Sigmoid diagrams

Sigmoid diagrams are occasionally seen on the back of traditional astrolabes. A sigmoid curve allows you to find the Sun's maximum elevation at a particular latitude on any day, and a sigmoid diagram may show several of these curves. It is necessary to know the maximum elevation of the Sun when using an alidade and the unequal hour arcs on the back of an astrolabe.

The characteristic 'S' shape of the curve allows the diagram to be readily identified. The quadrant displaying the diagram usually shows seven evenly separated quarter circles centred on the centre of the astrolabe, and each sigmoid curve extends between the inner and outer circles. The spaces between these circles are labelled with the signs of the Zodiac. On the diagrams drawn with the accompanying program, the names of the Zodiac signs are abbreviated to their initial letters.

To view the sigmoid curves, which are displayed on the back of the traditional astrolabe, you can repeatedly press the '7' or '8' key when the options for the upper left and upper right quadrants cycle through, the options including three different displays of sigma curves. Conversely, after displaying the back of the astrolabe (perhaps by pressing the f8 function key) you can select the curves from the menu:

Menu: Astrolabe: /reverse - upper left quadrant /...
Menu: Astrolabe: /reverse - upper right quadrant /...

This will lead to menu options (among others) of:

UL Sigma Curve: latitude
UL Sigma Curves: odd + latitude
UL Sigma Curves: even + latitude

The first sigmoid diagram only displays the sigmoid curve for the currently selected latitude, which appears in red. The second diagram adds a set of curves for odd latitudes, and the third adds a set for even latitudes.

To use the sigma diagram to find the maximum elevation of the Sun on any day, first use the calendar and Zodiac scales on the back of the astrolabe to find the current position of the Sun on the ecliptic circle. That is, find the Sun's current position within a Zodiac sign. Then, identify this position between the quarter circles of the diagram and find the crossing point of this with the sigmoid curve relating to your latitude. If you move the alidade to align with this point, you can read the elevation of the Sun for that day on the outer scale of the back of the astrolabe.

It is worth noting that an alternative diagram which also shows the maximum elevation of the Sun for specific latitudes has the quarter circles showing the divisions of the Zodiac spaced asymetrically, not with equal spacing as on the sigmoid diagram. The resultant curves are each shaped like a 'C' rather than being sigma shaped, and appear rather uninteresting in comparison. They can't be displayed by this program at present.

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