Gnomons
The gnomon was introduced by Anaximander in 534 B.C., but was used by Pytheas in 330
A.D. to navigate. It was a vertical stick, later positioned in sundials, that was to measure the shadows of sun at equinox when the sun is parallel to the equator
(Pinotsis, 2005). Defining the ration of the gnomon’s shadow to
its length results in the tangent between the
gnomon and the sun’s rays (Pinotsis, 2005). In reverse,
the angle created by the end shadow point and the tip of
the gnomon, was the altitude of the sun.
Kamals
Some measurements were taken by fingers or thumbs (Ifland, 2000). This worked on the principle that one finger, or thumb, or kamal, will block the view or subtend the same number of degrees in the sky if held at the same distance from the observer (Ifland, 2003; Iowa State University, 2000), so it can also be used to measure distance of celestial objects. A sailor would sight a known star and using a finger, kamal, and eventually crossstaff, move it to or from his eye until it filled the space between the star and the horizon. If using kamal, an Arab navigational aid, the navigator would subtend the view between the horizon and the star while holding the connected string between his teeth to mark the distance, then tie a knot at that place (Ifland, 2003). To maintain that latitude, the sailor knew where to position the string.
Astrolabes and Quadrants
The first recorded mentions of astronomical quadrants and astrolabes date back to the Arabs in the eighth century. Yet the first mention of the marine quadrant did not occur in the western world for another 500 years (Cardoza, 1996). The quadrant also worked by measuring the angle between the
sun or star and the horizon.
Cross Staff
The use of the cross staff gave rise to the term “shooting the sun” due to the way it was held and pointed toward the sun, similar to an archer taking aim (Ifland, 2003). The crossstaff worked by sighting the sun and the horizon at the same time, and measuring the angle, thus the altitude. The cross staff was first described in 1342 by Levi ben Gerson (Cardoza, 1996; Ifland, 2003).
Back staff or Davis Quadrant
The back staff or Davis Quadrant was called a quadrant for its ability to measure up to 90 degrees and was named after Captain John Davis. It was designed to save the navigator from the need to stare directly at the sun for the time it took to get the reading. Rather, the navigator faced away from the sun and measured the shadow cast by the sun, similar to the gnomon, but was almost impossible to use for sighting night stars or the moon (Ifland, 2003). The limitations of early tools were that at twilight, morning and evening and noon, if the horizon were sharp and clear, navigators could make their sightings; at other times, they could not. (Clark, 1993).