Foucaut projections (1862), according to Waldo Tobler (1973).
Parameter alpha between 0 (sinusoidal projection) and 1 (Lambert cylindrical projection).
Initial research by Philippe Rivière for d3-geo-projection issue #66.
Note that this is the easy part of #66 :)
References:
Capitaine De Prépetit Foucaut, Notice sur la construction de nouvelles mappemondes et de nouveaux atlas, pp. 5-10, Arras, France, 1862.
Coup d’oeil historique sur la projection des cartes de géographie, M. d’Avezac - 1863.
Traité des projections des cartes géographiques; représentation plane de la sphère et du sphéroïde, by Germain, Adrien Adolphe Charles - 1866.
Tobler, W. R., The Hyperelliptical and Other New Pseudo Cylindrical Equal Area Map Projections, Journal of Geophysical Research, Vol. 78, no. 11, April 10, 1973.
d3-geo-projection already has a (different) projection by Foucaut, named “Stereographic Equivalent” (See this demo by Jason Davies).