Ten years ago, when I started writing on the physics of vibration, I had in mind a single volume. Four years ago I was reconciled to the need for two, and now must confess that the complexity of the subject has made it advisable to get the second of the projected three parts into print without waiting for the third to accompany it between the same covers. It is still my hope to do justice to the vibrations of extended systems, but the difficulties are considerable and not made easier by the vigour with which some of the central topics are being pursued at present.

Of all the encouragement I have enjoyed I particularly wish to record with the warmest thanks the help of Dr Edmund Crouch and Dr John Hannay who long ago, as research students, derived for me some solutions of Schrödinger's equation which provided a stout anchor for my thoughts: Dr Bob Butcher who has firmly guided me in my brief excursions into structural chemistry and molecular spectra: and Dr Andrew Phillips who devoted more time than he could have been expected to spare to a critical reading of much of the typescript. If the state of that typescript as delivered to the printers did not achieve even a modest standard of tidiness, the fault is entirely the consequence of copious afterthoughts on my part, and in no way to be blamed on Mrs Janet Thulborn whose patient and faithful typing deserved better respect, and has certainly earned my gratitude.