The book is necessarily an introduction rather than a treatise. The subject is too new and too unformed to justify a more comprehensive treatment. We have tried to draw its main outlines for the use of those who wish to understand its general bearings, and we hope that our statement may even be of some service to those who wish to make its acquaintance practically and to share in the fascinating research work which it offers. No doubt the latter will consult also the original papers. Considering the purpose which we have had in view we have refrained from the discussion of a number of interesting points of contact with other sciences and with older work, such as for example the remarkable investigations of Pope and Barlow. We have not even given a complete account of all the experimental investigations that have been made in connection with the subject itself, and have been content with the merest allusion to the serious mathematical discussions which it has received at several hands. The publication of the book has been delayed by the difficulties of these times, which have also hindered to continuance of some researches and the publication of others that are almost or quite complete. A few result which could not be included in the book itself are given in supplementary notes at the end. The same circumstances have left me to write this preface alone. Probaby, however, I should have demanded the privilege in any case. I am anxious to make one point clear, viz., that my son is responsible for the 'reflection' idea which has made it possible to advance, as well as for much the greater portion of the work of unravelling crystal structure to which the advance has led.

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