Table 3-1    TM Scale Factor By UTM Easting     3-7  Gauss-Kruger Projection a.  General.  The Gauss-Kruger Projection can be described as the Transverse Mercator Projection derived by mapping directly from an ellipsoid which is tangent to the cylinder.  See Figure 3-8.  It is a conformal projection with many similarities to the Transverse Mercator Projection.  The tangent point is the meridian of longitude chosen as the Central Meridian for the projection.  As with Transverse Mercator, the Gauss-Kruger Projection depicts 60 zones and area distortion is the same as described in paragraph 3-6b above.  Many geodesists consider the Gauss-Kruger and Transverse Mercator Projections to be the same, except for scale factor.    Figure 3-8  Gauss-Kruger Projection b.  Distortion of Lines.  When a meridian is tangent to a cylinder of projection, there is no distortion along that line.  Figure 3-9 shows that all lines which are not located on the central meridian are longer on the projected surface than they are on the ellipsoid.  For example, line A'M is longer than line AM when A represents the meridian located three degrees from the central meridian, A' is the projection of that meridian onto a cylinder, and M is the central meridian (tangent point). c.  Scale Factor.  For the Gauss-Kruger Projection, the scale factor at the central meridian is Unity (1.000 or Exact).  The factor increases outward toward the zone limits in excess of 1.004 at the equator. 3-8  Polar Stereographic Projection a.  General.  The Polar Stereographic Projection is used for mapping the earth's polar regions and identifies those regions as North and South zones.  The North zone extends from the North Pole to 83° 30' N latitude; the South zone extends from the South Pole to 79° 30' S latitude.  It is a conformal azimuthal projection which is developed by projecting a polar region onto a plane which is either tangent to an ellipsoid at the pole or secant to the ellipsoid at a specific latitude.  This text will discuss only the secant condition.  See Figure 3-10.  The plane is perpendicular to the polar axis of the ellipsoid and the origin of the projection is the opposite pole.  See Figure DRAFT 3-7