Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 238

Fig. 5.41 Reduced latitude u

9
=

1
W cos B

cos u ﾼ

p

1

: ð 5 : 74 Þ

e 2 ;

sin u ﾼ sin B

W

V

p

Introducing W ﾼ 1 e 2 , we get:

9
=

1
V

cos u ﾼ p cos B

1 e 2

: ð 5 : 75 Þ

1
V sin B

;

sin u ﾼ

Dividing the two equations in ( 5.74 )or( 5.75 ) by each other results in:

p

1

tan u ﾼ e 2 tan B : ð 5 : 76 Þ

Equation ( 5.76 ) is the formula for transformation between the reduced latitude
u and geodetic latitude B. It follows from ( 5.76 ) that the reduced latitude u and
geodetic latitude B of the same point have a specified corresponding relationship.
Generally, geodetic latitude is greater than the reduced latitude.
Taking the derivative of ( 5.76 ) results in the differential relations between u and
B as follows: