plane is described by the formula where H is the height of the style above the plane, and t is the time (in hours) before or after the center-time for the polar dial. The center time is the time when the style's shadow falls directly down on the plane; for an East-facing dial, the center time will be 6am, for a West-facing dial, this will be 6pm, and for the inclined dial described above, it will be noon. When t approaches ±6 hours away from the center time, the spacing X diverges to +∞; this occurs when the Sun's rays become parallel to the plane. Vertical declining dials A declining dial is any non-horizontal, planar dial that does not face in a cardinal direction, such as (true) North, South, East or West. As usual, the gnomon's style is aligned with the Earth's rotational axis, but the hour-lines are not symmetrical about the noon hour-line. For a vertical dial, the angle between the noon hour-line and another hour-line is given by the formula below. Note that is defined positive in the clockwise sense w.r.t. the upper vertical hour angle; and that its conversion to the equivalent solar hour requires careful consideration of which quadrant of the sundial that it belongs in. where is the sundial's geographical latitude; t is the time before or after noon; is the angle of declination from true south, defined as positive when east of south; and is a switch integer for the dial orientation. A partly south-facing dial has an value of + 1; those partly north-facing, a value of -1. When such a dial faces South (), this formula reduces to the formula given above for vertical south-facing dials, i.e. When a sundial is not aligned with a cardinal direction, the substyle of its gnomon is not aligned with the noon hour-line. The angle between the substyle and the noon hour-line is given by the formula If a vertical sundial faces true South or North ( or , respectively), the angle and the substyle is aligned with the noon hour-line. The height of the gnomon, that is the angle the style makes to the plate, , is given by : Reclining dials The sundials described above have gnomons that are aligned with the Earth's rotational axis and cast their shadow onto a plane. If the plane is neither vertical nor horizontal nor equatorial, the sundial