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+ y 02 Y
y 00 2
+ y 30 X
x 00 3
+ y 21 X
x 00 2 Y
y 00 +
ρ
ρ
ρ
ρ
y 00 3 +
+ y 12 X
x 00 Y
y 00 2
+ y 03 Y
ρ
ρ
ρ
+O(4) .
Box 21.29 (The polynomial coecients, the East components, namely x MN , the datum trans-
formation of conformal coordinates).
x 00 = δL
a 1 cos b 0 sin 2 b 0
2(1 − e 2 sin 2 b 0 ) 3 / 2
a 1 cos b 0
(1 − e 2 sin 2 b 0 ) 1 / 2 + δE 2 δL
(1 − e 2 sin 2 b 0 ) 3 / 2 A 1
e 2 )sin b 0
δLδB a 1 (1
a 1 ,
x 10 = 1 − δE 2
a 1
sin 2 b 0
e 2 sin 2 b 0 ) + δB (1 e 2 )tan b 0
A 1 ,
e 2 sin 2 b 0 )
2(1
(1
x 01 =[ δL sin b 0 ] a 1
A 1 ,
x 20 =
a 1
A 1
2
−δL cos b 0 (1 e 2 sin 2 b 0 ) 3 / 2
2 a 1 (1
,
(21.87)
e 2 )
x 02 + δL cos b 0 (1
a 1
A 1
2
e 2 sin 2 b 0 ) 3 / 2
2 a 1 (1 − e 2 )
,
x 11 = δB 1+ e 2 sin 2 b 0 2 e 2 sin 4 b 0
a 1 cos 2 b 0 (1
e 2 sin 2 b 0 ) 1 / 2
cos b 0 sin b 0
e 2 sin 2 b 0 ) 1 / 2 − δE 2
a 1 (1
e 2 )(1
a 1
A 1
2
.
x 30 = δB tan b 0 [1 + 3 e 2
sin 2 b 0 (4 + 11 e 2
3 e 4 )+2 e 2 sin 4 b 0 (7
e 2 )
4 e 4 sin 6 b 0 ]
6 a 1 (1
e 2 )cos 2 b 0
a 1
A 1
3
−δE 2 1 2sin 2 b 0 (2 e 2 )+ e 2 sin 4 b 0
6 a 1 (1
,
e 2 ) 2
x 21 = + δL sin b 0 (1
a 1
A 1
3
e 2 sin 2 b 0 ) 2 (1 + 3 e 2
4 e 2 sin 2 b 0 )
,
(21.88)
2 a 1 (1
e 2 ) 2
x 12 = δB tan b 0 [2 + 3 e 2
− e 2 sin 2 b 0 (11 + e 2 )+ e 2 sin 4 b 0 (4 + 5 e 2 ) 2 e 4 sin 6 b 0 ]
2 a 1 (1
e 2 )cos 2 b 0
a 1
A 1
3
2sin 2 b 0 + e 2 sin 4 b 0
2 a 1 (1 − e 2 ) 2
δE 2 1
,
x 03 =
a 1
A 1
3
e 2 sin 2 b 0 ) 2 (1 + 3 e 2
4 e 2 sin 2 b 0 )
δL sin b 0 (1
.
6 a 1 (1
e 2 ) 2
 
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