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specifically the functions F
1
and F
2
of (
6.1
), i.e., to establish the functional
relationship between the plane coordinates (x, y) and the geodetic coordinates
(L, B). Since the geodetic latitude B is related to q, the projection problem is to
establish the functional relationship between (x, y) and (L, q). The geodetic longi-
tude L of a point is referenced to the initial geodetic meridian. If another meridian
L
0
is instead referred to rather than the initial geodetic meridian, then L should be
transformed into the longitude difference l, where l
dL.
Therefore, establishing the relationship between (x, y) and (L, q) will be changed
into that between (x, y) and (l, q). We assume their relationship is:
ﾼ
L
L
0
, and dl
ﾼ
x
ﾼ
f
1
q
ðÞ
;
l
:
ð
6
:
7
Þ
y
ﾼ
f
2
q
ðÞ
;
l
The total differential of the above equation gives:
9
=
ﾼ
∂
x
þ
∂
x
dx
q
dq
l
dl
∂
∂
:
ﾼ
∂
y
þ
∂
y
;
dy
q
dq
l
dl
∂
∂
Substituting the above equations into (
6.5
) yields:
2
3
2
3
2
2
ﾼ
∂
x
þ
∂
x
∂
þ
∂
y
þ
∂
y
4
5
4
5
ds
2
q
dq
l
dl
q
dq
l
dl
∂
∂
∂
0
1
0
1
0
1
0
1
"
#
2
"
#
dq
"
#
2
2
2
2
dq
2
dl
2
∂
x
∂
y
∂
q
∂
x
x
l
þ
∂
q
∂
y
y
∂
x
∂
∂
y
∂
@
A
@
A
@
A
@
A
ﾼ
þ
þ
dl
þ
þ
:
∂
q
∂
q
∂
∂
∂
∂
l
l
l
With
9
=
0
@
1
A
0
@
1
A
2
2
∂
x
∂
y
E
ﾼ
þ
∂
q
∂
q
ﾼ
∂
x
q
∂
x
l
þ
∂
y
q
∂
y
F
,
ð
6
:
8
Þ
∂
∂
∂
∂
l
;
0
1
0
1
2
2
∂
x
∂
y
∂
@
A
@
A
G
ﾼ
þ
∂
l
l
we obtain:
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