The Theory of the Visual Threshold: II. On the Kinetics of Adaptation.

I. The production of a neural effect resulting in visual discrimination on the basis of brilliance requires the summation of a very large number of elements of effect produced by a large number of excitable neural units. The expression of the cumulative resultant is in terms of "elements of action" which are definable by the analytical relation of excitability to time, intensity and other experimentally controlled variables. Sufficient objective evidence already exists to support the proposition that the intensity threshold of any one excitable unit intrinsically fluctuates. So also does its contributive efficiency in the production of the elements of effect. Excitability is defined as the reciprocal of the exciting intensity; it exhibits properties justifying the conclusion that, as so defined, it is proportional to a simple velocity constant.1 From these considerations it is deduced2 that the relation of photic excitability' (1/AIo) to exposuretime must appear as a probability integral in log texp.. This is thoroughly in accord with the experimental data.2 II. By homologous reasoning it is deduced that threshold excitability (1/A,o) should appear as a probability integral in log tD, where tD is elapsed time during dark adaptation. The argument, condensed, is that at any instant the units potentially excitable form a frequency distribution of d(k), where k is a velocity constant governing excitability; over the finite interval required for a measurement of excitability the production of elements of effect by units in a given d(k) class will decline with tC,.p, and the frequency distribution of elemental effects will then be one of -texp. d(k), or -texp. d(l/to), since k is proportional to a reciprocal time on the organism's time scale (to); hence, a frequency distribution of a d log t. Reasons have been given2 for expecting that this distribution must be Gaussian. If texp. is constant, the total effect obtainable is a probability integral in log I.3 During recovery from light adaptation the frequency distribution of the excitabilities is conceived to form at any moment a frequency distribution of d(K), where K is a momentary recovery velocity constant and proportional to 1/to; with passage of dark-time, the number of elements in a given d(K) class will decline, forming as a function of dark-time a frequency distribution in terms of -tDd(l/t), and thus of d log tD. At any time tD during dark adaptation, the excitability, measured by 1/ Alo, must then also be measured by the integral of d log tD up to log tD. We may take this, likewise, to be Gaussian. The tests made are of two kinds: the ability of 334 PROC. N. A. S.