drawn to several theses demonstrated by the authors last named, 

 and their importance lor eertain purpo-es has in -IK h casef 

 indicated as clearly as possible. 



Moreover abundant reference's to literature are made throughout, 

 so that the ^tudent who wishes to refer to or read the various authors 

 in their respective languages, will find his labour appreciably 

 ilitated. 



The examples, chosen from biological sciences and more especially 

 from morphological descriptions, for illustrating the applicability 

 of the symmetry-principle in this province, have no claim to 

 absolute correctness. It is in general impossible for a chemist or 

 physicist to judge the exactness of such descriptions in morpho- 

 by means of drawings only, unless he has by chance gone into 

 these subjects in detail. The instances mentioned must be considered 

 as somewhat preliminary, intended only to prove the possibility 

 of a form-description based upon the principle of symmetry. How- 

 ever it will not give much trouble to biologists to find the right 

 symmetry of each object, if only the general principles are once 

 clearly understood by them. The author will be grateful for sug- 

 gestions offered by his colleagues in a kindly spirit. 



When the present work was almost finished, a copy of a little 

 book in the Russian language from the hand of Professor (i. \Y. 

 Will IT: "Symmetry and its Manifestations in Nature", came into 

 the author's possession. It contains a short review of four lectures 

 delivered by the writer in 1907, at the request of the Society for 

 Popular University Instruction in Moscow. As the ran.^e and design 

 of these lectures are obviously quite different from those of the 

 present volume, there was no reason for the author to consider 

 his book as superfluous and to give up its publication. 



If the contents should instigate our students of natural philosophy 

 and our future investigators to some new experiments or to any 

 applications in the different fields of research, the writer would 



link himself amply rewarded for the work done in composing 



lis book. 



