Ewald Hering’s (1899) On the Limits of Visual Acuity: A Translation and Commentary: With a Supplement on Alfred Volkmann’s (1863) Physiological Investigations in the Field of Optics

Towards the end of the 19th Century, Hering and Helmholtz were arguing about the fineness of visual acuity. In a talk given in 1899, Hering finally established beyond reasonable doubt that humans can see spatial displacements smaller than the diameter of a foveal cone receptor, an ability we nowadays call ‘hyperacuity’ and still the topic of active research. Hering suggested that this ability is made manifest by averaging across the range of locations stimulated during miniature eye movements. However, this idea was made most clear only in a footnote to this (not well known) publication of his talk and so was missed by many subsequent workers. Accordingly, particularly towards the end of the 20th Century, Hering has commonly been mis-cited as having proposed in this paper that averaging occurs purely along the lengths of the edges in the image. Here, we present in translation what Hering actually said and why. In Supplementary Material, we additionally translate accounts of some background experiments by Volkmann (1863) that were cited by Hering.