History of the Oblique Hammer-Aitoff

[daan]

Having examined some of Schrader’s atlases that Hinks mentions, I don’t see that they declare any projection name for their (many) Hammer maps. I think we have to blame Hinks for this. Anyway, he describes the construction method of the Hammer, and so we have to suppose he referred to Hammer’s article, whatever he might has seen in an atlas. That does not mean that he understood the nuances of Hammer’s text, necessarily.

— daan

[quadibloc]

Having examined some of Schrader’s atlases that Hinks mentions, I don’t see that they declare any projection name for their (many) Hammer maps. I think we have to blame Hinks for this. Anyway, he describes the construction method of the Hammer, and so we have to suppose he referred to Hammer’s article, whatever he might has seen in an atlas. That does not mean that he understood the nuances of Hammer’s text, necessarily.

After reading this, I looked, and first found some pages from atlases in the 1920s which indeed appeared to use the Hammer projection with no note on the projection used. Then I found some earlier whole Schrader atlases available for download. In one, "Atlas de géographie moderne" from 1898, David Aitoff is listed as a collaborator in the creation of the atlas. There is a page at the start which describes various projections. Right after describing the Mollweide projection, the original Aitoff and the Hammer are described. But neither Aitoff nor Hammer is mentioned or credited, the projection is simply called "canevas dérivé".

I quote:

34. Canevas dérivé (fig. 29). On construit une projection méridienne quelconque et on réduit de motié les distances à l'équateur de tous les points de cette projection. Par les points marqués on fait passer des lignes réguilièrement courbes qui représenteront les méridiens et les parallèles. Ce canevas est équivalent lorsqu'on prent pour base un projection méridienne équivalente. Si on le fait dériver de la projection méridienne équidistante (fig. 11) la deformation dans la représentation de la terre tout entiere est relativement peu considérable.

34. Derived graticule (fig. 29). A meridional projection of some type is constructed, and the distances from the central meridian to all the points on that projection are reduced to one-half of their value. Through the calculated points, smooth curved lines are drawn to represent the meridians and paralells. The graticule is equal-area if the equatorial projection on which it was based was equal-area. If it is derived from the azimuthal equidistant projection (fig. 11) the distortion on a map of the whole world is relatively small.

My literal translation does not seem to find the part of stretching the projection to make up for shrinking the longitude. But indeed, this confirms what you have said: Schrader would have been of no help to Hinks. The same also appears in the 1904 edition.

Subsequently, I located an 1891 edition of the same atlas on Google Books, and this time the possibility of starting from an equal-area projection is not mentioned in that one, so I have not discovered that Aitoff anticipated Hammer, changing the history of cartography. Also, interestingly, where Aitoff's projection is used, it is labelled as such.