Geography Reference
In-Depth Information
5
17
121
137
1407
2
4
6
8
10

1
e
e
e
e
e
1
16
256
4096
8192
131072
1
1
103
1775
2
4
8
10
e
e
e
e
3
48
384
196608
3145728
3
43
17
467
4
6
8
10
e
e
e
e
5
1280
30720
24576
1572864
(60)
37
5
563
6
8
10
e
e
e
7
86016
10752
1572864
59
1853
8
10
e
e
9
589824
11796480
1543
57671680 e
10
11
4.2.2. The direct expansion of the transformation from authalic latitude function to
meridian arc
The whole formulas for the transformation from authalic latitude function to meridian arc are
as follows:
F
R
arcsin(
)
2
B

c
sin 2
c
sin 4
c
sin 6
c
sin 8
c
sin 10
(61)
 
2
4
6
8
10
B
sin 2
B
sin 4
B
sin 6
B
sin 8
B
sin 10
B
2
4
6
8
10
 
2
Xa
(1
eK
)
0
Expanding X as a power series of the eccentricity e at
e  by means of Mathematica yields
the direct expansion of the transformation from authalic latitude function to meridian arc
0
F
R
arcsin(
)
2
(62)
X
a k
k
sin 2
k
sin 4
k
sin 6
k
sin 8
k
sin 10
0
2
4
6
8
10
where
1
3
5
175
441
2
4
6
8
10
k
 
1
e
e
e
e
e
0
4
64
256
16384
65536
1
7
61
2719
30578453
2
4
6
8
10
k

e
e
e
e
e
2
24
1440
107520
8294400
61312204800
29
1411
180269
4110829
4
6
8
10
k

e
e
e
e
4
11520
967680
232243200
10218700800
(63)
1003
341
36598301
6
8
10
k

e
e
e
6

2903040
921
600
122624409600
40457
3602683
8
10
k
e
e
8
619315200
35035545600
1800439
122624409600
10
k

e
10
 
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