No apology is offered for what may possibly be considered as the non-mathematical character of a considerable portion of the book. The physical hypothesis has been kept intentionally in the foreground, and algebraic results have been where possible translated into their descriptive equivalents. This synthetic course, while more flexible, doubtless makes the exposition more difficult to follow, and apparently less exact, than would be a mathematical development from a system of initial hypotheses, in which attention would be demanded for the analytical processes alone: but on the other hand it exposes the whole situation, and conduces to the direct detection and examination of discrepancies that might possibly otherwise remain latent: it is thus, notwithstanding the somewhat imperfect focussing of the subject, more suitable for a theoretical procedure which is in the constructive stage.
The Essay in its present form was completed at the end of the year 1898, except as regards the Appendices D, E, and F, and the articles and footnotes distinguished by a double asterisk or other mark. In the revision of the sheets before publication the writer has however had the good fortune to obtain the collaboration of his friend Prof. A. E. H. Love, of Oxford, whose acute and vigilant criticism has led to many improvements in the exposition as well as the correction of various mistakes, thereby adding very substantially to the value of the work. For similar most valuable services relating to the latter half of the book, and for the greater part of the list of corrigenda - as regards some of which special apology must be made - the writer is indebted to his friend Prof. W. MCF. Orr, of the Royal College of Science, Dublin. Notwithstanding much increased confidence in the general validity of the argument, arising from the expert assistance and criticism thus most kindly afforded, many serious defects doubtless remain. Various questions not ripe for final definite treatment, and matters on which opinions can differ, have been passed under consideration: for instance, the discussion on the molecular basis of mechanics
