PREFACE. 



npHIS book contains descriptions of various problems of the kind 

 -*- usually termed Mathematical Kecreations, and a few Essays 

 on some analogous questions. I have excluded all matter which 

 involves advanced mathematics. I hasten to add that the con- 

 clusions are of no practical use, and that most of the results are 

 not new. If therefore the reader proceeds further he is at least 

 forewarned. At the same time I think I may say that many of 

 the questions discussed are interesting, not a few are associated 

 ' with the names of distinguished mathematicians, while hitherto 

 several of the memoirs quoted have not been easily accessible to 

 English readers. A great deal of new matter has been added since 

 the work was first issued in 1892, but insertions made since 1911, 

 when the book was stereotyped, have had to be placed where 

 room for them could best be found. 



In the first nine editions the book was divided into two parts, 

 most of the second being devoted to questions of a historical 

 character. There is ample precedent for including such matter 

 in books of mathematical recreations, but I have long felt that 

 much of the interesting and out-of-the-way information there 

 brought together would find a better place elsewhere. Accord- 

 ingly in this edition I have given up the division into two parts, 

 and have struck out most of the chapters in the second part such 

 as those on calculating machines, parallels, hyperspace, atoms and 

 ether, time and time measurers, etc. : earlier editions are acces- 

 sible for the matter now omitted. 



As now presented, the book contains only sixteen chapters, of 

 which the subjects are shown in the Table of Contents. Several 



