Scratch dials - a closer look

Updated 11 June 26

This replaces an earlier post.

As noted in the previous post, between the Spring and Autumn equinoxes, such dials, being South-facing, are in shadow nearer sunrise and sunset. Let's use Stellarium for a few examples at 51 degrees North:

- at the Summer solstice, the Sun enters the Southern half of the sky (i.e. lies due East) 3 hours and 40 minutes after sunrise, when its altitude is about 30 degrees and the dial therefore indicates the end of the second hour and the start of the third (no good if we need to know when the second hour starts and similarly for the final hour); the dial is illuminated by the Sun for just over half the daytime,

- about the start of Summer, May 4th say, the Sun enters the Southern half of the sky 2 hours and 20 minutes after sunrise, when its altitude is about 20 degrees and the dial therefore indicates part way through the second hour (again no good if we need to know when the second hour starts, but perhaps ok for the start of the final hour, which can be guessed at); the dial is illuminated by the Sun for just over two thirds of the daytime,

- even in mid-April, less than 4 weeks after the equinox, the Sun enters the Southern half of the sky 90 minutes after sunrise, when its altitude is about 13 degrees and the dial therefore indicates nearly the end of the first hour (and so is likely still usable); the dial is illuminated by the Sun for just over three quarters of the daytime. 

This demonstrates the limited usability of this type of dial when the Sun is North of the celestial equator - surely there were complementary dials for these months? Perhaps something as simple as a North-facing dial of the same type? In this case, it would need marks for the first two and final two hours only of the daytime. In the morning, the shadow cast by the gnomon would be horizontal at sunrise and would rotate until reaching a particular angle at which time the entire dial would go into shadow and the South-facing one would then be illuminated, continuing at the correct angle and hour. Later in the day, the process would be reversed as the South-facing dial went into shadow and the North-facing one became illuminated.