The fact that the earth is not a true sphere must be taken into account if accurate measurements are to be made from maps. For mathematical calculations, an ellipsoid is used as a best estimate of the earth’s surface. This allows conversion between geographic latitude and longitude, and the X (eastings) and Y (northings) coordinates of the projection. Projections are calculated on the most appropriate ellipsoid for a local area. The same projection on different ellipsoids are not equivalent.
You must note the ellipsoid of your map. If your data is represented on different projection and ellipsoids, you can apply a corrective shift if the extent of the area is small, for example, the area covered by a 1:10 000 map sheet.
To do this, you need the geographic latitude and longitude for the same points on the different ellipsoids. The difference between the points is calculated and that difference applied as a shift to the points in the reference ellipsoid. Consult your local or national mapping agency if you do not have this information.
The oblateness of earth causes the degrees of latitude to change slightly from the equator to the poles. Making accurate maps demands the exact positioning of earth's features and this in turn requires the exact plotting of the meridians and parallels that form the framework upon which details are positioned. Exact lengths of degrees of latitude and longitude can only be stated after the true dimensions of the earth’s spheroid are agreed on. For purposes of mathematical calculations an ellipsoid represents the best estimate of the earth's surface. A number of ellipsoids are in use around the world.
Computations for each spheroid are based on the lengths of the semi-major axis of the ellipsoid (representing the radius of the equatorial circle) and the semi-minor axis (representing exactly one half of the polar axis) according to the formula
f=(a-b)/a where f represents oblateness or flattening at the pole.