Previous Section	Projection Formula Table of Contents	Next Section

3.4.4.3 Cassini-Soldner

The Cassini-Soldner projection is the ellipsoidal version of the Cassini projection for the sphere. It is not conformal but as it is relatively simple to construct it was extensively used in the last century and is still useful for mapping areas with limited longitudinal extent. It has now largely been replaced by the conformal Transverse Mercator which it resembles. Like this, it has a straight central meridian along which the scale is true, all other meridians and parallels are curved, and the scale distortion increases rapidly with increasing distance from the central meridian.

The formulas to derive projected Easting and Northing coordinates are:

Easting:

Northing:

where

and M, the distance along the meridian from equator to latitude j, is given by:

with j in radians.

M₀ is the value of M calculated for the latitude of the chosen origin. This may not necessarily be chosen as the equator.

To compute latitude and longitude from Easting and Northing the reverse formulas are:

where r₁ is r calculated at j = j₁, and j₁ is the latitude of the point on the central meridian which has the same Northing as the point whose coordinates are sought, and is found from:

where:

Example:

For Projected Coordinate System Trinidad 1903 / Trinidad Grid

Parameters:

Note that the semimajor axis is given in links (Clarke's ratio). This will also be true of the False Easting and False Northing below. The final Easting and Northing values are also in this unit.

Forward calculation for:

gives the following easting and northing:

Reverse the calculations. Use the same parameters and use the E and N values to calculate the latitude and longitude:

Then

Previous Section	Projection Formula Table of Contents	Next Section

¹Value corrected from 1.0704468608 to 1.070468608 in 2006-01