1. The photochemical theories of vision cannot provide a valid interpretation of the facts over the whole range of brightness. The fact that liminal excitation is increased by the absorption of a very small number of quanta, each absorbing rod receiving a single quantum, excludes the intervention of the mass action law which is the basis of all photochemical theories.
2. Owing to the quantic structure of light and to the random distribution of quanta in a faint light pencil, there must exist numerical relations between the threshold energy on the one hand and the size of the retinal area stimulated and the stimulation time on the other, whatever may be the inner mechanism of liminal excitation. When taking as a basis Van der Velden's experimental results, viz. that two quanta absorbed during a certain interval of time are sufficient to raise threshold excitation, the probability calculus enables us to compute the course of threshold energy in relation to the stimulation time and to the stimulated retinal area. No arbitrary parameter is needed to do so; the only constant to be used is found by experiment.
3. The quantic and statistical theory of visual excitation that we put forward in the present paper enables us to predict the validity of Ricco's law within what we call a "quasi-independent unit" and the validity of Piper's law within a test area made up of a certain number of such units. This theory does not correspond exactly with Piéron's law for foveal threshold in relation to the size of the stimulated area, but the deviation is probably due to an artefact; viz., the action of the micronystagmus.
4. Experiment proves that in region IV of the retina, 15° temporally from the fovea of the right eye of two observers, Ricco's law applies strictly in rod vision from 2'12'' to 31'36'' and, perhaps, further on.
5. In the same region, from 12'30'' to 31'36'', Piper's law applies strictly in cone vision of extremely red light.
6. In peripheral vision with extremely red light the photochromatic interval has been found to be null.
7. Our theoretical interpretation of the term "quasi-independent unit" fits well with the histological data of the retina.
8. Numerical deviations of the theoretic time law of threshold intensity from the empirical course may be due to the existence of a relative refractory period of the ganglion (or bipolar) cells. This mechanism would be a sort of instantaneous adaptation of nervous elements and would explain the fact that the sensation level increases very much slower than the brightness level, in a range of the brightness scale where the photochemical adaptation cannot account for this phenomenon.