
−
(22.93)
−
E
2
sin
2
B
0
A
1
cos
B
0
1
2
sin
2
B
0
+
E
2
sin
4
B
0
−
E
2
)
√
1
γ
3
=
−
(22.94)
6(1
−
−
E
2
sin
2
B
0
A
1
cosB
0
sin
B
0
6
sin
2
B
0
−
E
2
(1 + 6
sin
2
B
0
−
γ
4
=
E
2
)
√
1
[5
−
24 (1
−
−
2
sin
2
B
0
9
sin
4
B
0
)+
E
4
sin
4
B
0
3
4
sin
2
B
0
]
−
−
(22.95)
A
1
cos
B
0
5+28
sin
2
B
0
−
24
sin
4
B
0
+
γ
5
=
−
−
E
2
)
3
√
1
[
120 (1
−
−
E
2
sin
2
B
0
+
E
2
1+16
sin
2
B
0
−
86
sin
4
B
0
+72
sin
6
B
0
+
E
4
sin
4
B
0
(
26 + +100
sin
2
B
0
−
−
77
sin
4
B
0
)+
E
6
sin
6
B
0
12
39
sin
2
B
0
+28
sin
4
B
0
]
−
(22.96)
tion
”
y
(
b, l
) is given in Table
22.18
,Eq.(
22.114
), “
b
-representation” subject to the coecients
{
y
10
,y
20
,y
02
,y
30
,y
12
,y
40
,y
22
,y
04
,y
50
,y
32
,y
14
,
}
of Table
22.19
.
22-34 The Second Boundary Condition or the Arc Preserving
Mapping of the Reference Parallel
Up to now we only succeeded to determine the
Northern harmonic map y
=
η
(
q,l
)interms
of relative isometric coordinates (
q,l
)of
Mercator type
or
y
=
y
(
b, l
) in terms of relative
Gauss
ellipsoidal coordinates
(
b, l
). By means of the second boundary condition we shall be able to
determine the
Eastern harmonic map x
=
ξ
(
q,l
)
or x
=
x
(
b, l
): The parallel circle also called
“
small circle
” which passes the
Taylor point
(
Q
0
,L
0
)or(
B
0
,L
0
) will be mapped according to its
length (Table
22.20
).
Indeed by means of Table
22.10
,Eqs.(
22.127
)-(
22.129
), we have succeeded to compute such
an arc length of a small circle from
L
0
to L
, the solution of the second boundary value problem.
(i)
Δx
= 0 (region operator)
(ii)
x
(0
,l
)=
β
1
l
Search WWH ::
Custom Search