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2
3
sin L
cos L
0
4
5 :
S 1
S T
sin B cos L
sin B sin L cos B
ð
7
:
20
Þ
cos B cos L
cos BsibL sin B
Substituting ( 7.19 ) and ( 7.20 ) into ( 7.18 ) yields:
2
3
sin L
cos L
0
4
5
ð
N
þ
H
Þ
cos B
ð
N
þ
H
Þ
cos B
J 1
sin B cos L
M
sin B sin L
M
cos B
M
:
ð
7
:
21
Þ
þ
H
þ
H
þ
H
cos B cos L
cos B sin L
sin B
We insert the Bursa-Wolf model ( 7.13 ) into ( 7.16 ) to get:
2
4
3
5
2
4
3
5 þ
,
dL
dB
dH
J 1 Δ
X 0
J 1 A da
df
J 1 QB
J 1 mB
Δ
Y 0
þ
ð
7
:
22
Þ
Δ
Z 0
with
2
4
3
5 ,
0
ʵ Z
ʵ Y
Q
ʵ Z
0
ʵ X
ʵ Y
ʵ X
0
and
2
3
ð
N
þ
H
Þ
cos B cos L
2
4
3
5 old
4
5
X
Y
Z
ð
N
þ
H
Þ
cos B sin L
B
:
h
i sin B
e 2
N 1
ð
Þþ
H
In the above equation, L, B, and H are the old geodetic coordinates and the
subscripts “old” are all omitted. Rearranging the above equation gives:
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