coplanar with the dial plate, we have : i.e. when , the critical declination value. Empirical method Because of the complexity of the above calculations, using them for the practical purpose of designing a dial of this type is difficult and prone to error. It has been suggested that it is better to locate the hour lines empirically, marking the positions of the shadow of a style on a real sundial at hourly intervals as shown by a clock and adding/deducting that day's equation of time adjustment. See Empirical hour-line marking, above. Spherical sundials The surface receiving the shadow need not be a plane, but can have any shape, provided that the sundial maker is willing to mark the hour-lines. If the style is aligned with the Earth's rotational axis, a spherical shape is convenient since the hour-lines are equally spaced, as they are on the equatorial dial shown here; the sundial is equiangular. This is the principle behind the armillary sphere and the equatorial bow sundial. However, some equiangular sundials—such as the Lambert dial described below—are based on other principles. In the equatorial bow sundial, the gnomon is a bar, slot or stretched wire parallel to the celestial axis. The face is a semicircle, corresponding to the equator of the sphere, with markings on the inner surface. This pattern, built a couple of meters wide out of temperature-invariant steel invar, was used to keep the trains running on time in France before World War I. Among the most precise sundials ever made are two equatorial bows constructed of marble found in Yantra mandir. This collection of sundials and other astronomical instruments was built by Maharaja Jai Singh II at his then-new capital of Jaipur, India between 1727 and 1733. The larger equatorial bow is called the Samrat Yantra (The Supreme Instrument); standing at 27 meters, its shadow moves visibly at 1 mm per second, or roughly a hand's breadth (6 cm) every minute. Cylindrical, conical, and other non-planar sundials Other non-planar surfaces may be used to receive the shadow of the gnomon. As an elegant alternative, the style (which could be created by a hole or slit in the circumference) may be located on the circumference of a cylinder or sphere, rather than at its central axis of symmetry. In that case, the hour lines are again spaced equally, but at twice the usual angle, due to the geometrical