Lee (1944) defines an authalic map projection to be one in which at any point the scales in two orthogonal directions are inversely proportional.
Authalic Projection
See also
Equal-Area ProjectionExplore with Wolfram|Alpha
References
Lee, L. P. "The Nomenclature and Classification of Map Projections." Empire Survey Review 7, 190-200, 1944.Referenced on Wolfram|Alpha
Authalic ProjectionCite this as:
Weisstein, Eric W. "Authalic Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AuthalicProjection.html