## Abstract

Two unusual measures of the occurrence of binary, ternary,... encounters are given, each by an appropriate line of reasoning. Both indicate deviations from the law of Guldberg and Waage at high densities. First, the close analogy between gases and emulsions, which was established by the experiments of Perrin, is brought into relation with experiments by W. S. Gosset on the distribution of the square cells of a haemacytometer as to the number of particles which they contain. This analogy indicates that, in a cubic centimetre containing n molecules, the number of simultaneously existing encounters of 2 or 3 or 4 molecules in a bunch will respectively be ${\textstyle\frac{1}{2}}$n$^{2}$$\omega _{1}$e$^{-n\omega _{1}}$, ${\textstyle\frac{1}{6}}$n$^{3}\omega _{1}^{2}$e$^{-n\omega _{1}}$, ${\textstyle\frac{1}{24}}$n$^{4}\omega _{1}^{3}$e$^{-n\omega _{1}}$, where $\omega _{1}$ is a constant of the order of 10$^{-22}$ cm.$^{3}$. Secondly, the problem is re-examined by a statistical argument after the manner of Bernoulli and Poisson, and various improvements are inserted. If there are n$_{1}$ molecules of one species and n$_{2}$ of another in a cubic centimetre then, during 1 sec. of the observer's time, the aggregate duration of binary encounters between unlike molecules, all of diameter $\sigma $ = 3 $\times $ 10$^{-8}$ cm., is found to be n$_{1}$n$_{2}\Omega $ exp {- 0$\cdot $79(n$_{1}$ + n$_{2}$) $\Omega $}, where $\Omega =\omega $/{1 - (n$_{1}$ + n$_{2}$) $\sigma ^{3}$2$^{-\frac{1}{2}}$}, and $\omega $ is of the order of $7\times 10^{-23}$ cm.$^{3}$. To specify a binary encounter it does not suffice to say that two molecules must meet; for one must also say that an enormous number of other molecules must keep away from the pair. The latter requirement, although obvious when mentioned, and well known in statistical theory, appears to have escaped notice in previous theories of collisions in a gas. The exponential factors in the above formulae express the probability that the extraneous molecules will keep away. The treatment emphasizes those statistical proprieties, but otherwise proceeds by easy approximations; so that the better determination of $\omega $, for particular reactions, is left to experiment.