The aim and scope of this book is indicated in the introductory chapter. The author is not blind to the fact that the student he had in mind when he wrote it is not going to read some parts of it without a serious mental effort; the necessarily mathematical form of the arguments entails that result. But he feels certain that any student with the average mathematical equipment acquired in the first two years of a University science course will not find it impossible to follow the details of the treatment, and as much assistance as possible is provided in explanatory appendices, in verbal interpretation and illustration. In the proofs no .steps are omitted. On that account the content of subjects dealt with has had to be restricted : otherwise the book would have grown to a length unsuitable for the type of reader whom it is intended to assist. The problems treated are concerned with systems in statistical equilibrium, although a short appendix refers to the subject of collision-frequency in gases and its bearing on chemical reactions.