In combining Parts 1 and 2 into a single volume only minor changes have been made, apart from the correction of errors. I have not attempted to bring the treatment up to date even for such rapidly expanding fields as the study of chaos in non-linear systems, but have been content to add a small number of references. Where an argument could be corrected, clarified or extended in the space of a few sentences, these are signposted in the margin and placed at the end of the chapter. The system of marginal cross-references has met with critical approval and I have taken the opportunity of adding to their number.

My hopes of ever completing a further volume on the vibrations of extended systems have by now grown faint. There are too many exciting new ideas that are not yet ready for the type of exposition that suited the present work. Fortunately the development, by both classical and quantal methods, of the physics of simple vibrators produces a reasonably selfcontained argument, and I am grateful, as always, to Cambridge University Press for making possible this synthesis of concepts which in modern physics should be regarded always as complementary, never as antagonistic.