PREFACE TO THE FIRST EDITION. 



The present book originated in a series of lectures delivered 

 by the author during the winter and spring 1916 1917 at the 

 University of Groningen. The matter of these was afterwards 

 augmented by the contents of some addresses held about ten years 

 ago at the University of Amsterdam, and by that of some others 

 delivered in various places in this country and in America. In 

 response to a desire, repeatedly expressed by some of his friends, 

 the author has finally resolved to publish these lectures in bookform. 

 Only in occasional passages, however, does it betray this devious 

 course of development. 



The aim of the writer in publishing this volume is by no means 

 to give an exhaustive "treatise" of the general doctrine of symmetry. 

 His purpose is merely to draw the attention of students of 

 mathematics and natural philosophy in general to a principle, of 

 which the significance in the morphological description of objects, 

 as well as in the definition of chemical and physical phenomena is 

 gradually becoming more and more evident in every domain of 

 research. 



The complete deduction of the properties and mathematical 

 character of symmetrical systems has been so ably treated by a 

 number of the best authors, and in such various ways, that there 

 is small chance of new points of view being found in the future. More- 

 over, the results have from time to time been summarised in a 

 number of papers which are accessible in most of the greater libraries 

 to every one who wishes to go further into these subjects. Hence 

 it appeared needless to repeat such an exhaustive treatment of 



