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Making the most out of our graphical telemetry computers.

Like with many complex instruments, there are multiple ways to solve certain problems and to measure the required inputs. Combining the various functions leads to a multitude of advanced uses.

## Determining Time for Ritual Use

Level: Intermediate

A Quadrant can be used to perform various tasks in ritual. This tutorial explains how to determine a specific unequal hour after sunrise for a given location.

### Unequal Hours

Temporal or seasonal or unequal hours were established in the ancient middle east as 1/12 of the night or daytime. Such hours vary by season and latitude; unequal hours are longer in summer than in winter.

Before the invention and wide adoption of clocks and watches, for centuries the world told time via a system of unequal hours to organize and communicate time. Depending on the date over the course of the year and also the latitude, the absolute duration of an hour would change. Only around the equator would an hour roughly stay the same.

Sunrise marks the beginning of the 1st hour, the middle of the day is at the end of the 6th hour and sunset at the end of the 12th hour. This meant that the duration of hours varies with the season. In the northern hemisphere, particularly in the more northerly latitudes, summer daytime hours are longer than winter daytime hours, each being one 12th of the time between sunrise and sunset. These variable-length hours are variously known as planetary, unequal, or seasonal hours and were in use until the appearance of the mechanical clock, which furthered the adoption of equal length hours (Neugebauer, 1969)

### Ritual Use

Unequal hours is the system used in Jewish law called Talmudic or Halachic hour; sha'ah zmanit -- proportional hour. A sha'ah zmanit is defined as 1/12 of the Halachic day, that is one 12th of time elapsed from sunrise to sunset, day hours therefore being longer than night hours in the summer; in winter they reverse.

Historically, the Halachic day is calculated by dividing the total amount of time between hanetz amiti[1] and shkiah amitis[2] into 12 parts. Each of these parts is considered a Halachic hour, sha'ah zmanit.

The hour has special meaning in Jewish law. When we say that a certain Mitzvah may be performed three hours into the day, this does not mean at three in the morning, or three clock hours after sunrise. Rather, an hour in Halachah means 1/12 of the day. Thus, if the Sun rises at 5 AM and sets at 7:30 PM, one sha'ah zmanit, or proportional hour, will be 72.5 minutes, and all calculations will use that number (Chabad, 2004, 2007).

Time is determined by reading the position of a cursor on the plumb line against the curved hour lines.

Overview of the Unequal Hour Quadrant: string with weight (1), degree arc (2), 12-o'clock line (3), cursor knot (4), unequal hour lines (5).

### The Procedure on the Unequal Hour Quadrant[3]

• Determine your local latitude (φ).
• Determine the declination (δ) for the day in question.
• Calculate the Sun's maximum noon altitude (H) and set the string to that value. We subtract our latitude from 90° and then add the Sun’s declination for that day: `H = (90° − φ) + δ`.
• Align the cursor knot with the 12-o'clock arc (the Sun's altitude at noon for that day).
• Take the instantaneous Sun altitude.
• Read the hour line which the cursor crosses for the time of day (you can check your results using Tycho, our high-precision Sun calculator).

### The Unequal Hour Lines

These are a set of arcs, starting with the sine arc at the 6th hour before or after noon, they can be used to determine the time of day according to the system of seasonal or unequal hours. The unequal hour lines themselves are universal and do not reflect knowledge of the seasons.

Preparing the Quadrant for reading the time in unequal hours: set the maximum noon altitude of the Sun on the degree arc with the string (1), align the cursor with the 12-o'clock line (the red arc) by sliding the knot along the string (2), then after taking the Sun altitude, read the hours on the closest hour line (3). In this example, the maximum noon altitude for that day is set to 37.5°.

### Measuring Sun Altitude

To take the time, we need the altitude of the Sun measured as an angle in degrees from the horizon. To achieve this, we hold the Quadrant upright and aim at the Sun; the plumb line measures the angular height from the vertical.

A shortcut to quick-and-easy Sun sighting is to hold up the Quadrant as is and rotate and tilt until the orientation with the smallest shadow possible is reached.

### The Steps

1. Steady the string and let the plumb line weight hang freely and perpendicular.
2. Roughly align the instrument so that the Sun is in the direction alongside the sighting edge.
3. Rotate and tilt the instrument in order for the sunlight to cause the smallest shadow possible.
4. Read the altitude of the Sun where the string crosses the degree arc for the resulting unequal hour.

Taking the Sun altitude with the Unequal Hour Quadrant: let the string with the weight hang freely (1), rotate the upright Quadrant in such a way that the Sun is aligned with the edge (2), thereby creating the smallest possible shadow (3), read the hour where the cursor crosses the closest hour line (4). The example shows the 6th hour, that is noon.

### Counting the (Unequal) Hours

The unequal hour lines start at the 1st hour with sunrise at 0°, with the end of the 6th hour marking noon on the 12-o'clock (sine) arc. From there, they go back to the 6th hour after noon (or the 12th hour of the day) ending at 0°, with a single figure marking the common 3rd hour line.

Counting the hours on the Unequal Hour Quadrant. In this example, the cursor sits on the 4th hour line, thus it is either the 4th hour of the day (2 hours before noon), or the 8th hour of the day (two hours after noon). (A different way of counting starts over at noon with the 1st, 2nd, and so on hours after noon.)

The Quadrant model to use for this task (among others), is the Wndsn Horary Quadrant Telemeter in acrylic or the Wndsn Mini Horary Quadrant Telemeter in brass.

For dozens of further Sun calculations and methods based on ancient formulas, see the comprehensive Wndsn Quadrant Telemeters: Official Manual (GQT5).

Footnotes:

1. Hanetz Amiti; true sunrise. According to the Alter Rebbe, hanetz amiti, true (halachic) sunrise, is when the top of the Sun’s disk is visible at an elevation similar to the mountains of Eretz Yisrael. The time is calculated as the point at which the center of the Sun’s disk is 1.583 degrees below the horizon.
2. Shkiah Amitis; true sunset. According to the Alter Rebbe, shkiah amitis, true (halachic) sunset, is when the top of the Sun’s disk disappears from view at an elevation similar to the mountains of Eretz Yisrael. This time is calculated as the point at which the center of the Sun’s disk is 1.583 degrees below the horizon (Chabad).
3. Using the equation `H = (90° − φ) + δ` for latitudes in the tropics, some calculations result in a Sun altitude greater than 90°. When this happens, the Sun at noon appears behind us when looking toward the equator. In these cases, Sun altitude can be calculated using `H = 90° − (H − 90°)` where H on the right side is the result of the previous equation.