From the previous section, we know that the gnomon must be set parallel to the Earth's axis in order to get a shadow angle that has a constant magnitude every day, given the same interval of time. However, regardless of the angle between the gnomon and the Earth's axis, the shadow angle does not move at a constant speed in any given day. Hence, to have markings that show equal hours on a sundial, we need to use tables and mathematical calculations. It is with these tables and mathematical calculations that we are able to divide a day into 24 equal hours. However, before these mathematical formulas were derived, people have different classification of time.
In antiquity, the daily arc of the sun, that is, the time from sunrise until sunset, as well as the night arc, was divided into twelve equally long parts. Since the time from sunrise to sunset was longer in summer than in winter, the "hours" of summer were also longer than the "hours" of winter. These unequal hours or temporary hours were used over much of the earth, for many centuries until the middle ages. The "hours" of any one day were equal, but the "hours" of the winter were short and the "hours" of summer long. It is for this latter reason that we refer to them as unequal hours.
In Europe between the 8th and the 15th century, sundials were built on church walls pointing due south. Their main purpose was to show times of prayer. They are called canonical sundials. Canonical sundials are not time measurement systems as we would think of them today, but had the task to divide the light of day into certain time periods. The timelines with a cross-line in Figure 11 indicate the hours of prayer.
For the canonical sundial in Figure 11, adjacent hour lines are at equal angles from each other. In ancient times, people have the misconception that the "hours" measured by this dial in a day are equal. However, in the section on vertical direct south dials, we show a formula which proves this thinking wrong. Hence, the "hours" measured by this dial are "unequal" hours which are not equal within a day.
Around the 14th century, the method for counting the hours changed. The irregular unequal hours were replaced by hours of equal length. The time beginning with the passing of the low meridian, about midnight, until the passing of the next low meridian, was divided into 24 hours of equal length. They were called equinoctial hours.
Figure 12 shows a south pillar of the Regensburg (German) cathedral which features two sundials. The one below shows temporary hour lines, which measures unequal hours, and a horizontal gnomon. Similar to the canonical sundial in Figure 11, adjacent hour lines are at equal angles from each other. Hence, this sundial again measures "unequal" hours which are not equal within a day.
The sundial above, dated 1509, shows equinoctial hours with a gnomon parallel to the earth's axis. This sundial is the vertical direct south dial that is commonly found today.
In the first case, the noon line indicates the transition from the 6th to the 7th hour and, in the second case, the more recent sundial, the noon line is the XII-hour line. Besides the division of the day into 24 hours of equal length from midnight to midnight, other hour classifications were also used.
In some areas of Europe, particularly in Northern Italy, after the introduction of the equinoctial hours, counting of the 24 hours began at sunset. Consequently, the first hour began at sunset.
The time is read from the shadow of a fixed point or node. The green curves in Figure 13 represent lines of declination. The green straight line in the middle represent the equinoxes, while the upper green curve represent the winter solstice and the lower green curve represent the summer solstice. In Figure 13, only 3 lines of declination are shown. In the actual dial, lines of declination for other days are also shown. The dates corresponding to the lines of declination are stated at the side of the dial (not shown in Figure 13). Usually, only the zodiac signs, and not the actual dates are given.
When reading the dial, the shadow of the node will fall on one of these green lines. We can thus get the date by reading the corresponding date stated at the side of the dial.
A table of dates and the corresponding sunset times is usually provided at the bottom of the dial.
To explain how to use sundials that use Italian hours, we shall use an example. If the shadow of the node falls on the intersection point of the green straight line in the middle and the blue line indicating the 17th Italian hour (point A), the date of reading is on one of the equinoxes, because this green line represent the equinoxes. Let's assume that the date of reading is on the vernal equinox (21st March). Since the sun sets at 6p.m. on 20th March, the time of reading is thus 17 hours after 6p.m., which is 11a.m. on 21st March.
Babylonian hours are measured using the same principles as Italian hours, the only difference being that the counting of the 24 equally long hours started with sunrise.
Again, a table showing dates and the corresponding sunrise time is usually provided at the bottom of the dial.
If the shadow of the node falls on the intersection point of the green straight line in the middle and the red line indicating the 5th Babylonian hour (point A), the date of reading is on one of the equinoxes. Let's again assume that the date of reading is on the vernal equinox (21st March). Since the Sun rises at 6a.m. on the vernal equinox, the time of reading is 5 hours after the Sun rises. Hence, it is 11a.m. on 21st March.
Note that sundials reading Italian and Babylonian hours can only be designed for use at a particular latitude.