Gauss and UTM Conformal Projections and the Plane Rectangular Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 270

9
=

0
@

1
A

0
@

1
A

2 2

∂ x ∂ y

þ

∂ q ∂ q

E
r 2 ﾼ

m 2 ﾼ ,

r 2

0 1 0 1 ð 6 : 16 Þ

2 2

;

∂ x ∂ y

∂

@ A @ A

þ

∂ l l

G
r 2 ﾼ

m 2

or ﾼ :

r 2

These two formulae are equivalent, only of different form. We can choose either
of these two formulae based on convenience for derivations. These formulae will be
used to study the scale factor of the Gauss projection.

6.3 Fundamentals of the Gauss Projection

6.3.1 History and Development of the Gauss Projection

Gauss projection is the abbreviation for Gauss-Kr¨ger projection, also known as
the transverse cylindrical conformal projection, which is one of the conformal
mappings of the Earth ellipsoid onto a plane. The Gauss projection was first
credited to Carl Friedrich Gauss, a German mathematician, physicist, astronomer,
and geodesist. During the period 1820-1830, when Gauss dealt with the triangula-
tion results in Hannover, Germany, he used the ellipsoidal transverse Mercator
projection that had a constant scale along the central meridian, which was a subject
of his own investigations. However, he did not publish or release the results. The
concluding formula for such a projection was found in the letters he wrote to his
friends.
This projection was adapted by Oskar Schreiber in his topic Theory of Projection
Methods of Hannover Land Surveying (Theorie der Projektionsmethode der
hannoverschen Landsvermessung) published in 1866 (Schreiber 1866) and thus
brought the theory of the Gauss projection to the attention of the public.
A more detailed elaboration on the theory of Gauss projection and the practical
formulae was provided by the German geodesist Louis Kr ¨ ger in his Conformal
Mapping of the Earth Ellipsoid to the Plane (Konforme Abbildung des
Erdellipsoids in der Ebene) published in 1912 (Kr¨ger 1912). Kr¨ger thoroughly
studied and complemented the Gauss projection in this topic, which enabled such a
projection to be widely used in many countries. This projection was therefore called
the Gauss-Kr¨ger projection, more usually known as the Gauss projection.
To apply the Gauss projection conveniently, the German scholar Boaga in 1919
suggested adoption of projection zones 3 wide. Each zone is assigned a false