Aitoff and Hammer

O NE of the most familiar combinations of personal names in our literature on map projections is Aitoff-Hammer. The projection with which this conjunction of the surnames of David Aitoff (i854-I933) and Ernst Hammer (i858-i925) is associated is the projection of the entire sphere in an ellipse obtained by transforming J. H. Lambert's equivalent azimuthal projection of a meridional hemisphere. In the works on map projections written in English the contributions of Aitoff and Hammer to the invention of this projection are lamentably confused. Even Deetz and Adams,' whose accounts of the origins of projections are usually dependable, do scant justice to Hammer. No comparable confusion is to be found in the German literature.2 It is my purpose here to assign the credit due respectively to Aitoff and Hammer and, if possible, to separate the two names, leaving each as a convenient designation for a distinct projection of the whole surface of the earth. First, then: the equivalent projection of the earth commonly designated AitoffHammer, or often simply should be credited exclusively to Hammer. It is difficult to understand how a reader of Hammer's description of the projection3 could gain the impression that the one he exhibits in his accompanying illustration is Aitoff's invention. Not only does Hammer put the adjective in the title of his article; in a context that distinguishes the projection to which he applies it from Aitoff's he refers to the accompanying illustration as a neue fldchentreue Abbildung der ganzen Erdoberfldche (letterspaced in the original). Hammer's projection of I 892, by whatever name it is called, is familiar and still in use. What of Aitoff's, which Hammer mentions in the title of his article and describes in the course of introducing his own? True, Aitoffs projection was introduced rather obscurely, in an Atlas of Modern Geography published in I889 by the Paris firm Librairie Hachette et Cie.4 On the back of Map 2 of this atlas is an article, Projections des Cartes Geographiques, signed D. Aitoff, who was evidently responsible for the projections used in the atlas. Aitoff calls No. 34 of his list of projections, which he illustrates by a drawing, Canevas derive. He describes how it was constructed: by halving the ordinates of an equidistant azimuthal meridional hemisphere. Concerning its properties he says: Ce canevas ne jouit d'aucune propriete geometrique des projections; il n'est pas equiva

Hammer · Engineering · Historical Geography and Cartography · Mechanical Engineering