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2
3
sin L
cos L
0
4
5
:
S
1
S
T
ᄐ
ᄐ
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
ᄐ
:
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
ᄐ
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
ᄐ
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
ᄐ
4
5
X
Y
Z
ð
N
þ
H
Þ
cos B sin L
B
ᄐ
:
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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