Editing Transverse Mercator projection (section)

===Convergence===
[[File:Transverse mercator convergence.svg|right|thumb|upright|The angle of convergence]]

The convergence angle ''γ'' at a point on the projection is defined by the angle measured ''from'' the projected meridian, which defines true north, ''to'' a grid line of constant ''x'', defining grid north. Therefore, ''γ'' is positive in the quadrant north of the equator and east of the central meridian and also in the quadrant south of the equator and west of the central meridian. The convergence must be added to a grid bearing to obtain a bearing from true north. For the secant transverse Mercator the convergence may be expressed<ref name=merc/> either in terms of the geographical coordinates or in terms of the projection coordinates:
:<math>
\begin{align}
\gamma(\lambda,\varphi)&=\arctan(\tan\lambda\sin\varphi),\\[5px]
\gamma(x,y)&=\arctan\left(\tanh\frac{x}{k_0a}\tan\frac{y}{k_0a}\right).
\end{align}
</math>