d.  Distortion of Lines.  Figure 3-7 shows a cross section of an ellipsoid and a cylinder of projection which is secant to the ellipsoid.  The cross section is made by passing a plane through the ellipsoid at the equator.  Line A'M'D' represents the surface of the cylinder.  Line AMD represents the projected portion of the ellipsoid surface.  M is the central meridian; M' is the projection of the central meridian onto the cylinder.  A and D are the meridians located three degrees from the central meridian; A' and D' are the projections of those meridians onto the cylinder.  B and C are the points where the cylinder intersect the ellipsoid creating the secant condition.  Note that line BM'C is shorter than line BMC; this shows that any line which lies between the lines of secancy is shorter on its projected plane (map) than it is on the ellipsoid surface.  Note also that lines A'B and CD' are longer than lines AB and CD respectively; this shows that any line which lies between the lines of secancy and the edges of the projection are longer on the projected plane than they are on the ellipsoid surface.   e.  Scale Factor.  For the Transverse Mercator Projection, the scale factor at the lines of secancy is Unity (1.000 or Exact).  The scale factor decreases toward the Central Meridian to 0.9996; the scale factor increases toward the zone limits to approximately 1.001 at the equator.  See Figure 3-7.  Table 3-1 lists the scale factors of the Transverse Mercator Projection as applied to the UTM grid system. DRAFT 3-6 Figure 3-9  Line Distortion and Scale Factor in the Gauss-Kruger Projection 3° 3° A' A M Scale Factor: 1.0   TANGENT POINT