Longitude Act passed in July 1714. For details on many of the efforts towards determining the longitude, see History of longitude. The Longitude Act offered a series of rewards, rather than a single prize. The rewards increased with the accuracy achieved: £10,000 (worth over in ) for anyone who could find a practical way of determining longitude at sea to an accuracy of not greater than one degree of longitude (equates to at the equator). The reward was to be increased to £15,000 if the accuracy was not greater than 40 minutes, and further enhanced to £20,000 if the accuracy was not
Lambert cylindrical equal-area projection as, "Notes and Comments on the Composition of Terrestrial and Celestial Maps". Lambert's projection is the basis for the cylindrical equal-area projection family. Lambert chose the equator as the parallel of no distortion. By multiplying the projection's height by some factor and dividing the width by the same factor, the regions of no distortion can be moved to any desired pair of parallels north and south of the equator. These variations, particularly the Gall–Peters projection, are more commonly encountered in maps than Lambert’s original projection due to their lower distortion overall. where "φ" is the latitude, "λ" is the longitude