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Van der Velden and Bouman studied the area-intensity relationship in an attempt to prove their «two-quantum theory αof the visual absolute threshold. The present experiments demonstrate the non-uniformity of the larger retinal areas used by these authors. The variation of sensitivity with retinal position is so large in these areas that it invalidates the attempted proof of the two-quantum theory, while suggesting that the retinal threshold n is equal to at least 3 quanta. Van der Velden et Bouman ont étudié la relation entre l'aire et l'intensité dans le but de vérifier leur «théorie des deux quanta αpour le seuil absolu de la vision. Les expériences ci-dessous montrent que les grandes surfaces rétiniennes utilisées par ces auteurs ne sont pas du tout uniformes. La variation de sensibilité avec la position sur la rétine est tellement grande dans ces régions, qu'elle infirme la tentative de preuve de la théorie des deux quanta. Les expériences indiquent que le seuil rétinien n est probablement égal au moins à trois quanta. Beim Nachweis ihrer Behauptung, dass zwei Quanten die absolute Sehschwelle darstellen, haben van der Velden und Bouman die Beziehung zwischen Feld und Intensität untersucht. Die vorliegenden Versuche zeigen die Ungleichförmigkeit so grosser Netzhautpartien, wie die genannten Autoren sie verwendet haben. Die Änderung der Empfindlichkeit mit der Lage auf der Netzhaut ist in diesen Teilen so stark, dass damit der angestrebte Beweis für die Gültigkeit jener Behauptung misslungen sein dürfie. Man darf wohl sagen, dass die Netzhautempfindlichkeit n bei mindestens drei Quanten liegt.

The simplest interpretation of the uncertainty of seeing observed at the absolute threshold is based on the theory of quantum fluctuations and assumes that in any given trial the light is seen when the retina has been acted upon by at least n quanta. When this assumption is true the frequency-of-seeing curve is a simple Poisson sum of parameter n, and the “mean threshold intensity,” that is the mean number of quanta I(55%) acting on the retina for a frequency of seeing of 55%, is very nearly equal to n. Biological variations of n would make the curve shallower than it would be if n were constant and approximately equal to the “mean threshold intensity,” I(55%). The same result is valid in the case of all other complications which might occur with regard to the physiological mechanisms involved, and which would make the simplest interpretation invalid. Thus the slope of experimental curves obtained under suitable conditions must be smaller than or equal to the slope of a simple Poisson sum the parameter of which is approximately equal to the “mean threshold intensity.” From the slope of such curves, therefore, it is always possible to derive a lower value for the “mean threshold intensity.”