Cartographic Grids from Iran: An Early Version of the Retro-Azimuthal Orthographic Projection?

Abstract

In this paper the cartographic grids engraved on two antique instruments from Iran for finding the sacred direction and distance to Mecca are discussed. It appears that these grids can be well explained in terms of the Mecca-centred retro-azimuthal orthographic projection described in 1968 by J. E. Jackson. In this projection the lines of constant latitude reduce to a set of ellipses with their major axes parallel to the equator and the lines of the constant longitudes reduce to a set of non-equidistant straight lines parallel to the north-south direction. It is shown that the curves actually engraved on the instrument conform to this projection and can be fairly easily constructed. This interpretation of the grid on the Iranian instruments stands in contrast with another explanation, recently proposed by King (1999), which is based on medieval Arabic concepts such as the so-called 'methods of the zijes'. Insufficiently accurate workmanship makes it impossible to distinguish between the two explanations through the study of the instruments themselves. The newly gained insight into the projection itself, however, shows that a direct relation between the Iranian maps and Islamic mappings insight knows from the ninth century, as suggested by King, does not exit. Thus, it is concluded that it is as yet completely unknown when and where the very idea behind the Iranian cartographic grid was first conceived, and that the quest for their historical background is still open.