Editing Equation of time (section)

==== Continuity ====

For the choice of the appropriate branch of the {{math|arctan}} relation with respect to function continuity a modified version of the arctangent function is helpful. It brings in previous knowledge about the expected value by a parameter. The modified arctangent function is defined as:
: <math>\arctan_\eta x = \arctan x + \pi\operatorname{round}{\left( \frac{\eta - \arctan x}{\pi} \right)}</math>.
It produces a value that is as close to {{math|''η''}} as possible. The function {{math|round}} rounds to the nearest integer.

Applying this yields:
: <math>\Delta t(M) = M + \lambda_p - \arctan_{M + \lambda_p} \left( \cos{\varepsilon}\tan{\lambda} \right)</math>.
The parameter {{math|''M'' + ''λ''<sub>p</sub>}} arranges here to set {{math|Δ''t''}} to the zero nearest value which is the desired one.