Geography Reference
In-Depth Information
For the same reason, we introduce the following new variable
t
sin
(36)
and then denote
2
2

dB
(1
e
sin
B
) cos
B
ft
()
(37)
2
d
(1
e
) cos
Using the same procedure as described in the former section, one arrives at
dB
1
2
4
6
8
10
B
sin
B
sin
B
sin
B
sin
B
sin
(38)
2
4
6
8
10
d
2
1
e
where
11
21
2
4
6
8
10
B

2
e
e
e
17
e
25
e
2
2
2
14
62
1369
3005
4
6
8
10
B
e
e
e
e
4
3
3
24
24
56
614
4909
(39)
6
8
10
B

e
e
e
6
5
9
20
8558
7367
8
10
B
e
e
8
315
35
4174
63
10
B

e
10
Integrating the both sides of (38) gives the inverse expansion of conformal latitude as
B

b
sin 2
b
sin 4
b
sin 6
b
sin 8
b
sin 10
(40)
2
4
6
8
10
where
1
5
1
13
3
2
4
6
8
10
b
   
e
e
e
e
e
2
2
24
12
360
160
7
29
811
81
4
6
8
10
b
e
e
e
e
4
48
240
11520
2240
7
81
3029
(41)
6
8
10
b
e
e
e
6
120
1120
53760
4279
883
8
10
b
e
e
8
161280
20160
2087
161280
10
b
e
10
3.1.3 The inverse expansion of the authalic latitude
Inserting (18) into (15) yields
 
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