A mathematical theory of thick emulsions, based upon a previously published theorem, is developed. All important properties of the <i>H</i> and <i>D</i> curve and the Kaiser function are deduced and physical interpretations of the parameters of both functions are given. Deviations from Beer's law by a photographic emulsion are seen to be responsible for the occurrence of reciprocity failure phenomena. The occurrence of a reverse primary process is shown to be capable of invalidating the Poisson distribution of exposure.

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