Whitehurst & Son sundial (1812)
To construct a sundial, one must understand the geometry of the solar system, and particularly how the sun will cast a shadow onto a flat surface, in this case a horizontal surface. Each day over a yearly cycle the shadow will be different from the day before, and the shadow is specific to the location of the dial, particularly its latitude. The dial is designed to tell local apparent time so the longitude is not important. In this case, noon will be at the point when the sun is highest in sky and due south, and standard time would be when the sun was due south at another point such as the Royal Observatory at Greenwich. Derby is at 1° 28′ 46.2″ West of Greenwich,  so the sun is approximately 5 mins and 52.05 s later in reaching noon. And also when telling the time, we must consider the equation of time. That is to say, as the earth moves around the sun in a slight ellipse, day length slightly varies everyday. For example, the difference from the average becomes up to 16 minutes in November and February. This equation of time had been really unknown for a long time until people started comparing sundials with mechanical clocks. If a clock ignores this difference, it measures average time. If a clock is re balanced each day to make them correspond with the natural cycle, it measures local mean time. A fixed noon and fixed day are essential for railways timetabling, so Greenwich Mean Time was adopted. In the case of Midland Railway, it was by January 1848.