Nicolas Auguste Tissot

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Nicolas Auguste Tissot (1824-1897) was a 19th century French cartographer, who in 1859 and 1881 published an analysis of the distortion that occurs on map projections. He devised Tissot's Indicatrix, or the distortion circle, which when plotted on a map will appear as an ellipse whose elongation depends on the amount of distortion by the map at that point. The angle and extent of the elongation represents the amount of angular distortion of the map. The size of the ellipse indicates the amount that the area is distorted.

Born in Meurthe-et-Moselle (Nancy, France), Tissot was trained as an engineer in the French Army from which graduated as capitaine du génie. In the early 1860s he became an instructor in geodesy at the reputed Ecole Polytechnique in Paris. Around the same time, he indulged a research program meant to determine the best way of cartographic projection for a particular region and presented his findings to the French Académie des sciences.^[1] Nicolas Auguste Tissot is best remembered for his Indicatrix or ellipse indicatrice (also known as distortion circles), which is a mathematical tool to measure distortions in a map. In the eighteenth century, the German cartographer Johann H. Lambert enunciated a mathematical theory of map projections and attendant characteristics of distortions that any given projection involved. Along with Carl F. Gauss, Tissot further developed this theory in the later part of the nineteenth century.^[2] In fact, Tissot’s research in the mid-1850s on the ways and means to find the best projection for a particular region led him to develop what he saw as optimal projection. While not quite equal-area or conformal, his projection resulted in “negligible distortion for a very small region.” Subsequently, his optimal projection was adopted by the geographic service of the French Army.^[3] While his first concepts regarding cartographic distortions developed in mid-century, it was only with the publication of Mémoire sur la représentation des surface et les projections des cartes géographiques in 1881 that the Tissot’s Indicatrix became popular.^[4] In the book, the French geographer argued for his method when he reportedly demonstrated that “whatever the system of transformation, there is at each point on the spherical surface at least one pair of orthogonal directions which will also be orthogonal on the projection.”^[5] Tissot employed graphic device which he called ellipse indicatrice, the distortion circle which when plotted on a map reveals the amount of distortion by the map at the particular point where the ellipse has been plotted. The cartographer cum mathematician suggested that the angle and extent of the elongation of the distortion circle represented the amount of angular distortion of the map while the size of the ellipse was revelatory of the amount of distortion in area.^[6] In a nineteenth century cartographic context in which professionals were looking for ways to apply mathematical principles to the science of mapping and the map projection, Tissot’s theory was favorably received, at least in continental Europe.^[7] Even in the more restrained Anglo-American academic world, a columnist of Science, a publication sponsored by the American Association for the Advancement of Science, hailed the method deployed by the French cartographer and encouraged his readers to study Tissot’s work in the hope that such a study “will lead to the adoption of better projections than those which are at present in use.”^[8] The legacy of Tissot’s method is still vivid today as suggested by the authors of Map Projections for Europe who can still argue that since Tissot’s famous analysis regarding distortion, there has been no major scientific development in the metric interpretation of deformation, except with Eduard Imhof’s Verzerrungs-gitter or deformation grid.^[9]

ENDNOTES

1. ^ M. d’Avezac, “Coup d’œil historique sur la projection des cartes de géographie,” Bulletin de la société de géographie (January-June 1863), pp. 438-462.
2. ^ Frank Canters, Small-Scale Map Projection Design (London: Taylor &, Francis 2002), p. 5.
3. ^ John Snyder, Flattening the Earth: Two Thousand Years of Map Projections (Chicago: University of Chicago Press, 1993), p. 143
4. ^ Nicolas Auguste Tissot, Mémoire sur la représentation des surface et les projections des cartes géographiques (Paris: Gauthier-Villars, 1881).
5. ^ Robinson et al., Elements of Cartography 5th Edition (New York: John Wiley & Sons, 1984), p. 81.
6. ^ Borden D. Dent, Cartography: Thematic Map Design 2nd Edition (New York: Wm. C. Brown, 1990), pp. 53-55; Robinson et al., Elements, pp. 81-86; “Tissot’s Theory of the Projection of Maps,” Science, 2 November 1888, p. 207.
7. ^ Arthur H. Robinson, “The Use of Deformational Data in Evaluating World Map Projections,” Annals of the Association of American Geographers 41, 1 (March 1951), pp. 59-60.
8. ^ “Tissot’s Theory…,” p. 207.
9. ^ A. Annoni et al. (eds.), Map Projections for Europe (European Communities, 2003), p. 78.