Geography Reference
In-Depth Information
arcsin(tanh )
sin 2
q
(56)
X
a j
j
j
sin 4
j
sin 6
j
sin 8
j
sin 10
0
2
4
6
8
10
where
1
3
5
175
441
2
4
6
8
10
j
1
e
e
e
e
e
0
4
64
256
16384
65536
1
1
9
901
16381
2
4
6
8
10
j
e
e
e
e
e
2
8
96
1024
184320
5898240
13
17
311
18931
4
6
8
10
j
e
e
e
e
4
768
5120
737280
20643840
(57)
61
899
14977
6
8
10
j
e
e
e
6
15360
430080
27525120
49561
41287680
175087
165150720
8
10
j
e
e
8
34729
82575360
10
j
e
10
4.2. The direct expansions of transformations between meridian arc and authalic
latitude function
4.2.1. The direct expansion of the transformation from meridian arc to authalic latitude
function
The whole formulas for the transformation from meridian arc to authalic latitude function
are as follows:
X
ae
2
(1
)
sin 2
K
0
B
a
a
sin 4
a
sin 6
a
sin 8
a
sin 10
(58)
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
FR
sin
Expanding
F
as a power series of the eccentricity
e
at
e
by means of Mathematica
yields the direct expansion of the transformation from meridian arc to authalic latitude
function
0
X
ae
2
(1
)
sin
K
(59)
0
2
Fa
sin 3
sin 5
sin 7
sin 9
sin11
1
3
5
7
9
11
where
