An equal-area map projection mapping all parallels of latitude into truly-spaced, parallel, straight lines along which exact scale is preserved. The equator is used as the standard parallel of latitude. The sinusoidal map-projection is also known as Mercator's equal area map projection and the Sanson-Flamsteed map projection. It was used in the Mercator-Hondius atlases as early as 1606 and may for this reason be called the Mercator-Sanson map-projection. It is improperly referred to as Flamsteed's map projection, modified Flamsteed's map-projection and Sanson's map-projection. It is a variant of the Bonne map-projection in that the equator is used as standard parallel of latitude, and a refinement of the Plate Carree map-projection in that the x-coordinates are corrected for convergence of the meridians. It is defined for the mapping of the sphere onto the plane by the formulas x = k R ₁ Δλ cosφ and y = k R ₂ φwhich x and y are the rectangular, Cartesian coordinates of that point, in the plane, which corresponds to the point, on the sphere, at longitude λ _o + Δλ and latitude φ; λ _o is the longitude of the central meridian. R ₁ and R ₂ are the radii of curvature along the parallel of latitude and along the meridian, respectively, and k is the scale factor. The corresponding formulae for transformation from the rotational ellipsoid to the plane are obtained by substituting N, the radius of curvature in the prime vertical, for R ₁ and s, the length of arc corresponding to φ, for R ₂ φ.