 The noon hour line points true North, whereas the hour lines for 6am and 6pm point due West and East, respectively; the ratio of the short to long axes equals the sine sin(Φ) of the local geographical latitude, denoted Φ.All the hour lines converge to a single centre; the angle θ of a given hour line with the noon hour is given by the formula

where "t" is the time (in hours) before or after noon.However, the vertical gnomon does not always stand at the centre of the hour lines; rather, to show the correct time, the gnomon must be moved daily northwards from the centre by the distance

where "W" is half the width of the ellipse and δ is the Sun's declination at that time of year.