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The first postulate:
Δ =0: r = f (0) = 0
1
1
=0
A 1 (1
E 2 )
2 E ln 1+ E
1
f (0) = c 2
E 2 +
n
1
E
1+ 1
1+ 1
1 / 2
c 2 = A 1
n
E 2
2 E
E 2
2 E
ln 1+ E
1
c = A 1
ln 1+ E
1
n
(19.40)
E
E
1
ln 1+ E
1
1 / 2
f ( Δ )= A 1
(1 E 2 )cos Δ
1
E 2 cos 2 Δ + 1 E 2
ln 1+ E cos Δ
1
n
E
.
2 E
E cos Δ
A first form of the mapping equations is given by
=
1 −E sin Φ 1 / 2 .
α
r
n 1
2 E ln 1+ E
(19.41)
(1 E 2 )sin Φ
1
E 2 sin 2 Φ + 1 E 2
A 1
ln 1+ E sin Φ
1 −E
The second postulate:
Δ 1 = π
A 1 sin Δ 1
(1 − E 2 cos 2 Δ 1 ) 1 / 2 = f ( Δ 1 ) n
sin Δ 1
2
Φ 1 :
E 2 cos 2 Δ 1 ) 1 / 2 =
(19.42)
(1
= n 1
ln 1+ E
1 / 2
E 2 )cos Δ 1
E 2
2 E
(1
1 − E 2 cos 2 Δ 1 + 1
ln 1+ E cos Δ 1
1 − E cos Δ 1
1 − E
sin 2 Δ 1
1
1 − E 2 cos 2 Δ 1
ln 1+ E
1 −E
.
n =
(19.43)
(1 E 2 )cos Δ 1
1 −E 2 cos 2 Δ 1
+ 1 E 2
2 E
ln 1+ E cos Δ 1
1 −E cos Δ 1
1
19-233 Equiareal Mapping: The Variant of an Equidistant and Conformal Mapping
on Two Parallel Circles (Albers Equal Area Conic Mapping)
In contrast, we here use the two postulates of equidistant mapping on two parallel circles Φ 1 and
Φ 2 . We finally arrive at the relations ( 19.46 )-( 19.49 ).
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