by the formula below. Note that advances counterclockwise with respect to the zero hour angle for those dials that are partly south-facing and clockwise for those that are north-facing. within the parameter ranges : and . Or, if preferring to use inclination angle, , rather than the reclination, , where : within the parameter ranges : and . Here is the sundial's geographical latitude; is the orientation switch integer; t is the time in hours before or after noon; and and are the angles of reclination and declination, respectively. Note that is measured with reference to the vertical. It is positive when the dial leans back towards the horizon behind the dial and negative when the dial leans forward to the horizon on the Sun's side. Declination angle is defined as positive when moving east of true south. Dials facing fully or partly south have = +1, while those partly or fully north-facing have an value of -1. Since the above expression gives the hour angle as an arctan function, due consideration must be given to which quadrant of the sundial each hour belongs to before assigning the correct hour angle. Unlike the simpler vertical declining sundial, this type of dial does not always show hour angles on its sunside face for all declinations between east and west. When a northern hemisphere partly south-facing dial reclines back (i.e. away from the Sun) from the vertical, the gnomon will become co-planar with the dial plate at declinations less than due east or due west. Likewise for southern hemisphere dials that are partly north-facing. Were these dials reclining forward, the range of declination would actually exceed due east and due west. In a similar way, northern hemisphere dials that are partly north-facing and southern hemisphere dials that are south-facing, and which lean forward toward their upward pointing gnomons, will have a similar restriction on the range of declination that is possible for a given reclination value. The critical declination is a geometrical constraint which depends on the value of both the dial's reclination and its latitude : As with the vertical declined dial, the gnomon's substyle is not aligned with the noon hour-line. The general formula for the angle , between the substyle and the noon-line is given by : The angle , between the style and the plate is given by : Note that for , i.e. when the gnomon is