is said to be reclining or inclining. Such a sundial might be located on a South-facing roof, for example. The hour-lines for such a sundial can be calculated by slightly correcting the horizontal formula above where is the desired angle of reclining relative to the local vertical, L is the sundial's geographical latitude, is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and t is the number of hours before or after noon. For example, the angle of the 3pm hour-line would equal the arctangent of cos(L + R), since tan 45° = 1. When R equals 0° (in other words, a South-facing vertical dial), we obtain the vertical dial formula above. Some authors use a more specific nomenclature to describe the orientation of the shadow-receiving plane. If the plane's face points downwards towards the ground, it is said to be proclining or inclining, whereas a dial is said to be reclining when the dial face is pointing away from the ground. Many authors also often refer to reclined, proclined and inclined sundials in general as inclined sundials. It is also common in the latter case to measure the angle of inclination relative to the horizontal plane on the sun side of the dial. In such texts, since I = 90° + R, the hour angle formula will often be seen written as : The angle between the gnomon style and the dial plate, B, in this type of sundial is : Or : Declining-reclining dials/ Declining-inclining dials Some sundials both decline and recline, in that their shadow-receiving plane is not oriented with a cardinal direction (such as true North or true South) and is neither horizontal nor vertical nor equatorial. For example, such a sundial might be found on a roof that was not oriented in a cardinal direction. The formulae describing the spacing of the hour-lines on such dials are rather more complicated than those for simpler dials. There are various solution approaches, including some using the methods of rotation matrices, and some making a 3D model of the reclined-declined plane and its vertical declined counterpart plane, extracting the geometrical relationships between the hour angle components on both these planes and then reducing the trigonometric algebra. One system of formulas for Reclining-Declining sundials: (as stated by Fennewick) The angle between the noon hour-line and another hour-line is given