7. The Unequal Hours (2)

A previous section introduced the concept of medieval unequal hours and described how to configure the astrolabe to show the night sky at any given time in this system of timekeeping.

In the upper half of the central portion of the reverse side of the mother, there is a second tool for calculating the time in unequal hours. This is a simple but imprecise tool, consisting of six partial arcs of circles all passing through the centre of the astrolabe.

Before using these, it is necessary to calculate the maximum altitude at which the Sun will appear – at noon – on the day of observation. This can be determined experimentally by rotating the front side of the mother, once the location of the Sun along the ecliptic has been found. The answer varies little from one day to the next, and so only needs to be looked up rather infrequently.

Returning to the reverse side of the astrolabe, the scale of degrees marked along the central part of the alidade should then be studied to find the point on the scale corresponding to the maximum altitude of the Sun. We shall call this point on the alidade X.

The present altitude of the Sun should then be determined – perhaps by making an observation by sighting it along the alidade.

Keeping the alidade pointing to this altitude, the position of the point X among the six circular arcs should be determined. The smallest circle is drawn such that the point X always lies on it at noon. The point X crosses each of the other circles at hourly intervals. Each circle is crossed twice each day, once as the Sun is rising, and once as it is setting.

Thus, the gap between the zero-altitude line and the largest circle represents the first or the twelfth hour of the day, and the gap between the two smallest circles represents either the sixth or the seventh hour; it is necessary to determine whether the Sun is rising or setting to know which.