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Sphere No. 9: an ‘Instrumentum Azimuthale’

Spring, 1999

In the Cosmographia of Apianus and Gemma Frisius, following the explanation of how to rectify a terrestrial globe in its stand with respect to the local horizon, three methods are promised for finding the true meridian at any point on the earth. The first is the familiar method of bisecting the angle between shadows of the same length, cast by a vertical gnomon before and after noon. The third uses the magnetic compass of a diptych dial, taking due account of magnetic variation. Between these, the reader is offered a method altogether more complicated.

Gemma Frisius described the second operation as, unlike the other two, a method ‘per organum speciale’, because one step required an instrument specially designed for the purpose, the ‘instrumentum azimuthale’ (illustrated on the left). The technical content of this planispheric projection of the sphere is slight: a central horizon line has a scale of azimuths, azimuthal lines rise to the zenith every 10 degrees, and at each end of the horizon is a vertical altitude scale.

An interesting feature of this woodcut, however, is that, as originally printed in Cosmographia, it was not intended to be an illustration: it was, quite simply, an instrument. We tend to think of the book having some four paper instruments: the volvelles or diagrams with moving parts. But the static diagrams can also be presented as instruments. The reader is not told what they might figure or represent, but told instead how to use them.

The process for finding the meridian begins by using another instrument in Cosmographia, the universal astronomical instrument introduced by Gemma (illustrated on the facing page). For the place, date and time in question, this instrument yields the altitude of the sun, which can be transferred to the instrumentum azimuthale by setting a rule between this altitude value on the two vertical scales. A second parameter from the universal instrument set for the position of the sun is then transferred to the altitude line of the instrumentum azimuthale using a pair of dividers. For this to work the projected spheres on both instruments must be the same size, which they are to a millimetre.

This operation yields the azimuth of the sun. The local meridian can then be found by applying the azimuth angle to the shadow cast by a vertical gnomon on a horizontal surface. Cosmographia describes this operation as involving the use of a divided circle inscribed within a square, with the gnomon at its centre: the azimuth value on the circle can be made to coincide with the shadow and the edge of the square indicates the meridian.

Instruments have iconographical conventions. This one is supported by a disembodied hand and arm, and although the lower semicircle has no function in the operation, it is included as the ‘Inferius Hemisphærium’ and embellished with southern constellations, such as Hydra, Crater and Corvus. Two points are thus reinforced within the sixteenth-century understanding of cosmography: its method is operational – practitioners do things with instruments – and its reference is universal.