Geography Reference
In-Depth Information
A comparison of the coecients of the two polynomials
Δx
(
Δα
)and
Δy
(
Δα
)
constitutes the fifth step:
Δx
(meta-equator)
⇒
Δα
:
q
1
b
1
α
1
+
l
1
β
1
=
s
1
.
(16.67)
Δα
2
:(
q
1
b
2
+
q
2
b
1
)
α
1
+
l
2
β
1
+(
q
1
b
1
−
l
1
)
α
2
+2
q
1
b
1
l
1
β
2
=
s
2
.
Δy
(meta-equator)
⇒
Δα
:
−l
1
α
1
+
q
1
b
1
β
1
=0
,
Δα
2
:
l
2
α
1
+(
q
1
b
2
+
q
2
b
1
)
β
1
2
q
1
b
1
l
1
α
2
+(
q
1
b
1
−
l
1
)
β
2
=0
.
−
−
(16.68)
A matrix version of the above equations is
⎡
⎤
⎡
⎤
⎡
⎤
q
1
b
1
l
1
α
1
β
1
α
2
β
2
s
1
s
2
0
0
0
0
⎣
⎦
⎣
⎦
⎣
⎦
q
1
b
2
+
q
2
b
1
l
2
q
1
b
1
− l
1
2
q
1
b
1
l
1
=
.
(16.69)
−l
1
q
1
b
1
0
0
−
l
2
q
1
b
2
+
q
1
b
1
−
2
q
1
b
1
l
1
q
1
b
1
−
l
1
1st row, 3rd row
⇒
q
1
b
1
α
1
+
l
1
β
1
=
s
1
,
−
l
1
α
1
+
q
1
b
1
β
1
=0
⇒
(
q
1
b
1
l
−
1
+
l
1
)
β
1
=
s
1
,α
1
=
q
1
b
1
l
−
1
β
1
(16.70)
⇒
β
1
=
l
1
s
1
(
q
1
b
1
+
l
1
)
−
1
,
α
1
=
q
1
b
1
s
1
(
q
1
b
1
+
l
1
)
−
1
.
2nd row, 3rd row
⇒
(
q
1
b
2
+
q
2
b
1
)
α
1
+
l
2
β
1
+(
q
1
b
1
−
l
1
)
α
2
−
2
q
1
b
1
l
1
β
2
=
s
2
,
l
2
α
1
+(
q
1
b
2
+
q
2
b
1
)
β
1
2
q
1
b
1
l
1
α
2
+(
q
1
b
1
−
l
1
)
β
2
=0
−
−
⇒
(
q
1
b
2
+
q
2
b
1
)
q
1
b
1
s
1
(
q
1
b
1
+
l
1
)
−
1
+
l
2
l
1
s
1
(
q
1
b
1
+
l
1
)
−
1
−
s
1
=
(16.71)
=(
l
1
−
q
1
b
1
)
α
2
−
2
q
1
b
1
l
1
β
2
,
(
q
1
b
2
+
q
2
b
1
)
l
1
s
1
(
q
1
b
1
+
l
1
)
−
1
− l
2
q
1
b
1
s
1
(
q
1
b
1
+
l
1
)
−
1
=
=2
q
1
b
1
l
1
α
2
+(
l
1
−
q
1
b
1
)
β
2
,
q
1
b
1
−
α
2
β
2
=
l
1
2
q
1
b
1
l
1
2
q
1
b
1
l
1
q
1
b
1
−
l
1
−
=
s
2
(
q
1
b
1
+
l
1
)
−
1
l
1
l
2
s
1
(
q
1
b
2
+
q
2
b
1
)(
q
1
b
1
+
l
1
)
−
1
q
1
b
1
s
1
−
−
(
q
1
b
1
+
l
1
)
−
1
l
2
q
1
b
1
s
1
(
q
1
b
1
+
l
1
)
−
1
(
q
1
b
2
+
q
2
b
1
)
l
1
s
1
−
⇒
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