Unequal Hours
Before we had clocks and watches, it was commonplace to divide the hours of the day into two sets of twelve hours, each between sunrise and sunset. This meant that hours during the daytime were longer in the summer and shorter in the winter. They are called Unequal Hours because they change in length during the course of the year.
The bottom half of the Plate, underneath the horizon, shows twelve curved lines. These are segments of equal length for any sky object that passes through them.
To tell the Unequal Hour time, first get the Ecliptic Longitude of the current day, as normal. Here it is September 30th and 189º.
Take a sighting of the Sun (DO NOT LOOK DIRECTLY AT IT) using the alidade on the back – you can use an approximation if you have a nice shadow down a wall, for example. Say the Sun appears to be around 48º in Altitude. If it is night time, use a star instead, the same principle apples.
Rotate the Rete until the scale curve intersects the 48º Altitude line (make sure to use the side that will give you a sensible time of day, morning or afternoon).
Line up the Ruler on the current Ecliptic Longitude, here 189º, and read that it is currently 13:15 Solar Time.
Draw a line diametrically opposite (or rotate the Ruler until it is exactly 12 hours ahead) and you will have a reading of the Unequal Hour; here, it is just into the 7th Hour.
Your mileage may vary a little on this one – it depends on how accurate you can judge the Sun’s altitude.
A second method
The Unequal Hours also appear on the back of the Astrolabe. To use these, first you need to find out the maximum altitude the Sun will reach on this day. Using the Ecliptic Longitude, put this value on the Rete in alignment with the Meridian. Here, we’re using 189º again. We can read the Sun should reach 57º in Altitude today.
Take a sighting on the sun (AGAIN, BE CAREFUL!) to get its current altitude. Let’s say it is at 33º.
First, move the alidade to the Sun’s maximum altitude for the day. See where the alidade crosses the innermost circle (this one represents noon). Here, it’s a shade over 14º on the scale.
Next, move the alidade to the Sun’s current altitude, in this case 33º. See where the 14º mark lies in the hour circles now. It’s between the 2 and 3. Reading the hours as a complete ring from the left, continue counting up past 6 and we’re in the 9th Unequal Hour of the day.
Using the Shadow Square
This is found on the back of the astrolabe. It is used to find heights and distances of objects.
You can start by finding the height of the ceiling of the room you’re standing in. The easy way is to rotate the alidade into the corner of the shadow square so it’s at 45º, then walk towards the corner of the room until you can sight it along the alidade. Your eye is then at the same distance from the corner as the height below it. Measure the distance between you and the wall, then add your own height (to eye level) in order to find the height of the ceiling.
There are two scales on the shadow square, one divided into tenths and one into twelfths. You can use either.
For each scale, the Umbra Versa side (the vertical one) measures angles under 45º whereas the horizontal Umbra Recta scale measures angles above 45º. Be sure to measure the scales from the correct side of the alidade, through the center of the instrument.
You’re essentially finding the length of one side of a triangle.
Finding heights
Say you want to find the height of a tree. Pace a distance out from the tree. (If you need to measure how long your pace is, walk ten steps and measure that length, then divide by ten to get an average pace length). Imagine we measure 75 paces/meters/feet whatever from the tree.
Hold up the astrolabe and sight the top of the tree using the alidade. If the alidade crosses the Umbra Versa scale then it is shorter than our paced measurement. Say it reads 6/12, then the tree’s height is 6/12 = 1/2 of our paced measurement, I.e. about 37.5 units tall.
Maybe you have a taller tree and the alidade crosses the Umbra Recta scale, this time at 4/12.
This time, since we know the tree is taller than our paced measurement, we say it is 12/4 = 3/1 = 3 times as tall as our pacing, i.e 4*75=225 feet. (Hey, maybe it’s a Redwood!)
Finding distances
Suppose you have to cross a river and you need to know how wide it is. You know you are 6 feet tall.
Hold up the astrolabe and take a sighting on the opposite river bank. If the alidade reads 3/12 on the Umbra Versa, this time you are finding the longer side of the triangle and will need to treat it as 12/3 = 3/1 = 3*6 = 18 feet across.
Introduction
Parts & Plates
Finding Times
Finding Positions
Unequal Hours & Shadow Square