Editing Latitude (section)

===Rectifying latitude===
{{see also|Rectifying radius}}
The '''rectifying latitude''', {{mvar|μ}}, is the meridian distance scaled so that its value at the poles is equal to 90 degrees or {{sfrac|{{pi}}|2}} radians:
:<math>\mu(\phi) = \frac{\pi}{2}\frac{m(\phi)}{m_\mathrm{p}}</math>

where the meridian distance from the equator to a latitude {{mvar|ϕ}} is (see [[Meridian arc]])
:<math>m(\phi) = a\left(1 - e^2\right)\int_0^\phi \left(1 - e^2 \sin^2 \phi'\right)^{-\frac{3}{2}}\, d\phi'\,,</math>

and the length of the meridian quadrant from the equator to the pole (the [[Meridian arc#Polar distance|polar distance]]) is
:<math>m_\mathrm{p} = m\left(\frac{\pi}{2}\right)\,.</math>

Using the rectifying latitude to define a latitude on a sphere of radius
:<math>R = \frac{2m_\mathrm{p}}{\pi}</math>

defines a projection from the ellipsoid to the sphere such that all meridians have true length and uniform scale. The sphere may then be projected to the plane with an [[equirectangular projection]] to give a double projection from the ellipsoid to the plane such that all meridians have true length and uniform meridian scale. An example of the use of the rectifying latitude is the [[equidistant conic projection]]. (Snyder, Section 16).<ref name=snyder/> The rectifying latitude is also of great importance in the construction of the [[Transverse Mercator projection]].