الفهرس 
AcknowledgementOnly 14 pages are availabe for public view
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Abstract
Traditionally, we consider map projections• to be concerned with the transformation of a mapping the earth, conveniently assumed to be an ellipsoid.Recent geodetic advances, including satellite observations and gravimetric and astrogeodeticmeasurements, have shown that the earth is better represented by a triaxial ellipsoid. The triaxiality of the earth is attributed to mass anomalies in the earth’s intcrior.The exploration of other bodie~ in the solar systcm has shown that the biaxial ellipsoid does not fit these bodies satisfactorily. Recent geodeticadvances, including satelliteobservations and measurements of gravity field have shown that although these worlds are irregular, the triaxial ellipsoid is an acceptable approximation of their figures.
Since a conformal representation is necessary for precise mapping at large-scale, and since the Transverse Mercator l1r0jection is by far the most convenient, this thesis addresses the mathematical formulation of this projection for the triaxial ellipsoid.
The difficulties of the con formal representation of the triaxial ellipsoid anse from the following:
1- the eccentricity of the meridian varies with longitude;
2- the horizontal plane sections are ellipses; consequently, the geographic and the geocentric latitudes change from one point to another on the same horizontal section;
3- the angles at which meridians cut horizontal plane sections are not generally right angles; 4- the length of an arc of meridian varies with longitude as well as with latitude; and
5- the normal to the surface through any P9.int is not generally normal to the meridian in its plane.
To tackle these problems, the following set of curvilinear parameters is used: one of which is the familiar longitude A and the other is the polar coordinate X of the normal to the meridian in its plane. Points of equal polar coordinate fall on the envelope of the sections at