Editing Mercator projection (section)

==== On other parallels ====
On any other parallel the scale factor is sec ''φ'' so that
:Parallel distance = ruler distance × cos&nbsp;''φ'' / RF &nbsp;&nbsp;&nbsp; (parallel).

For the above model 1&nbsp;cm corresponds to 1,500&nbsp;km at a latitude of 60°.

This is not the shortest distance between the chosen endpoints on the parallel because a parallel is not a great circle. The difference is small for short distances but increases as ''λ'', the longitudinal separation, increases. For two points, A and B, separated by 10° of longitude on the parallel at 60° the distance along the parallel is approximately 0.5&nbsp;km greater than the great circle distance. (The distance AB along the parallel is (''a''&nbsp;cos&nbsp;''φ'')&nbsp;''λ''. The length of the chord AB is 2(''a''&nbsp;cos&nbsp;''φ'')&nbsp;sin&nbsp;{{sfrac|''λ''|2}}. This chord subtends an angle at the centre equal to 2arcsin(cos&nbsp;''φ''&nbsp;sin&nbsp;{{sfrac|''λ''|2}}) and the great circle distance between A and B is 2''a''&nbsp;arcsin(cos&nbsp;''φ''&nbsp;sin&nbsp;{{sfrac|''λ''|2}}).) In the extreme case where the longitudinal separation is 180°, the distance along the parallel is one half of the circumference of that parallel; i.e., 10,007.5&nbsp;km. On the other hand, the [[geodesic]] between these points is a great circle arc through the pole subtending an angle of 60° at the center: the length of this arc is one sixth of the great circle circumference, about 6,672&nbsp;km. The difference is 3,338&nbsp;km so the ruler distance measured from the map is quite misleading even after correcting for the latitude variation of the scale factor.