The purpose of this paper is to develop and to consider in detail some of the expressions which may be applied to reactions involving simple hæmolytic systems. In doing so, a number of rather unusual conditions have to be considered; these may first be set down. 1. It has been shown (1) that the curves obtained by plotting the amount of hæmolysis, expressed as a percentage of the total, against time, are sigmoid in form, the sigmoid curve often presenting a considerable degree of skewness in one or the other direction. In explanation of this form, it was suggested that the cells of the system present different degrees of resistance to the action of the lysin, these resistances being distributed according to a symmetrical frequency curve, and that the skewness encountered is due to the presence of secondary reactions, principally the reaction of the liberated cell-contents with the lysin. Such suggestions are, in general, in agreement with the findings of Brooks (2), of Fulmer and Buchanan (3), and of other workers on hæmolysis and the allied problem of bacteriolysis. To the two papers mentioned the reader is referred for excellent discussions of both facts and elementary theory, as well as for reviews of the literature. It appears that the bulk of the recent investigation has shown that these variations in cell resistance, and the distribution of these resistances, are of fundamental importance in problems of this kind, and that it is completely fallacious to deal with such problems without allowing for the heterogeneity of the material involved.
Elementary Theory of Quantum-Mechanical Collective Motion of Particles, II
