Datum Problems - Map Projections: Cartographic Information Systems - page 534

Box 21.17 (Transformation of the coecients of a conformal series under a curvilinear datum
transformation, including the change of form parameter by δE 2 , transformation close to the
identity).

X 10 = A 1

a 1 ( x 10 + x 10e 2 δE 2 ) , X 12 = A 1 a 1 ( x 12 + x 12 ,e 2 δE 2 ) ,

X 11 = A 1

a 1 ( x 11 + x 11 ,e 2 δE 2 ) , X 30 = A 1 a 1 ( x 30 + x 30 ,e 2 δE 2 ) ,

(21.73)

y 00 + y 00 ,e 2 δE 2 + y 00 ,e 2 e 2 ,

( δE 2 ) 2
2

Y 00 = A 1

a 1

Y 01 = A 1

a 1 ( y 01 + y 01 2 δE 2 ) , Y 02 = A 1 a 1 ( y 02 + J 02 ,e 2 δE 2 ) ,

(21.74)

Y 20 = A 1

a 1 ( y 20 + y 20 ,e 2 δE 2 ) , Y 21 = A 1 a 1 ( y 21 + y 21 ,e 2 δE 2 ) ,

Y 03 = A 1

a 1 ( y 03 + y 03 ,e 2 δE 2 ) .

Box 21.18 (Transformation of the coecients of a conformal series under a curvilinear datum
transformation, including the change of form parameter by δE 2 , East components X MN ).

x 10 ,e 2 =

a 1 cos b 0 sin 2 b 0
2(1 e 2 sin 2 b 0 ) 3 / 2 ,

x 11 ,e 2 =
= a 1 sin b 0 (2 − 3sin 2 b 0 + e 2 sin 2 b 0 )
2(1

=

−

,

e 2 sin 2 b 0 ) 5 / 2 −

x 12 ,e 2 = (21.75)

9sin 2 b 0 +11 e 2 sin 2 b 0 6 e 2 sin 4 b 0 +2 e 4 sin 4 b 0 )

4(1 − e 2 sin 2 b 0 ) 7 / 2

= a 1 cos b 0 (2

− −

,

x 30 ,e 2 =
= a 1 cos b 0 (2 − 3sin 2 b 0 − 3 e 2 sin 2 b 0 +6 e 2 sin 4 b 0 − e 2 sin 6 b 0 − e 4 sin 6 b 0 )
12(1

.

e 2 sin 2 b 0 ) 3 / 2

− e 2 ) 2 (1 −

Box 21.19 (Transformation of the coecients of a conformal series under a curvilinear datum
transformation, including the change of form parameter by δE 2 , North components Y MN ).

y 00 ,e 2 =

a 1

4 ( b 0 + 3 2 sin 2 b 0 + 3

5

8 e 2 [ b 0 +2sin2 b 0 −

= −

4 sin 4 b 0 ]+